ECON 310 Class Notes - Emily Goldstein
23 August 2017
Producer theory: how firms make decision; we want to maximize profit
● How do firms make decisions?
○ How to produce?
○ What to produce?
○ How much to produce?
○ How much to charge for it?
○ How to compete with other firms?
Thinking about costs…
Cost: value measured by what must be given or done or undergone to obtain something. This class addresses economic cost… what you
give up to make the good.
● Direct costs are involved in the production process
● Indirect costs are costs that the firm has to experience participating in the market
○ For this class we are going to focus in direct costs
● In modern economies we have to think about human capacity & technology. Modern economies aren’t simple.
○ Think Google, Facebook → Capital must include human capital
Economic costs
● Lebron James starting a pizza shop would have a huge opportunity cost
○ When would it be optimal for the professor or Lebron James to open a pizza shop
■ Class won’t focus on opportunity cost; it’s too case specific.
■ We want to remove the company specifics and just look at the equation itself
● Economic costs are all about finding the best alternative. To determine if one option is the best alternative, we need only compare
it to the best alternative.
● Assuming economic costs requires us to explicitly solve for only one profit level to determine if one is the best.
25 August 2017
Producer theory: 2 step process: How to produce & how much to produce
● How firms make optimal decisions on capital & labor
Production process:
Production ​Function​: It’s an abstract concept.
● Inputs (L & K) → Production function → outputs (goods to be sold)
● Capital + Labor = finished product
○ Raw materials aren’t included as they are considered fixed costs
○ Also known as the technology function; math.? Function
● Equivalent to how efficient labor and capital are working together
This is a production function:
*This equation informs efficiency
Firms/ Managers must...
Produce ​on​ the function so there is no waste & use the right level of inputs. Need the most efficient and most output producing function.
*the later is wasting labor!
Goldstein 1
● Highest amount produced at certain bundle or lowest amount of inputs for highest output
Productive measures help determine best place on the production function:
Total product​:​ TP = the maximum level of output that can be produced with a given number of inputs
● Measures the maximum output th can be produced with a given input.
● This is equivalent to Q aka it is a certain amount of products
Average Product of Input:​ AV​1​ = total product/ quantity used of input
● For instance, Average product of Capital = AP​K​ = Q/K
● Measures, ​on average,​ how much each unit of input contributes to the total output of the firm.
Marginal Product of Input:​ think growth rate!
● MP​1​= Change in Total Product/ Change in Quantity Used of Input
● For instance, Marginal Product of Labor = MP​1​ = ΔQ / ΔL
● This measures how much ​each additional unit​ of input contributes to the total output of the firm.
○ If labor increases a little bit what will be the effect on the product… the increase of the 101st worker
○ The growth rate as you increase labor or capital
○ Based on inputs (K or L); as you inputs Q increases and grows faster.
● The curvature or slope is the marginal increase
● Slope is the acceleration of the total product, the highest speed is right before marginal product is zero. Only at zero will it start to
fall.
● Incentive to fire labor starts at negative returns (negative slope)
○ Higher (K & L) will increase productivity to a certain point (where the lines cross)
■ This will always be the peak
Returns to an input:
● Observational principle: As the usage of an input increases, its value to a production process initially increases, then begins to
decline, and eventually becomes negative.
○ Firms that have increasing production should scale
28 August 2017
Marginal Product of Labor (MP​L​) is determined by the slope of the Total Product curve; how fast a product grows as you add labor
○ Where MP​L​ is negative there are decreasing gains
Example 2.1 - K is fixed, only decision is how much Labor
●
*Note: Q = TP!!
If Q @
3
K=4 and L=1 → Q = −1
+ 1.5 *
10
TP
2.4
So… AP​1​ = L → 1 = 2.4
2
1 − 3(1) + 4 → Q = 2.4
−23
+ 1.5 * 22 − 3(2) + 4 → Q
10
So… AP​2​ = TLP → 3.2
= 1.6…
2
ΔQ
− 2.4
Then… MP​L​ = ΔL → MP​2​ = 3.22−1
= 0.8
= 0.8
1
If Q @ K=4 and L=2 → Q=
= 3.2
*MP​L​ is the change in TP from the last worker*
Goldstein 2
Use the right level of inputs:
Value of Marginal Product of Input:
● VMP = Price x MP
○ Price is the price of the good you sell (not the price of the machine to make it, etc.)
P ΔQ
● Value Marginal Product of Labor = VMP​L​ = ​ ΔL
This measures how much ​value​ ​each additional unit​ of input contributes to the firm.
○ What are the benefits in dollars? How much extra money is made form an additional unit?
Common Sense Principle:
● An input should only be used up to the point where its marginal benefit equals its marginal cost in the range of diminishing marginal
product.
○ Example: Once your business is established, you should hire more employees until the value of another employee is
exceeded by the wage you would have to pay him.
■ “More of the same” is generally a poor management style.
○ How much output to produce is the same question as how much of an input to use… production function gives us output.
Example:
●
Blue line is the contribution of each additional worker in dollars
○ Assume the firm is a price taker in the market (see wage line!)
Labor: Optimal choice
● P * MP​L​ > wage → incentive to increase labor
● P * MP​L​ < wage → incentive to decrease labor
● P * MP​L​ = wage → firm has to incentive to deviate
○ Is is the optimality condition! This equates to zero ​marginal ​profits, as profit from the last worker is zero. However profits
from the previous workers was positive, so this condition will equate to peak ​total​ profit!
■ Note: workers contribute what they cost
○ P * MP​L​ → VMP​L​ (value of marginal product of labor)
■ The firm’s choice variable is labor, as it is a price taker
■
●
Goldstein 3
“An input should only be used up to the point where its marginal benefit equals its marginal cost in the ​range of diminishing marginal
product​”
● Our assumptions about the shape of the TP curve, MP eventually has to fall, so it crosses MC twice or never. The first time it
crosses signifies operating at a loss.
● With a labor only technology:
○ Choose L* such that P * MP​L​ = wage
■ (L* = optimal amount of labor)
○ So F(L*) = Q*
*Always make decisions in the range where MP​L​ is decreasing*
When Q=F(L) and the VMP​L​ and wage intersect, labor is maximized.
Marginal Product per dollar should be equal:
Using the last principle, we know:
● We should hire employees until a new employee’s additional value equals the wage rate.
● We should purchase capital until a new machine’s additional value equals its cost.
○ However, when a tradeoff exists between “labor” and “capital”, how many of each should we utilize?
Restaurant example: What is the optimal input allocation?
● Imagine you are opening a restaurant
● All job candidates are either cooks or waiters
○ Cooks are very rude
○ Waiters don’t know how to cook
● Compare:
○ 6 cooks, 1 waiter
○ 2 cooks, 2 waiters
○ 1 cook, 3 waiters
30 August 2017
Isoquants: Iso is a prefix that means same.
● Goal: fix Q, so we can plot all the capital and labor allocations that yield Q.
● Need to address capital and labor, but can’t graph in 3-D, so we need to fix Q… which is done through isoquants: a set of K,L that
produce the same amount of output
● The shape of an isoquant reflects the ease with which a producer can substitute among inputs while maintaining the same level of
output.
K
L
Q
2
½
1
1
1
1
½
2
1
●
●
●
As you increase labor your
marginal product of K increases, as you have to decrease the
amount of K
Where the isoquant is very steep you are willing to give up more K for L, but as it flattens this decreases
Want to use? The L & K where the contribution equals the marginal cost.
Goldstein 4
○
Slope of isoquant = marginal rate of technical substitution (MRTS) =
ΔK
ΔL
● Isoquants always have a negative slope
1 September 2017
Isoquants: way to represent all possible allocations of K + L for all the same outputs.
● Where the isoquant is steep, there is more willingness to give away more capital
ΔK
ΔL
●
MRTS =
●
Also equivalent to MRTS =
○
→ amount of K you have to give up to get one unit of labor; this is also the slope… aka
MPL
MPK
rise
run
When L goes up, K decreases; we are in an area where marginal returns are decreasing
Which one is an isoquant?
Not the blue circle as it isn’t smoothly declining
The red line; has an irregular slope and is very inefficient;
NO!
● The green lines IS as it is smooth and has a
decreasing/negative slope
-------------------------------------------------------------------------Remember:
● The isoquant represents all combos of capital and labor
that have the same input
● The line represents one fixed level of output and all the
ways to get that level
● This allows us to avoid the third dimension
● The shape of an isoquant reflects the ease with which a
producer can substitute among inputs while maintaining
the same level of output.
●
●
So if I get rid of one machine, how much labor must I hire to produce the same level of output?
There are 8 sewing machines and one employee…
If there is a disproportionately large number of machines, it
shouldn’t take too many additional employees to offset the loss. SO
the steepness of the isoquant tells us something about the
trade-off.
● The tradeoff between inputs at a given output level is the
slope of the line tangent to the curve.
● This can be calculated through MRTS…
Goldstein 5
So what is slope?
Marginal Rate of Technical Substitution ​(MRTS)
● The rate at which inputs (such as labor and capital) can be substituted for each other to maintain a given output level.
● The slope of the line tangent to the isoquant corresponding to a given output level.
●
MRTS​KL​ =
ΔK
ΔL
=
MPL
MPK
For instance, MRTS​KL​ is the number of employees that can be fired with the addition of a single unit of capital (and still have the
same level of output)
●
By the 3 worker, the company is already saturated with
labor, so by L=4 the MRTS is decreasing.
Now suppose Q=2K+L and the manager must produce 5 units of output.
●
●
●
The MRST is -0.5
The slope stays the same, it’s a ​linear​ isoquant!
○ This means it is a perfect substitute quantity
The outcome for a production function like this is to choose what
is cheapest.
Substitutability
Inputs can be:
● Perfect complements
*Inputs that go into a perfect complement are fixed.
● Complements/Substitutes
● Perfect substitutes → linear production function
These are determined by looking at the MRTS → these are the 3 types of isoquants you can have
Isoquants → to realistically mimic actual production processes, we assume isoquants are ​convex​ (bowed in toward the origin), and
increasing in output as more inputs are used.
Isocosts Lines: ​→ same cost combination of L + K that costs the same
Goldstein 6
● Illustrates the combinations of inputs (K,L) that cost the producer the same amount.
● The steepness of an isocost line reflects how much more expensive one input is relative to the other.
W = price of labor
r = price of capital
●
C
r
= labor cost ;
C
w
= capital cost →
C
r
C
w
=
w
r
● As the slope of the isocost tells us how many units of K you must sell reflective of cost and labor
6 September 2017
Isocost lines → same cost
**Price and labor are assumed to be fixed**
● Because trade-off is always the same, the slope of the isocost must always be the same.
Example:
●
●
●
●
●
●
You can do this for other costs as well. As the slope of these lines are also
●
●
●
●
Assuming price and labor are fixed
r=5
w=3
C = $15
The line is easy to draw, as you just need 2 points.
Spend all on capital, all on labor and connect.
w
r
.
Note the slopes of the isocost lines are w/r, where w is the
wage rate and r is the price of a unit of capital.
This intuitively makes sense bc the tradeoffs should be
based on the ratio of the prices
The increases in cost shift the isocost curve to the right, but
keep the same slope
The slope will only change if the inputs? Change
The slope of the isocost lines are w/r which is found by…
→ This is just rise over run!
What happens to the isoquants if an input cost changes? What happens to the isocost if an input cost changes?
Assume capital costs $5/unit and labor now costs $7.50/unit (instead of $3). What different combinations of capital and labor will cost the
producer exactly $15?
Goldstein 7
●
●
●
As a result the line is a lot steeper.
This steeper line means that the capital is now ​cheaper
relative to labor.
When the cost of an input good changes, the isocost lines
rotate i.e. the line pivots around the cost that stays the same.
Optimal choice of K and L
Assume you want to produce the quantity level represented by the isoquant, below. If the price of capital is $5 and the price of labor is $3,
what is the cheapest way to produce? (Note: want input blend that will give q (optimal output) as cheap as possible)
●
●
●
●
●
The linear lines are isocost; the curve is the isoquant
@ Red there the bundle is cheap, but it’s not producing
enough output (orange curve)
The slope of all isocosts are parallel
The optimal choice is the lowest isocost that intersects with
the isoquant. This is where the isocost is ​tangent​ (intersecting
only once) with the isoquant.
Any isocost below the isoquant is not feasible, anything above
the tangent isocost is not optimal, it’s too expensive.
○ In order to be tangent the slope of both curves must
be the same.
Cost Minimization Principle:
● The mix of labor and capital used to minimize the costs of a production process is that mix which ensures the slope of the isocost
lines is tangent to the slope of the isoquant passing through that point. In other words...
● The mix of labor and capital used to minimize the costs of a production process is the mix that ensures…
○
MPL
MPK
■
=
w
r
→
MPL
w
=
MPK
r
→ cost minimization principle!
The cost minimization principle is the marginal product per dollar spent should be equal for all inputs. Aka the
optimal bundle will be found where the marginal product per dollar spent is equal for all inputs.
MP
This is from the slope of the isoquant = M P L ​and the slope of the isocost =​ wr .
K
■ b/c in order for the isocost and isoquant to be tangent the slope of BOTH curves must be the same! The value
per dollar of input spent should be equal for all inputs. Using this, if I know how much value each of my inputs
is adding, I can determine how much more/less I should use of each.
● Consider this: If the last employee hired provided a value of $10 to the firm and cost $5, you are receiving $2 value/$1 spent on
labor. If the last machine purchased provided a value of $30 to the firm at a cost of $10, you are receiving $3 value/$1 spent on
capital. You would have been better served to spend your labor money on additional machines, getting more value per spending
dollar.
Sample questions:
■
●
●
Suppose it became illegal to hire illegal immigrants. How will this affect low-wage U.S. born workers?
Suppose tax laws are written that make capital cheaper for companies. How will this affect workers?
Goldstein 8
Optimal Input substitution:
A firm initially produces ​Q​0​ by employing the combination of inputs represented by
point A at a cost of C​0​.
Suppose ​w0​ ​ ​ falls to ​w​1.​
●
●
The isocost curve rotates counterclockwise; which represents the same
cost level prior to the wage change. The slope of the new isocost line
represents the lower wage relative to the cost of capital.
To produce the same level of output, Q​0​, the firm will produce on a lower
isocost line (​C​1)​ at a point B.
○ This equates to hiring more employees and fewer machines.
Which makes sense as if you employ two inputs and one gets
cheaper… wouldn’t you use more of the cheaper one?
Input Substitution Principle:
● If an input gets cheaper, the firm should use more of that input and less of other inputs (since it is relatively cheaper).
● If an input gets more expensive, the firm should use less of that input and more of other inputs (since it is relatively more
expensive).
Example:
Assume you are utilizing an optimal input mix when Congress unexpectedly increases the minimum wage. You should:
A. Invest in more equipment and fire some employees.
B. Invest in less equipment and hire more employees.
C. Keep your input mix the same.
D. Invest in more equipment and more employees.
This is a shock to the market, as the price of labor goes up. So the economy must move to a more capital intensive labor w/
employment levels falling. So A?
Rule of thumb: Whenever inputs change, shift to the more relatively cheaper option.
8 September 2017
Review: the optimality condition is the contribution of each add’l cost of labor is equal to the contribution of another add’l increase in capital.
However, there are exceptions to this…
Cases in which M RT S = wr will not work:
●
1.
Perfect Substitutes → ​Firms will always, in this situation, choose either all labor or all capital.
●
●
●
●
●
●
Labor is much more expensive than capital due to the steep slope.
The best choice is no labor and all capital due to the slope of the isocosts.
The slope of the isocost relationship between isocost and isoquant forces the firm to choose
all capital. It is steeper than the isoquant or the MP​L
This is a linear isoquant
$1 spent on capital brings a higher return than $1 spent on labor.
MPL
MP
○
< rK
w
If the isoquant and the isocost have the same slope, all conditions on the slope will be
optimal.
2. Perfect Compliments
●
Here there is only one optimal point.
Cost Function - ppt 3
Goldstein 9
Production functions: the production process whereas ​cost functions​ are a company's costs
● A cost function can summarize all the costs
“The ​harder it is to produce​ a given level of output the ​more it costs​ the firm”
● “​Harder it is to produce” → production function
● “More it costs” → cost function
Economists are only concerned with two cost measures: fixed costs and variable costs.
Total costs:
● TC(Q) = Total Cost of producing Q units of output
● TC is the lowest possible cost
○ Fixed costs:
■ FC = Costs that ​do not v​ ary with output
■ Plug in 0 at Q will give you fixed costs
○ Variable costs:
■ VC (Q) = Costs that ​vary​ with output.
● Example: TC(Q) = 100 + 4Q + 5Q​2
○ 100 = FC ; 4Q + 5Q​2​ = VC(Q)
Example 3.1 → ​this will be on exam.
Assume 4 machines have been purchased that each cost $3. The following chart shows the output that can be generated with these
machine and various labor levels. The wage rate is $2/worker. Note: capital isn’t always fixed.
Here the MP​L​ is going up, but cost of labor is fixed, so the production
cost will decrease as you add labor.
Cost and Productivity
Recall the assumption: As the usage of an input increases, its value to a production process initially increases, then begins to decline, and
eventually becomes negative.
This is a production function.
Question: If the value to production of an input starts small, then increases, then becomes small again, what does that mean for the cost of
manufacturing the good?
● A: It will start out expensive, then it will get cheaper, then it will get expensive again.
Goldstein 10
○
○
○
At first, we will need lots of inputs in order to out first units of output. Thus, the first few units of output are expensive.
As we move on to produce more output, our inputs become more effective and thus cheaper.
Then inputs become ineffective again…becoming more expensive.
Cost function
Up until the 6th output, the MP​L​ is decreasing, after it starts
increasing.
Notice total cost is on the y-axis and output is on the x-axis (output
MUST be on the x-axis).
This graphically shows the answer from before.
● The first units of the good cause a large jump in cost.
● Think of start-up companies. CEO may have to answer his
own phone and do his own paperwork. Not buying in
bulk….etc.
● The next units do not cost much extra.
● Specialization takes over, can buy in bulk,etc. WANT TO BE
HERE.
● The last units once again cause a large jump in cost. Need
major investment in R&D, new locations, etc.
● We name these three regions “Startup, Efficient, and
Oversized”.
Assume fixed costs are $3:
The VC line is the difference from the TC and the FC, thus the distance between
the TC and the VC at any point is always the FC.
● The curvature of the TC curve will be the same shape as the VC curve,
TC gets its shape from the VC.
● The VC will be the FC minus the TC.
Now lets use these curves to deconstruct a firm's cost and the importance of those
costs as it grows in size
● Fixed costs originally make up most of a startup company’s costs. So
what does this mean for a new company debating entry?
● After it has produced a sufficient number of units, the fixed cost is
spread out through the units, and the major costs that matter are the
variable costs.
● The that FC are very important at the birth of a company. Note that this
is often when companies are looking for investors. As the company
grows the FC become less and less important and operating costs (i.e.
variables costs) dominate their optimization problem.
Cost Measures:
Total​ Cost​:
1. TC(Q)=Total Cost of producing Q units of output
2. TC(Q)=FC + VC(Q)
Average ​Total Cost:
1. ATC: Total Cost/ Units of Output or C(Q)/Q
2. Measures, ​on average​, how much each unit of output contributes to the total const of the firm. I.e. just per-unit cost
Marginal Cost:
1. MC = Change in Total Cost/ Change in Output
2. Measures how much ​each additional unit​ of output costs to the firm.
a. This isn’t usually calculated, but it is critical to how a manager should make output decisions.
11 September 2017
Cost function will always be a function of output/ how many units are being produced.
● Cost functions are always increasing… it costs more to make more
Goldstein 11
Cost Measures (continued):
T C(Q)
● ATC = Q → TC(Q) is the TC of producing Q units
●
MC =
○
ΔT C
ΔQ
→ can also be written as MC =
ΔV C
ΔQ
FC isn’t a function of Q, it’s just a number, so MC can =
ΔT C
ΔQ
OR
ΔV C
ΔQ
.
Total ​Variable​ Cost:
1. VC = Costs that vary with output
Average ​Variable​ Cost:
1. AVC = Total Variable Cost/ Units of Output
2. Measures, ​on average​, how much each unit of output contributes to the total variable cost of the firm.
These are just like total/average/marginal cost, but with Variable.
Total ​Fixed​ Costs:
1. FC = Costs that do not vary with output
Average ​Fixed ​Cost:
1. AFC = Total Fixed Cost/ Units of Output
2. Measures, ​on average​, how much each unit of output contributes to the total fixed cost of the firm
NOT SURPRISINGLY… ​ATC = AVC + AFC
● TC = VC + FC
● TC/Q = VQC + FQC → ATC = AVC + AFC
Question: Having defined Marginal (Total) Cost, why don’t we need to also define Marginal (Variable) Cost and Marginal (Fixed) Cost?
● A: Increasing production does not affect fixed cost, so MFC = 0, so MVC = MC.
● In other words… MFC is always zero, because of this MVC is MC.
Average Total Cost (ATC) Curve
The ATC curve will be high for low levels of production, as a larger quantity will lower
the AFC. I.e. Large scale can lower fixed costs!
● The more you produce the lower your ATC will be.
● AVC will depend on the production function
● A firm is only maximizing profit if it's minimizing cost
If AFC approaches zero, and ATC = AFC + AVC, then what do we know about AVC
when output is large?
Goldstein 12
The marginal cost curve will look like the following.
● Write the equation for marginal cost on the board and step quickly
through it’s shape (show in relation to the TC curve).
● Once again, we see the relationship between Average and
Marginal. In particular, the only way Average Total Cost could be
decreasing is if each additional unit had a cost that was lower
than the current average.
●
●
●
●
●
For completeness (and because we’ll be using it in the future), we
also add the AVC curve. For the same reasons , the MC cost
curve intersects it at its minimum.
Note why the shape of the average variable cost curve makes a
lot of sense. Go back to ATC=AVC+AFC. What happens to AFC
over time?
The AVC in this case begins to upward slope as it has reached its
optimal output.
Where the MC and the AVC intersect is optimal
The MC pulls the AVC down, and after they intersect the AVC is
basically stationary.
Sunk Costs
● A cost that cannot be recovered
○ NOTE: Sunk costs are a subset of fixed costs
○ b/c the cost is gone, it shouldn’t affect any decision making.
○ In economics all rational decisions are made on the margin. Only marginal cost and marginal benefits matter.
Long-Run Costs
● Short run: the timeframe in which fixed costs cannot be adjusted
● Long Run: the timeframe in which fixed costs can be adjusted. All costs are variable!
○ Fixed costs are not always fixed; in the long run, all costs are variable thus the question is how does one optimally
decide how much capital to invest
● Think entry and exit time-frames as defining the short-run and long-run
○ Note: long-run could be 1 day (a lemonade stand owner can turn over their fixed costs almost immediately) or it could be
10 years (a multinational corporation sells off all its subsidiaries)
●
●
●
●
●
The ATC curve for a small company should have reasonable fixed costs
(thus ATC for small quantities isn’t “too” large), but due to its lack of
efficiency, it will likely get very expensive at high output levels.
○ This is a short-run cost curve, since it assumes a small factory
will be used.
The Medium-sized factories will cost more per unit at low-output levels due
to the increased fixed costs. However, at higher output levels it will be
significantly cheaper due to the efficiency gains.
The size of the factory is determined by how much stuff you intend to
produce.
○ This is a story of fixed costs and efficiency gains.
Large factory will have extremely expensive upfront costs, but will have
lower per-unit costs at high output levels due to the extreme efficiency.
For small output levels, small factories will be cheapest (per unit) due to
the low fixed costs. For medium output levels, medium factories will be
cheapest because the don’t have the fixed costs of large factories but
have more efficiency gains than small factories. For high output levels,
large factories will be cheapest due to the efficiency gains.
Goldstein 13
Long Run Average Cost Curve
●
●
●
●
If we could have factory sizes between Small and Medium, between Medium
and Large, and between every other size level, this envelope would “smooth
out”.
We call this envelop the Long Run Average Cost Curve, since it shows us the
cheapest way to produce each level of quantity, assuming we can adjust the
fixed costs.
The black line represents the lowest possible cost for each scale of
production.
Economies of scale (gets cheaper to produce another) is achieved where the
LRAC is downward sloping
Long Run Average Cost Curve (LRAC)​:​ A representation of the minimum average cost of producing alternate levels of output, allowing for
the optimal selection of ​all​ variables of production (both fixed and variable).
● Once we have this curve, you’ll notice that producing at different levels leads to different average cost levels…even in the LR. We
have come up with terms to describe the relationship between output and average costs.
Economies of Scale (Increasing Returns to Scale)​: ​The range of a LRAC curve for which increasing the size of operation decreases the
minimum average cost
● If we scale our facilities up, we will increase our returns since average costs will drop.
Diseconomies of Scale (Decreasing Returns to Scale)​: ​The range of a LRAC curve for which increasing the size of operation increases
the minimum average cost.
● If we scale our facilities up, we will decrease our returns since average costs will increase.
Constant Returns to Scale: ​The range of a LRAC curve for which increasing the size of operation does not change the minimum average
cost.
● Means that scaling our facilities up will result in identical average costs.
● Note: the “relevant range” that is often discussed in business texts tends to imply a CRS. For small changes, most operations are
in the CRS range. One extra pound of cheese produced at a Kraft plant won’t really have an almost identical average cost to the
previous pound. However, 200,000 extra pounds will likely cause average costs to increase since additional facilities would be
needed.
Long Run Average Cost Curve (LRAC)​: A representation of the minimum average cost
of producing alternate levels of output, allowing for the optimal selection of ​all​ variables
of production (both fixed and variable).
● CRS range is where the line is flat i.e. costs not increasing w/ output.
● Diseconomies of scale starts where marginal cost intersects the actual cost
● Economies of scale is less expensive to produce, diseconomies of scale is
where it is increasingly expensive to produce.
● LRAC: For every scale of production, what is the lowest cost of production
Question: Would you expect the software industry to have decreasing, increasing, or constant returns to scale?
● Is that marginal costs are effectively zero once the software is written. Thus, the more you sell the cheaper they are per unit since
the fixed costs of development is spread over more and more units. This is true in any industry with extremely high upfront costs
and very low marginal costs, such as power companies or cable companies.
● Fixed costs drive the cost function after the FC there is almost no other costs
● A: Increasing returns to scale.
13 September 2017
Economies of ​Scale​: ​The condition in which an expansion of output results in a lower long-run average cost.
● Lower per-unit cost by increasing output. Think Wal-Mart.
Economies of ​Scope​: ​The condition in which the total cost of producing two goods together is less than the cost of producing each of the two
goods separately. “Lower per-unit cost by producing something else”
● Sometimes it is cheaper to produce two goods then just one good. Ex. Wendy’s makes chili as they have a lot of ground beef from
the hamburgers, but Chick-Fil-A doesn’t make chili as it doesn't as they don’t have beef intensive products.
● This demonstrates that “sharing resources” is one way economies of scope can occur.
Goldstein 14
Economies of scope usually occur bc either the products share inputs (national & local wireless) or there are cost
complementarities.
Economies of scope can be difficult to achieve. For the last corollary, consider the employees you are looking to fire. If, for instance, they
are very nice people and they make all your employees happier and more productive, maybe they are actually better than a more
“competent” employee.
● Synergy Principle: Exploit cost synergies for competitive advantage.
● Corollary: Be aware of strategic acquisitions that can result in economies of scope.
● Corollary: Be aware of a resource’s effect on your entire business, not just its primary mission.
New Slide deck: ​Specialized Investments
Transaction Costs: ​Costs in addition to labor & capital
1. Costs in excess of the actual amount paid in a transaction.
2. Costs not directly relatable to the value of a market transaction.
3. Non-productive costs.
These all mean the following:
-For the producer/seller: “all cost not directly related to the creation of the TV.”
-For the buyer: “all costs paid in addition to the transaction cost.”
● Search and information costs
○ Searching for the best deal (buyer) or advertising (seller)
● Bargaining costs
○ Labor negotiations in the NBA (both producers and sellers), legal fees are huge as well as lost profit from not playing
● Enforcement costs
○ Quality control
○ Seller of organic foods must certify that they are organic to the buyer
● *Specialized investments* needed to facilitate the exchange
○ This is what we are really interested in.
Specialized investments
● Investments that only have value within the context of a relationship-specific exchange.
○ An investment that only has value if you have a relationship with another firm
○ Only makes sense to buy this input if you need it. Only profitable between the firm that makes it and the direct seller.
● Site Specificity:​ Buyer and seller of a good must locate their facilities close to each other.
○ Ex. the only way that the investment into a coal power plant is worthwhile is if there is a coal mine nearby
● Physical Asset Specificity:​ Capital equipment is specific to a particular purchasing firm.
○ As a seller, I need a supplier to make me something that is exactly to my specifications and only to my specifications.
This happens a lot in manufacturing and IT.
○ This is an actual input good itself.
● Dedicated Assets:​ ​General investment is only profitable if a particular buyer purchases the good produced with the investment.
(Similar to physical asset specificity, but on a larger scale)
○ A physical asset that is specific and sold to only one company and only one market. If Walmart stops buying, the
factory’s capital will be worthless.
● Time-Specificity:​ ​Investment only has value if final product can reach the user in a short period of time.
○ Similar to site specificity. Ex. A fishermans investment in a boat only has value if they can get to a market in a reasonable
enough time to sell the fish.
○ Lower transportation costs have made this less of an issue.
■ When it is beneficial to make a contract with a firm than buy it off the market.
● Human Capital: ​Specific skills necessary for work in a firm that are not transferable to other firms. Skills that are only useful for a
particular market.
Question: In the presence of specialized investments such as site specificity, physical asset specificity, dedicated assets, time specificity,
and/or human capital, why are transaction costs such as bargaining expected to be significantly higher? In other words, these things make
transactions costs much higher, why?
● A: One consequence of specialized investments is that buying the capital are ​sunk costs​. You can’t get them back. So you want to
build as cheap a plant/physical asset as possible.
●
Goldstein 15
Think about dedicated assets example (factory only has value if Walmart sells toy). Why would bargaining costs then be higher
once the plant is constructed? (1) Walmart holds all of the cards…they know the other will go out of business without them so they
can demand a low price. This is how Walmart prices that are so low.
The Hold-Up Problem:​ ​Once a firm makes a specialized investment, the other party may attempt to “rob” it of its investment by taking
advantage of the investment’s sunk nature.
●
Costly Bargaining:
● Attorney costs
● Opportunity cost of time
● Possible lost exchange
Underinvestment:
● Lost exchange
● Increased search costs
Firms have bargaining power in relation to their level of specialty each producer more does. So if you want high quality product
signing a contract to establish cash flow is best.
● Think about the NFL negotiations. Players make an investment in their body…which is only valuable in the NFL. Owners make
investment in stadiums, which are only valuable with good players playing. Both are trying to hold-up one another, making
bargaining very expensive.
● Because we know that firms behave this way, firms protect themselves at times by under-investing.
Industry Structure and Transaction Costs
●
Spot exchange:
● few rules
● no long term contracts
● Why low enforcement costs? If tobacco looks right and price is right then transaction takes place.
● Why high on the other costs? No specialized investment.
Contacts:
● Can fix some of these problems
● Long term agreement makes bargaining costly and force of law makes enforcement costly
● Search and hold-up are small because contract protects parties.
● Many non-formal (implicit) contracts exist to keep people in check. Game theory talks about this a lot.
Vertical Integration
● Buyer and seller or seller and supplier
● With a bigger, more diverse company it becomes increasingly difficult to make sure that your workers are doing what you want
(often why with buyouts old employees stay in place).
● Firm produces its inputs inself. This depends on expenses + marginal cost & benefit.
Enforcement
Bargaining
Search
Hold-Up
Spot Exchange
Low
High
High
High
Contract
Medium
Medium
Medium
Medium
Vertical Integration
High
Low
Low
Low
Goldstein 16
Industry Makeup Principal: ​Transaction costs are a main driver in observed industry structure.
●
Purchased Inputs Intensity (PII) is the ratio of input costs to sales price at whatever stage of the production cycle a firm is in. The PII can be
interpreted as the amount of value a firm adds to a production process. The lower the PPI, the more “value” the firm is adding to the input goods.
As firms vertically integrate, we would expect them to include more of the production stages in their operations, increasing the value the firm is
adding to its input goods (thus lowering its PPI). The “theory” we have proposed would indicate that in areas where transaction costs are most
likely, vertical integration would be more likely. This should manifest itself in low PPI’s. If we look at assorted industries throughout the nation, in
the area where most employees exist (implying low transaction costs since the industry is geographically concentrated in that area), PPI’s are
consistently higher than in neighboring areas. In other words, vertical integration is most likely when it’s hard to find suppliers (in this case due to
geographical constraints).
Contract Terms - Specificity
●
●
●
●
●
●
●
●
●
●
●
Marginal Benefit is the avoidance of hold-up costs.
Assume MB is independent of contract length
Avoid same amt. of hold-up costs each year
MC is increasing because, the farther out you contract, the more
complex the contract gets.
If you have more specialization, it makes more sense to write a longer
contract.
Due to the need for specialization, will need larger contract
The intersection of MB & MC will inform length of contract
What if the contracting environment becomes more complex? (i.e. there is
another possible supplier in the future).
If the production becomes more complex, a firm might want a shorter
contract for more flexibility.
A more difficult/ complex market or uncertain future will shift the MC of the
contract itself
○ It makes it more expensive b/c the uncertainty.
Now it's the same cost, but for a much shorter contract
15 September 2017
Contracting Principle: ​Utilize Contract Terms to minimize input costs
How to extract more effort from workers…
●
●
Paying employees more can make the firm more profitable
○ Note: Not all incentive schemes are created equal, b/c this some
are better with regard to different types of workers.
The firm is better off sharing profits with the employee… pay more to make
more.
Goldstein 17
Types of Incentive Contracts
Profit sharing: ​Profit sharing means that pay is tied to profits. This is suitable for top managers and small firms
● Ex. Stock options at startups
● Good strategy when workers can directly impact the profits. It is better when workers can impact revenue ​and​ cost.
Revenue Sharing: ​If worker can’t impact cost, revenue is a better option
● It’s important to recognize that this incentive contract can be risky if increased sales would imply significantly higher costs.
● In addition, it’s important that the sales teams do not have significant pricing power. As they would lower the price considerably in
order to make the sale.
○
Consider, for instance, an individual who tends to tip very well. It is not uncommon for wait staff to notice this and start reducing the
price of items to nothing. While the wait staff receives fantastic tips (i.e. revenue sharing), the firm is actually losing profits.
Generally used for salesmen and service-oriented professions. Ex. Real estate agent → house is priced before the agent enters
the picture.
Piece Rates: ​the more you produce, the more you get paid.
● Suitable when productive is “if effort, then output”
● Need some way to ensure that output meets a standard.
●
●
It is very important to incorporate a quality check in these contracts.
○ i.e. if you told me you’d pay me $1000 per song I wrote, I’d have 20 albums worth of material in about a day. Each song would sound
suspiciously like “row-row-row your boat”, unfortunately. Individuals would trade quality for quantity.
Bonus/ Raise Based on Spot Checks:​ Instead of measuring every sale/unit produced/profit level, managers can instead make spot
checks. If it’s high quality, giving them a bonus or raise.
● This lowers enforcement costs significantly. The key is that the checks must be random. Otherwise, you will only put forth your best
effort when you know you will be monitored. On the flip side, you will shirk when you know you will not be monitored. When they
get out into the working world, note what happens when the manager leaves for the afternoon.
*​For all Incentive Contracts, beware of perverse incentives!
● No Child Left Behind
○ Testing focused on things that can be easily quantified
● Sales people offering excessive discounts
○ Selling on price instead of value
● Overbilling if you are paid hourly and not monitored
● Competition instead of cooperation between employees
○ Fighting over a promotion or bonus pool
Tournament/ Prize Style of Pay:​ Pay a few people at the top lots of money. Everyone else works harder to try to get to that spot.
● Good if you can only monitor the relative performance of your employees
● Encourages risk-taking
● Pits employees against each other
● One justification for high CEO pay
Besides an incentive contract, why might a worker avoid shirking?
18 September 2017​ - Notion of Industry (Last topic of exam #1)
The size of firms sales size the industry, but that isn’t always true for all markets. This can be misleading.
● Typically focusing on revenue here
● Looking at the biggest firm gives us a good idea of ​how big the industry is​.
By looking at measures of technology, we might get an idea of the productivity of capital and the future growth prospective (fewer employees
needed). However, the difficulty is that technology within an industry is hard to gauge.
Goldstein 18
Technology Measures:
R&D as a percentage as sales.
Company
Industry
R&D as a % of Sales
Bristol-Myers Squibb
Pharmaceuticals
17.0
Ford
Motor vehicle and parts
4.3
Goodyear Tire and Rubber
Rubber and plastic parts
1.9
Kellogg
Food
1.5
Proctor & Gamble
Soaps and cosmetics
2.8
Technology measures the return on investment/ the productivity of capital
Doesn’t say how advanced, but rather, how much of budget is going into being advanced.
Not surprising that Bristol-Myers spends so much on R&D, since it only makes money on new drugs. Once patents have expired,
competition drives profits down extremely quickly. Thus, a firm must always create the next big thing. As an aside, this can lead to
perverse incentives in testing/safety issues.
Second is employees per million dollars in sales
●
●
●
Industry
Employees per $1mil in sales
Petroleum-refining
1
Beverage
17
● Tech IS productivity of inputs.
● Labor is a better common input than capital.
● Intuitively, one can think about this as: “more sales per worker means better machines are being used.”
Advertising/Profit Measures
Advertising/Profit as a percentage as sales.
Company
Industry
R&D as a % of Sales Advertising as a % of Sales Profit as a % of Sales
Bristol-Myers Squibb
Pharmaceuticals
17.0
7.6
10.2
Ford
Motor vehicle and parts
4.3
3.1
5.1
Goodyear Tire and Rubber Rubber and plastic parts
1.9
2.0
0.7
Kellogg
Food
1.5
9.0
9.4
Proctor & Gamble
Soaps and cosmetics
2.8
10.4
13.5
*Notice that higher advertising is associated with higher profit.
●
●
●
●
Advertising as a % of sales gives an idea of how important it is to a firm to differentiate their product through either informative or
persuasive means (we’ll talk about these later).
Advertising reveals the importance of product differentiation.
Advertising is tricky as there are different reasons for advertising. For the course, advertisers want to charge consumer opinions on
a product. This is to make consumers less bothered by price changes.
Note that advertising does seem to have a relationship with profit as a % of sales. In particular, advertising is about creating a “mini-monopoly” via
differentiation which we’ll discuss in significant detail in the coming chapters. For instance, soap is soap is soap. However, we constantly see
soaps trying to differentiate themselves. Dove soap vs. other soaps.
Goldstein 19
Industry Concentration
Four-firm Concentration Ratio (C​4​): →
● where S​1​ are the sales of the industry’s largest firm, S​2​ are the sales of the industry’s second largest firm, S​3​ are the sales of the
third largest firm, S​4​ are the sales of the industry’s fourth largest firm, and S​T​ are the total sales in the industry.
● Note: the numerator is just the top 4 firms, but the denominator is all firms. This tells us how big the ​top 4 firms are​.
Alternatively, →
Where w​1​ is the market share of the industry’s largest firm, etc.
○ w ↓ 1 = S↓1
S↓T
Bad b/c a concentrated industry leads to higher prices & fewer options.
○ Less competition, higher the profit margins.
● Drawback of these measures is that sometimes can have just 2 firms, but they compete so intensely that prices are kept very low.
Herfindahl-Hirschman Index (HHI):
●
H HI = 10, 000 ∑ w21 ; ​where w​1​ is the market share of the industry’s largest firm, etc.
*This measure is really important for the DOJ when determining the legality of mergers, monopolies & the concentration of industries.
● The HHI weight larger companies more strongly. This is a more useful measure. Instead of having market shares in a linear way,
the HHI index will punish/show more competition in cases where there are large firms taking up the market.
○ It is also more complete as it includes all firms in the industry.
● An HHI with a 10,000 is 100% concentration of one firm. The HHI should fall in the 0 -10,000 range.
● Good thing about HHI:
○ All firms matter
○ Weighs big firms more (note that an industry is less competitive with large firms…HHI penalizes and industry for this).
Goldstein 20
See that C4 and HHI almost always have a strong relationship with one another.
*Note* the high HHI implies potential market power in the markets. As we will see with
game theory, however, it may or may not manifest itself through actual monopolistic
pricing behavior.
20 September 2017
Limitations of Concentration Indices
1. Only includes American firms
a. If it’s a small American company (but the only one) in a large global market, it will have an HHI of 10,000. However, it
actually has no market power
2. Ignores local concentration
a. Gas station in the middle of nowhere
3. Industry definitions are unclear
a. Walmart? etc.
Question: If mergers result in increased market power, why would the DOJ ever allow one to occur?
● Because they firms/firm can become more cost effective by merging. So if there is already sufficient competition then prices rising
too much isn’t a concern, but prices can lower due to cost savings.
● Even without competition, sometimes we allow monopolies to form because of the cost-savings that can arise.
○
Mergers:
●
●
Cable; Power; Water
Vertical Integration & Conglomerate Mergers are okay typically in the eyes of the DOJ, but horizontal integration is very closely scrutinized.
CM is when one company is doing well, the other company will support it. Cash flow is used as insurance.
Lerner Index:
;
where P is the market price and MC is the marginal cost of producing the good.
Can be rearranged to:
-Lerner Index is a direct quantification of the pricing power in the market. It’s directed
very closes to the markup in an industry. The higher the markup, the higher the Index.
-So even w/ a few firms a low Index can mean that mergers are okay.
-Tells you if market concentration impacts the cost.
-Optimal choice is where price=cost i.e. perfect competition L=0.
-As firms have more market power, we move from a perfect competition, thus prices will
increase. L=0 → Price=MC → perfect competition.
*In industries w/ high fixed costs, the MC can be quite low, but this doesn’t always mean the Lerner Index will account for this. I.e. Microsoft; Big Pharma.
● Note: HHI and Lerner often tell the same story.
---MIDTERM ONE---
Goldstein 21
Supply and Demand
Perfect competition occurs in a market in which:
1. There exists many small firms (HHI very low).
2. There exists many individual buyers.
3. Firms sell “identical” products.
4. Every buyer and every seller has full information about the price and quality of goods.
5. Transaction costs are very low.
6. No barriers to entry/exit.
Or, more simply, a market in which every participant recognizes they are too small to have the ability or desire to affect the market price.
Basically, there are many small firms.
● These types of markets aren’t very realistic, but provide a good baseline for analysis
● This is essentially what occurs when more and more firms enter a market and we’re assuming more realistic assumptions (our
monopolistic competition discussion will cover this)
● “perfect competition” is the “best” outcome in a very specific economic environment (no externalities).
Two Rules for Demand
Consumer preferences are assumed given, but that they are…
1. Complete: Property of preferences
a. Can always make a decision between two things; I can always make a decision
i.
Indifference is okay.
2. Transitive: Internally consistent
a. If I’d rather have an Apple than a Banana and I’d rather have a Banana than a Cookie, then I’d rather have an Apple than
a cookie
b. A > B and B > C implies that A > C
Problem with non-transitive preferences
A>B>C>A
●
Money Pump:
○ Two players: Scammer and Sucker
○ Sucker starts with C
○ Scammer: I’ll give you B if you give me C plus a penny
○ Scammer: I’ll give you A if you give me B plus a penny
○ Scammer: I’ll give you C if you give me A plus a penny
Sucker has exactly what he started with (C), but paid $.03
Scammer can repeat this until the Sucker is out of money
Individual Demand
*The demand function maps price of good and quantity demanded*
● “Law” of Demand: As price decreases, individuals demand more and more of
the good.
○ This really just says that the demand curve slopes down…or in
other words, in order to get people to buy more of a good, the price
has to be lowered.
○ A theory bc it isn’t always true. Imagine an item whose value is
inherently tied to its price (Jewelry and other status goods)
Market Demand
Note that if we know individual demands, we can determine the market demand curve by
horizontally adding the quantities at each price.
● Market demand is the summation of all the demands; summation of everyone’s
demand
● Thus, if Individual A would purchase 40 units of the good if the price were $20
(which is the dual interpretation of the behavioral “black box”) and Individual B
would purchase 13 units of the good if the price were $20, then both individuals
together would purchase 53 units of the good if the price were $20.
● When plotting P & Q any changes in price will be reflected in the cure, other
changes will impact the intercept.
● Only shocks to price will impact quantity demanded; if you change income then
the whole demand curve will shift.
Goldstein 22
Demand Function:
In general, assume demand functions are in the form:
*Everything else: cultural, weather, etc. Literally anything else that impacts demand.
Demand is the correspondence between a set of prices and quantity demanded at their cost points
● We will not address Giffen goods → goods that violate law of demand
●
●
Note: Demand vs Quantity demanded are different.
From a stationary point, Q​d​ only changes if the price
changes.
Income rises...
*A change in demand (i.e. incomes change) means the whole curve moves*
● Income leads to a change in demand, not Q​d​ (which only results from a
change in price). Note that a change in demand results in a shift of the
entire demand curve.
● Willingness to pay for the good actually changes (at every level of
consumption)
○ This is a normal good. As you get richer, you demand more.
Rule:
●
If something changes that can be found on an axis, you are dealing with a Change in Quantity Demanded. The underlying
consumer “willingness to pay” has not changed.
● If something changes that is NOT found on an axis, you are dealing with a Change in Demand. The underlying consumer
“willingness to pay” has changed. Ask yourself “for a given quantity level, would the consumer be willing to pay more or less for
the good?”. This will dictate the direction of the shift.
Graphically, what happens…
● to the demand for peanut butter if jelly becomes cheaper? → Decreases
● to the demand for ramen noodles if your income increases? → Decreases (inferior good)
● to the demand for pizza if the price of pizza drops? → increases
● to the demand for houses if you know a tax credit goes into effect next month? → Demand shifts up.
Income: → remember: this stuff shifts the ENTIRE CURVE.
● Normal Good: A good whose demand increases (shifts up/right) when consumer incomes rise. Examples: cars, clothes (in
general), electronic equipment.
● Inferior Good: A good whose demand decreases (shifts down/left) when consumer incomes rise. Examples: ramen noodles,
discount clothes, bus travel.
○ So why do companies do this? To provide insurance against the business cycle. Not everyone will be rich all the time.
Goldstein 23
Price of related goods:
● Complementary Goods (Complements): Goods in which a price decrease of one good results in an increased demand of another
good. Examples: Gas/SUVs, hotdogs/buns, bicycles/helmets
○ If you buy more of one, you’ll need more of the other. ↑ P​y​ = ↓ Q​xd
● Substitute Goods (Substitutes): Goods in which a price decrease of one good results in a decreased demand of another good.
Examples: Coke/Pepsi, chicken/beef, Mac/PC.
○ Can replace one with the other. ↑ P​y​ = ↑ Q​xd
Advertising and consumer tastes: Companies try to impact attitude towards a good, which will shift the whole demand schedule
● Informative Advertising: Advertising designed to increase consumers’ demand through information about the existence or quality of
a product. I.e. Little kids love iPads!
● Persuasive Advertising: Advertising designed to increase consumers’ demand through appealing to their emotions and general
sensibilities. I.e. Nike running: just do it.
Number of consumers
● Population: more consumers = increase in demand; more people will shift the demand to the right
○ Think about demand for homes in a town after a new car factory is built.
● New Market Segment: Find new consumers for your product
○ Think about demand for iPads after parents realized that it was portable entertainment for kids.
Consumer Expectation:
● If you expect prices to go up in the future, your demand for the good will increase today; consumers are forward thinking
Consumer Surplus:
● The “extra” value a consumer gets over and above the amount they have to
pay for it.
● The area between the demand curve and the price
● The demand curve is “willingness to pay at different quantity levels.” At any
quantity, if I actually pay what I am willing to pay then you can think of the
purchase as being a wash (because I was indifferent between the money and the item at that price).
● If I get the item for less than WTP, then I am really better off by purchasing.
● In this case will consume 7 units; the area underneath the demand curve is the consumer surplus. The richer you are the more
consumer surplus you have.
Firm Theory:
● Firm decision making process: given the market price, how much do I want to produce?
○ While consumers maximize “utility,” firms maximize ​profits
○ Profit is a much more concrete concept than utility
● With demand we assumed that consumers could somehow convert items into dollars, so that for every quantity level, there was a
price that would induce them to purchase the quantity.
● With supply, we will assume that there is a minimal price that a manager requires to produce different quantities of a good.
● While there is a black box here, as well (managers are just people, after all), we actually know a little more about what’s going on
underneath the curtain. This is because we know the ALL managers are profit maximizers. So by understanding the input costs,
transaction costs, contracts, etc. we understand their optimization problem a bit better.
● Perfect competition: revenue = P * Q
○ Price is fixed for every Q.
Profit Function: π (Q) = P * Q − C (Q)
● π → Profit
● P * Q → revenue; depends on the economic environment
● C(Q) → cost function; depends on the w,r and Q=F(K,L)
● Economic environment, firm (input and technology)
● P is determined in the market i.e. an individual firm has no market power/can’t set prices
● The revenue function P * Q is linear by Q. The marginal revenue is equal to P.
Goldstein 24
Supply:
*The yellow line is price → This is perfect competition*
● What should the firm do if the price of a good is $4?
● Will sell until the amount the firm will produce is $8, where price=MC
● Price is fixed as varying Q doesn’t impact price. So you just want the
intersection of MC and Price.
○ Which in this case is 8. P=MC also impacts the supply curve
The price is set at $2...
If the firm is committed to producing, then the intersection is the best they can do
(Price = MC)
● The per-unit price is below the average (per-unit) variable cost. Thus,
they are losing money and they’d be better off if they didn’t produce.
● Why look at AVC instead of ATC?
●
●
●
●
The green rectangle is revenue = P * Q
The red is total variable cost = AVC * Q → AVC = VC/Q
Revenue and costs on the graph so negative profit
When price is high enough to reach the lowest part of the AVC then it
can operate. Even though it can’t cover fixed costs
○ b/c MC is a function of Q, firms, even if they aren’t super
efficient are encouraged to produce more/enter the market at
this point.
Firm Decision Making Process: In other words, a firm’s supply curve is their MC curve above the AVC curve. This leads to the decision rule.
The red line is the supply curve. The supply curve tells us for a given price, this is
the amount that a seller is willing to supply.
● Question: The “Law of Supply” states that supply curves are upward
sloping. In terms of Marginal Cost, what is this law really saying?
○ Marginal cost slopes up, indicating that, at some point, there is
diminishing productivity​.
● Demand slopes down; supply slopes up. If prices are higher you will
have more sellers but fewer buyers.
○ I.e. minimum wage laws
Supply function:
Use a mathematical function to summarize this decision in a similar manner to
demand
● A production substitute is something that you could produce with roughly
the same inputs as what you already have (think farmer, who could
produce corn instead of tobacco). Tie this to opportunity cost.
● Price will cause the curve to shift up and down, everything else will
impact the intersection.
Goldstein 25
Change in the quantity supplied:
●
●
For a given input price level (W), price of production substitutes (P​r​), and
“everything else” (H), a change in the quantity supplied (Q​s​) results from
a change in the sale price of the good (P​x​).
Just like we had to change in quantity demanded, now we have a
change in quantity supplied.
Change in supply:
●
This is nothing but the MC curve. What happens to marginal costs if
input costs rise?
○ If prices increase, the curve will shift up and assuming price is
constant the firm will just produce less.
○ Left/in and right/out with supply
○ Decrease → left (up)
Rule: If something changes that can be found on an axis, you are dealing with a Change in Quantity Supplied. The underlying
ability/willingness to produce has not changed.
● If something changes that is NOT found on an axis, you are dealing with a Change in Supply. The underlying ability/willingness to
produce has changed. Ask yourself “for a given quantity level, would the marginal cost increase or decrease?”. This will dictate the
direction of the shift.
Graphically, what happens…
1. To the supply of cars if rubber prices increase? → shift left, decrease car production as cost of input increasing
2. To the supply of houses if more development firms enter a market?
3. To the supply of cigarettes if the government imposes a $1.00 sales tax? → shift left
4. To the supply of 12” oil pipes if the price of 14” oil pipes increases? → decrease 12” production, increases 14” production; this
could be a preference shock (shift along the curve)
The opportunity cost is stressed since this is the reason firms would reduce supply now if they expect prices to increase in the future. Always
focus on the marginal cost interpretation. Note for the #4, this is the marginal opportunity cost.
27 September 2017
Under perfect competition → this is the solution to the firm’s problems
1. R = MC → Q*
2.
Given Q*, choose K,L such that
MPL
MPK
=
w
r
Input Prices​: As input price increases, marginal costs increase. This is a “decrease/inward-shift” in supply.
● Input prices are already included in the cost function
● Just like with demand we can name all of the shifters. Recommended that you make a list of these.
Technology: A technological advancement reduces marginal cost, “increase/outward-shift” in supply.
Government Regulation: A government regulation limiting the use of technology increases marginal cost, “decreasing” supply.
● With government regulation, think of technology as anything that allows one to produce more efficiently. Currently, we have
technologies that are efficient, but they pollute. Cap and trade will force companies to trade these efficient technologies for less
efficient ones, meaning higher marginal costs.
Number of firms: As more firms enter a market, the market supply will increase.
● As firms leave a market, market supply will decrease. This can be caused by natural disasters, bankruptcy, industry migration, etc.
Substitutes in production:​ As similar products are sold for a higher price, firms will change production to produce the alternative goods.
● This shows how a producer can use the same inputs to produce different goods.
● Whichever good has the higher price, the firm has a greater incentive to produce that good.
Taxes:​ ​A tax on a firm is just an additional marginal cost the firm has to pay. Thus, an increase in the tax rate will result in a decrease in
supply.
Goldstein 26
There are different ways to analyze taxes in a supply/demand framework. We will take the easiest approach and assume it always
gets charged to the producer.
● Spend some time to talk about tax incidence. Doesn’t matter who is taxed or which curve you shift.
● We assume taxes are during the production process.
○ Marginal costs will increase, supply will decrease.
Expectations:​ If a firm expects to be able to sell its good for more tomorrow, the opportunity cost of selling today increases. Thus, an
increase in expected future prices will result in a decrease in supply today.
● Think of selling your house. If you expect high housing prices next year then this is equivalent to a high opportunity of selling now.
Thus, increase in marginal cost.
● Agents expectations about the future will impact behavior today.
Producer Surplus:
1. The firm’s benefit over-and-above the 2nd best alternative on which the firm could
have spent the variable cost.
2. The firm’s “profit”.
3. The area below the price and above the supply (MC) curve.
● Just like with demand we spoke about consumer surplus…now we talk about
producer surplus.
● Can think of PS as profit.
● Recall the supply curve is the marginal cost curve above the minimum of the AVC curve. If we draw the full MC curve out, we can
ask “how much profit will be made on the 1st unit of the good?”, then “on the 2nd?” and so on, until we get the entire PS.
● The area below the demand curve and actual price → this is profit!
○ The overall profit is the profit from the each possible outcome.
● Alternatively, we can start with revenues and subtract out the costs.
● The point of this slide is to introduce the fact that revenue can be read off the graph as the area of the price/quantity rectangle.
NEW SLIDE DECK
Competitive Equilibrium
●
●
●
●
●
At the high price, there are more sellers than buyers, so there is
pressure to lower the price.
When the price is lowered there are two effects:
○ Some sellers are no longer interested in selling
○ Some buyers are not interested in buying that were not before
at the high price.
Over time prices will continue to drop until quantity demanded is equal to
the quantity supplied.
Surplus: original difference in demand and supply
○ Firms are producing too much of the good. This puts pressure
to sell at a lower price.
Surplus​: The market condition in which the quantity supplied exceeds the quantity demanded. “Market pressure”
Results in pressure on suppliers unable to sell their goods to undercut the suppliers who can, driving prices down.
Prices will not be stable if a surplus exists
Prices don’t move because they are “supposed to”… market pressures force prices down.
If a surplus exists, there will be pressure to decrease the price. This will cause suppliers to provide less and buyers to want more of the good.
Ultimately, prices will go down until every seller who wants to sell the good will be able to. Then, no one will have an incentive to offer a
different price.
Surplus → DWL
Goldstein 27
●
●
●
●
Shows a surplus.
Note the consumer and producer surplus at this level.
Adding these two gives us some measure of societal welfare (whether
or not this is a good measure is hotly debated…no metric for equality
here).
/​
The deadweight loss is a consequence of not having
​ an
equilibrium
Shortage:​ The market condition in which the quantity demanded exceeds the quantity supplied.
● Results in pressure on buyers unable to purchase a good to offer more money to the limited suppliers, driving prices up.
● Prices will not be stable if a shortage exists.
● Jargon: Focus on the fact that prices will not stay the same. There will be pressure to rise.
● So we have seen that if the price is below the intersection of S&D that we are not in equilibrium because prices are not stable.
We’ve also seen that they aren’t stable above the crossing. So where does an equilibrium exist?
● Price ceilings​ are not a good idea bc of this. They create artificial shortages.
● If a shortage exists, there will be pressure to increase the price. This will cause suppliers to provide more and buyers to want less
of the good. Ultimately, prices will go up until every consumer who wants the good will have one. Then, no one will have an
incentive to offer a different price.
●
●
●
●
Now that price is $20… the quantity supplied is less than the quantity
demanded.
This is a shortage
○ Upward pressure on prices.
Consumers will pay more for the good
Note that the result of this shortage will be that buyers offer higher
prices, as prices rise due to this market pressure more sellers will be
interested in selling and fewer buyers will be interested in buying.
Market Equilibrium​:​ The price at which:
1. Quantity demanded equals quantity supplied.
2. No shortage exists
3. No surplus exists
4. There is no pressure on any buyer or seller to change the price.
Market Equilibrium Principle:​ In a perfectly competitive market, buyers and sellers acting in their best interests will result in a stable
price/output combination.
● Actually quite a significant prediction: people acting entirely in their best interests will end up with a predictable, stable outcome.
○ Price acts as a signal of value.
Comparative Statics
● Comparative: We only want to compare two scenarios; we don’t need numbers
○ A is more than B, rather than A=10 and B=3
● Statics: Static means not moving.
○ We just want a snapshot of A and a snapshot of B
● Something changes. How are price and quantity affected? → how do shocks impact the equilibrium quantity?
Question: How will the equilibrium price/quantity of corn change if ethanol is used as a primary alternative energy source?
● A: The demand curve shifts up, demand increases. Supply isn’t impacted. Remaining at the old price market can’t last, it must
move the equilibrium up.
● Will likely result in an increase in corn prices and the amount of corn being produced.
Goldstein 28
How will advances in technology impact the curves? → Decrease marginal cost, so supply increases
●
●
●
●
●
This shows a supply shock. The supply curve decreases
Higher quantity, lower price
When the shocks come together they have a rise in quantity
At the original price, this will result in a surplus incentivizing those firms
who could not sell their good to lower their price.
○ This will drive quantity and price down.
Advances in agricultural biotechnology can help push down food prices
while leading to an increase in total output.
Rules to determine how prices will change in the presence of “shocks”:
1. Ask “will this shock cause a demand shift?”
2. If so, shift the demand curve in the corresponding direction and determine how equilibrium price/output will change.
3. Ask “will the shock cause a supply shift?”
4. If so, shift the supply curve in the corresponding direction and determine how equilibrium price/output will change.
5. Repeat as necessary if multiple demand/supply shifts exist.
a. “Reset” your graphs; we want to look at each shock separately
6. Compare the demand/supply outcomes to determine the final direction of the equilibrium price/output changes. If any shock
causes price/output to change in the opposite direction as another shock, the result is ambiguous for that parameter.
*It’s important to look at each shift separately. The “magnitude” of the shift will dictate which price/quantity effect dominates, but we won’t
have information on magnitude. We can use data to back out which effects were the most dominant.
29 September 2017 - Review for Midterm II
1. Q​D​ = 80 - 4P ; Q​S​ = 4P.
a. Find the P*, Q*, TS
b. Policy: Q​S​ = 2P. Find the DWL.
D​
a). MCC → Q​ = Q​S​ (market clearing condition → equilibrium condition)
● 80 -4P = 4P → ​P* = 10
○ Plug it back into either supply or demand curve
● Q​S​ = 4P → 4(10) = 40 → ​Q* = 40
● To find TS → need CS + PS
● Area of CS triangle:
○ CS = ½ * (20 -10) * 40 = 2000
○ PS = ½ * (20 - 10)* 40 = 200
○ TS = 200 + 200 = ​400=TS
b). DWL → complete social cost of policy (Q​S​ = 2P)
● P =MC → P = Q/2 ; before: P = Q/4
● MCC: 80 - 4P = 2P
○ 6P = 80 → P = 80/6 = 13.3 = P​a​*
○ Q​S​ = 2P = 2(13.3) = 26.6 = Q​a​*
● PS​a​ = ½ * (13.3)(26.6) = 176.9
● CS = ½ * (26.6)(6.7) = 89.1
● TS = 266
● DWL = 400 - 266 = ​134
Goldstein 29
Q​D​ = 200 - 8P , Q​S​ = 2P
a. Find P*, Q*, TS
b. Implement price floor ​P​ = 22. Find the surplus, shortage and DWL.
c. Implement price ceiling P = 18. Find the surplus, shortage and DWL.
a). MCC → Q​D​ = Q​S​ (market clearing condition → equilibrium condition)
● 0= 200 - 8P → 8P = 200 → P = 25 ; Q= 200 - 8(0) → Q = 200
● 200 - 8P = 2P → 10P = 200 → ​P* = 20
● Q* = 2(20) = ​40 = Q*
● CS = 5 * (40/2) = 100
● PS = 20 * (40/2) = 400
● TS = 100 + 400 = ​500 = TS
b). ​P​ = 22 - Price Floor
● Surplus: Q​S​ - Q​D​ @ ​P​ = 22
○ Q​S​ = 2 * 22 = 44
○ Q​D​ = 200 - 8 (22) = 24
○ Q​S​ - Q​D​ = 44 - 24 = 20 = 20 (the # of items the firm has produced)
● CS = ½ (25 -22) * 24 = ​36 = CS
● Q​S​ @ 24: 24 = 2 - P → P =12
● PS: ½ (12 * 24) = 144 + (22-12) * 24 = 240 → ​PS = 384
○ PS = area (A) + area (B)
● TS: 384 + 36 =​ 420 = TS
● DWL: ½ (10 * 16) = ​80 = DWL
c). P = 18 - Price Ceiling
2.
@ P = 18: Q​S​ = 2(18) = 36
○ Q​D​ = 200 - 8(18) = 56
○ Q​D​= 56 - 36 = 20
● PS = ½ (18-36) = 324
● @Q​D​ = 36: 36 = 200 - 8(P) → P = 20.5 @ Q​D​ = 36
● CS: a + b = CS
○ A: (20.5 -18) * 36 = 90 + b: ½ (25-20.5) *36 = 81
○ CS= 90 + 81 = 171
○ TS: 324 + 171 = 495
● DWL: ½ (20.5-18) * 40 = 5
● This policy could be used to make the people happy bc ppl gets cheap goods, but
firm will be v unhappy
Price floor: ​A government imposed minimum price at which a good can be sold.
● If the price floor is above the equilibrium price, a surplus will ensue. (binding)
● If the price floor is below the equilibrium price, the market is unaffected. (non-binding)
● A price floor prevents things from going down.
● Ex. minimum wage, agricultural price supports
Price ceiling​: A government imposed maximum price at which a good can be sold.
● If the price ceiling is below the equilibrium price, a shortage will ensue. (binding)
● If the price ceiling is above the equilibrium price, the market is unaffected. (non-binding)
● Prevents things from going up.
● Ex. rent control, gas/natural gas price ceilings.
●
Goldstein 30
9 October 2017
Elasticity Motivation
●
●
●
●
●
Revenue = P * Q
Increase price, revenues will fall
○ This depends on consumer sensitivity
In this case, if we raise prices, the revenues decreases.
Raising the price means that fewer people will purchase the good
Thus, you’re getting a few of your customers to pay more, but at the
expense of losing your customer base.
Elasticity: ​is about putting numbers to cause-and-effect measurements. If x changes, how much does y change? If I increase the price, how
many fewer units will I sell?
● The responsiveness of one variable to a change in another variable.
● The percent change of one variable caused by a percent change in another variable.
● “B Elasticity of A”
E=
●
ΔQ
Q
ΔP
P
=
ΔQ
ΔP
*
P
Q
If price high and quantity low, elasticity will be large.
●
●
●
●
If E is positive an increase in price causes an
increase in Q, vice versa
Cross + income elasticity → only the sign
matters.
According to the law of demand what is the sign of own price elasticity of demand?
○ It is negative
Assume two goods are substitutes. What is the sign of their cross price elasticity?
○ Substitutes: Cross-price elasticity >0
○ Complements: <0
●
If something is elastic, a small movement results in a
big change.
Goldstein 31
●
●
●
Elasticity is a local measure → magnitude changes along the curve. Elasticity changes as you move along a demand curve. When
you have very high prices, demand is elastic.
Perfectly ​elastic​: The top part of an “E” looks like a horizontal line, which is a perfectly Elastic demand curve. Note if the price
changes at all, you lose all your business
○ The flatter the demand curve the more sensitive consumers are. Consumers are perfectly elastic to price here.
Perfectly ​inelastic​: An “I” looks like a vertical line, which is a perfectly Inelastic demand curve. Note you can change your price as
much as you’d like and the market won’t respond.
○ For the purposes of this class, we will say that the steeper the curve is, the more inelastic it is. Note that this is not
entirely accurate because demand becomes less elastic as one moves down the curve.
●
●
●
●
Business travelers are more inelastic than tourists.
Luxury automobiles are sensitive to price.
Young kids are way more price sensitive (to cigarettes)
than older individuals (possibly addicts). This actually
starts pointing at potential policy recommendations (huge
taxes, like New York) to prevent kids from taking up
smoking.
Note the negative sign on Ground Beef. The richer you
get, the less you consume.
Also, not non-business air travel happens a lot more the
richer you get.
What if I just want to maximize revenue?
● Revenue = Price * Quantity
● If a percentage increase in price is more than offset by a percentage decrease in sales, you should decrease your price to increase
revenues.
● %∆Revenue = %∆Price + %∆Quantity
● +0.6 = +1 + -0.4 → consumers don’t care about increases to price
● +0.2 = +1 + -0.8 → consumers are beginning to care about higher prices in the range.
● A firm has an incentive to increase price in the range where consumers are ​inelastic.
○ Elasticity changes along the curve, so if the firm continues to increase prices, elasticity will increase correspondingly.
○ When +1 = +1 + -1 → firm will be indifferent. Revenue is maximized when the firm is indifferent.
%ΔQ
● E = %ΔP → %∆Q = E * %∆P
If a percentage increase in price is more than offset by a percentage decrease in sales, you should decrease your price to increase
revenues.
--​ This says “if I know my customers have price elastic demand, decrease price
to increase revenue”
-- ​This is ​strictly​ a test for revenue. We generally don’t want to maximize
revenue, but instead maximize profits. However, in some cases marginal costs
are effectively zero, so this is all we care about.
Goldstein 32
In summary:
How price and elasticity (and revenue) changes with quantity
●
Small quantity levels (high price levels), very elastic → should lower prices
○ We’ll get a lot more customers if we do, and we’re not cannibalizing a large number of sales by lowering the price.
○ In the elastic range incentive to decrease price, in inelastic range incentive to increase
At high quantity levels (low price levels), we are very inelastic (thus we should raise our price).
○ We’ll lose a small percentage of our customers, but gain a lot on increasing the prices on everyone else.
These are relaxing the assumption that price is fixed.
●
|E| = 1​, peak of revenue function is where firms are indifferent & revenue is maximized too.
●
●
○ Peak of revenue curve is |E| =1!
Revenue = P * Q, under PC, P(Q) = P for all Q.
Less than PC:
○ P = a - bQ
○ Rev = P(Q) * Q = (a-bQ)Q - aQ - bQ​2
11 October 2017
%ΔQ
● Elasticity: %ΔP
●
●
●
Own price elasticity of demand: EQ​X​, P​X​ =
%ΔQ
%ΔP
Law of Demand implies → EQ​X​, P​X​ < 0
○ Sign of the # determined by the law of demand
● |EQ​X​, P​X​| < 1 ; inelastic
● |EQ​X​, P​X​| = 1 ; unit-elastic
● |EQ​X​, P​X​| > 1 ; elastic
Cross price elasticity:
●
●
EQ​X​, P​y​ =
%ΔQX
%ΔP y
● EQ​X​, P​y​ > 0, x,y are substitutes (price of y goes up, people buy more x)
● EQ​X​, P​y​ < 0, x,y are complements
Income elasticity of demand:
%ΔQ
● EQ​X​, I = %ΔIX ; EQ​X​, I > 0 , normal good; EQ​X​, I < 0 , inferior good
Goldstein 33
If a firm wants to maximize revenues, it has an incentive not to produce in the ​inelastic​ region.
INFLUENCES OF ELASTICITY
● Available substitutes: The more substitutes a good has, the more elastic it will be. Specifically, as prices increase, people will
consume less of the good and more of its substitutes.
○ Corollary: The “broader” the market, the more inelastic it is.
● Time: The more time a consumer has to plan her purchase, the more elastic the good will be.
○ Think about gas prices. More people are switching to hybrids after the gas hike of 2009. Often can’t do much in the
short-run, but in the long run they will change their preferences.
● Expenditure share: Cheaper goods tend to be more inelastic since an increase in price will not cause the consumer’s budget to
“break”.
○ If a home gets 10% more expensive, it might cause someone to not be able to afford it. If an egg gets 10% more
expensive, we’ll still probably be ok.
○ If prices increase for a cheaper good your elasticity won’t change much.
13 October 2017
Under-pricing
● Remember: total costs are always increasing with output. In particular, you can never produce a good for nothing (or less than
nothing)
● Corollary: if you produce less of a good, your total costs will go down.
The good on the left has a inelastic demand. If we’re inelastic, raising the price (and
selling less of the good) will result in increased revenues.
○ Think gasoline. If people just “have to have it”, raise your price. You’ll lose a
few customers, but not many.
● Profit = revenue - cost, revenue = P * Q
● Inelastic → P ↑ 1%, Q ↓ 1%
● Firm with market power would here produce in the inelastic region.
● Optimal price + quantity will ​never​ be in the inelastic demand region.
● V(Q​1​) < V (Q​0​)
Putting these concepts together…
● If the Law of Demand holds, an increase in price will result in a decrease in quantity produced. → a
decrease in quantity produced will always result in a decrease in Total Cost. → ​If demand is
inelastic​, ​an increase in price will also result in an increase in Total Revenue. ​(Inelastic means that higher price outweighs the lost
business form having fewer customers)​. → If revenue increases and cost decreases, profit increases
○ Profit = revenue - cost
○ If you’re inelastic, increase your price (and lower your output). This will result in lower costs and higher revenues.
Under-Pricing Rule: If the Law of Demand holds and demand is inelastic, an increase in price will result in a decrease in costs and an
increase in revenues. This will necessarily increase profits.
● This is only true for the short-term.
● Elasticity changes as prices change (move along the demand curve).
●
Goldstein 34
Look at what happens with profit and revenue as we increase output. Green box is profit. Look at revenue and profit graphs… (above!)
● Not perfect competition. This firm is price setting bc the demand curve isn’t horizontal. Firm has
market power, demand curve is downward sloping
● Firm wants to find peak of profit function optimizing condition. For the price setting firm is MR = MC
● Perfect competition: P=MC → Price is a known number determined by Q​S​ = Q​D​. E
When maximizing profit must consider costs! (see graphic to right)
● Elastic range depends on consumers sensitivities in determining price.
● When considering cost, firm will probably have to do something lower than Q.
●
●
Q maximizes revenue → E = -1 ; Optimal Q is from Q or less than Q , depending on marginal costs.
Costs always give firms the incentive to decrease quantity.
When maximizing revenue need the peak of the revenue curve, but profit function will
peak earlier. Point where revenue is maximized is way too high for profit maximization
● Profit is always maximized at a lower quantity (higher price) than revenue.
● Intuitively, this makes sense that if you don’t think about costs you will almost
always over-produce.
● Maximizing revenue doesn’t take into account the fact that a good gets more
and more expensive to produce. They are only maximized at the same point
when MC=0
● So, even if a manager knew exactly what the demand curve looked like and
could calculate elasticity at every point, they could find the revenue
maximizing point (price that yields 20 units) by looking for unitary elasticity, but
they could not find the profit maximizing price without knowing about the cost
structure, because costs change with producing more goods.
●
Q =20, but pea of profit maximization is where you want!
Over-Pricing Rule​: In order to know if you are over-pricing your goods (in a market with elastic demand), you must know your cost structure.
● Unless your marginal costs are zero, the profit-maximizing output level will be less than the revenue-maximizing output level.
○ Once we raise the price to a level that we become unit elastic, we won’t know exactly how much farther to raise the price
without knowing the cost structure.
● Unless your marginal costs are zero, if your sales force receives bonuses based on ​revenue​ and they have the ability to offer
pricing discounts, they will offer excessive discounts.
○ Because revenue maximizing is at a higher quantity (lower price) than profit max.
● If our MR=MC then the firm is overpricing.
Constant MC Markup Rule​: If your Marginal Costs are roughly constant in a relevant range, the profit maximizing price is:
Implications: (Note: this formula will be given on exam. Not an optimality condition, it’s just a condition that comes w/ the two. Can also be
E
written as... P = 1+E * M C
1.
2.
3.
●
●
●
As a good becomes more elastic, the optimal markup over marginal cost will become smaller.
As a good becomes more inelastic, the optimal markup over marginal cost will become larger.
As a market becomes perfectly elastic, profits will converge to 0.
We can determine the price that maximizes revenue by knowing the price elasticity of demand and the marginal cost (assuming
marginal cost is roughly constant).
What are we assuming about the market we are in right now? NOTHING. All market interaction with other firms is in the elasticity.
This ISN’T an optimality condition. Say MC = 2, E= -0.5 ; P= (-.05/(1-0.5))*2 → P=-2 → we can’t do P = -2
○ So E=-0.5 is impossible This is in the inelastic range. If E=-2 then P=4. That works.
Example:
1. Find the markup.
a. @ E = -1.05
i.
P =
b.
@ E = -1.5
i.
P =
−1.05
1−1.05
−1.5
1−1.5
= 21 ← Just the markup
=
−1.5
−0.5
= 3 ← Consumers are more elastic.
Goldstein 35
16 October 2017
1). E = -2 → P= 2 * MC (this is less sensitive than case 2)
2). E = -4 → P = 1.33 * MC (more sensitive consumers will give firm less reason to change higher prices)
● The closer the number gets to 1, the closer the firm is to perfect competition.
3). If E = -∞ the P = 1*MC, firm will have to charge whatever the MC is.
Constant MC Markup Rule:
● Is necessarily profit-maximizing
● Is based on demand (elasticity) and supply (marginal cost)
● Correctly uses marginal cost as the basis for markup
Cost-Plus Pricing Rule:
● Is not necessarily profit-maximizing
● Is based solely on supply.
● Incorrectly uses average cost as the basis for markup.
● Note: Cost-Plus is not based on econ fundamentals, and can therefore be wrong. It also doesn’t tend to take into account elasticity.
Elasticity is hard to capture. It depends on culture, region, level of education etc.
● So what the firm does is the Cost-Plus Pricing Rule
○ But this means the firm can really muss up
■ IF they misjudge the markup
■ Or if they are just beginning they can mess up the AC as for startup firms it's hard to measure MC, which they
use as a proxy for AC.
If Cost-Plus Pricing is incorrect, why is it so frequently used?
● Determining average cost is “easy” (and is already done as part of standard cost accounting.)
● For mature companies, MC is close to AC (because startup costs have already been paid)
● Determining marginal cost is more difficult.
● Determining market elasticity is much more difficult (expensive).
● If the Cost-Plus markup is tinkered with appropriately, the profit-maximizing price determined by the Constant MC Markup Rule will
likely be stumbled upon.
● However, with trial and error, it can still be approximately correct. It’s important to realize that our Constant MC Pricing Rule might
not be able to be applied since estimating demand is difficult. However, it’s what’s underlying things.
Demand Functional Forms
Two types of demand functions
● Linear: Q = a + bP​X​ + cP​y​ + dM + eH
ΔQ
Q
ΔP
P
ΔQ
ΔP
P
Q
P
Q
●
E=
●
Note: the slope is constant ( ΔP ).
●
●
High Q, low price is inelastic
%ΔQ
E = %ΔP → %∆Q = E%∆P
=
*
=b*
ΔQ
P
Q
makes it a local measure.
Elasticities extremely easy to calculate.
○ Own-price = bP​X​ /Q​X
○ Cross-price = cP​y​/Q​X
○ Income = dM/Q​X
● Note: Elasticity depends on where we are on the curve
Example: Suppose an economist is hired by a shoe company. He finds the demand: 𝑄 ↓ 𝑥 = 10 − 4𝑃 ↓ 𝑥 + 5𝑃 ↓ 𝑦 − 3𝐴 ↓ 𝑦
What will be the impact on demand if the shoe company raises the price of shoes from $100 to $110 and the company is currently producing
200 shoes?
bP
100
● Own-price Elasticity = Q X = −4P ↓x = (− 4)( 200
) =− 2
●
X
●
●
Q↓x
-2 = %∆Q ↓ x/10% → -2 *10% = %∆Q ↓ x → %∆Q ↓ x = -20%
If price increases by 10%, quantity sold will decrease by 20% (from 200 to 160)
Goldstein 36
Non-Linear demand functions:​ Q​x​ = a(P​x​)​b​(P​y​)​c​(M)​d​(H)​e
● Elasticities extremely easy to calculate.
○ Own-price = b
○ Cross-price = c
○ Income = d
○ “Everything else” = e
● *Note: one bad thing is that the elasticity does not change depending on where we are on the demand curve.
○ Log-linear assumes constant elasticities, which may or may not be realistic (of course, linear isn’t realistic, either)
● The estimated constants are our estimated elasticities, which makes interpreting data very easy.
● These are actually easier as the slopes are already in the function.
Log-Linear​: ln(Qx)= ln(a) + bln(Px) + cln(Py) + dln(M) + eln(H)
● Elasticities extremely easy to calculate.
○ Own-price = b
○ Cross-price = c
○ Income = d
Example: If an analyst for a major shoe company estimates the demand for its shoes is: ln Qx = 17 - .8ln(P​x​) + 3ln(P​y​) – 4ln(A​y​)
then what would be the impact on demand of a 20% increase in its competitors advertising budget, A​y​?
●
E ↓ Q ↓ x, A ↓ y =
%∆Q↓x
%∆A↓y
=
%∆Q↓x
20%
=− 4
●
If the firm wants to increase revenues, how should it change the price?
● E ↓ Q ↓ x, P ↓ x =− 8
● Absolute value of elasticity is less than 1, so demand is inelastic, so increasing prices will increase revenues.
● Note that the elasticity estimates tell us very important information. For instance, the negative coefficient on ln(Px) coincides with
the law of demand. The fact the coefficient is -.8 implies we are in the inelastic range. We can take these estimates and perform
our usual elasticity tests.
Practice problems:
1. Suppose Q = 200-4P
a. Find E​P​ @ P = 30
b. Find E​P​ @ P = 20
c. Find P,Q that maximize revenue.
a). Ep = -4 * PQ
Q @ p=30: Q = 200 - 4(30)= 200-120 → Q = 80
30
○ Ep = -4 * 80
= -3/2
b). Q @ P=20
● Q= 200 - 4(20) = 120
20
○ Ep = -4 * 120
= -2/3
c). E= -1
● Ep = -4* PQ , Q= 200 - 4P
●
●
●
-1 = -4* PQ → Q=4P → 4P=200 - 4P → 8P = 200 → ​P = 25
Q=200 - 4(25) = ​Q=100
Goldstein 37
2). Q​X​ = 80 - 2P​x​ + 0.4P​y​ + 2m → THIS WILL BE ON EXAM II
a). Find revenue maximizing P,Q
b). Find P,Q such that Ep​X​ = -0.8
c). If income increases 10% what is the new Q​X​? (Suppose initial Q​X0​ = 30, M​0​=5).
Demand Q​x​= 80 + 0.4p​y +​ 2m - 2P​X​ (intercept on the P,Q graph).*Increase in income shifts up the whole demand curve
a). E​px​=-1 → revenue maximizing!
● Epx = -2 * PQ = -1 → 2P​x​ = 80 - 2P​x​ +0.04p​y​ + 2m → 4P​x​ = 80 + 0.4p​y​ + 2m → ​Px​​ = 20 + 0.1P​X​ + 0.5m
○ This depends on other firms and wealth of the consumers. That’s why this isn’t a nice value for profit maximization.
@ M=5 and P​y​ = 10: P​x​=20 + 1 + 2.5 → ​P​x​=23.5​ (revenue maximizing price)
b). E​Px​= -0.8
● -2 * P/Q = -0.8 → P/Q=.4 ⇒ P = .4Q
● Q​x​ = 80 - 2(0.4Q) + 0.4P​y​ + 2m
● Q=80 - 2(0.4Q) + 0.4(10) + 2(5)
● Q​x​ = 80 - 0.8Q + 4 + 10
● 1.8Q = 94
● Q​X​ = 52.2 → P =0.4(52.22)
● P​X​ = 20.8
N (new) −O(old)
c). M​0​= 5, M​1​ = 5.5 →
→ percent change ; E​I​ =
O(old)
●
●
●
∆Q = Q​1​ - Q​0
-(80 - 2P​x​ = 0.4P​y​ + 2M​0​) → 2m​1​ - 2m​0​ = 2(m​1​ - m​0​) → 2(5.5 -1)= 1
Q​1 -​ Q= 1→ Q​1​-30 = 1 → Q​1​ = 31
Alt. way to do c, using approximation w/ elasticity
5
● E​I​ = 2 * 30
=10/30 = ⅓
%∆Q
%∆M
●
E​I​ =
●
If %∆M = 10, then %∆Q = 10 * (⅓) = 10/3 =
3.3%
Q −Q
100 ( 1Q 0 ) = 3.3%
●
%∆Q
%∆M
0
Help session notes:
● Q​X​= 80 -2P​X​ + 0.4P​y​ + 2m ; M​0​= 5 ; M​1​=5.5
● Q​X0​ = 30
● @Q​X0​ = 30 → M​0​ = 5 → 10% increase → 5 * .1 = 0.5 → 5 + 0.5 = 5.5
= M​1
● @Q​X1​ = _​?​_ → M​1​ = 5.5
● (.5 * 2m) = 1m → Q​X0​ = 30 + 1 = ​Qx1​
​ = 31
Q​1​ - Q​0​ = 30/100 * 10/3 → Q​1​-Q​0​ = 1 → Q​1​ =
31
Extra questions:
● Suppose this increases 75% instead of 10% → Q​X1​ = 37.5
● What is the elasticity of income for # c?
●
○
31−30
30
5.5 −5
5
=
(1/30)
.1
= 1/3 = E
In a perfectly competitive environment, to maximize profits produce the quantity level that ensures price equals marginal cost.
Assume that we are a firm and the market price is 4. We can ask “are we profit
maximizing?
● No, the firm will produce up until the point that price equals marginal
cost (assuming price is fixed).
When revenue is steeper than cost function… MR > MC → Q ↑
● Increasing quantity by one unit would increase overall profit in this
range.
When revenue is flatter than cost function… MR < MC → Q ↓
Goldstein 38
Looking at the same concept in a more general setting by removing the “marginal” notions...
●
●
●
●
●
●
●
Perfect competition as revenue curve is linear
○ Compare total cost curve to revenue curve. In this case, notice the
revenue curve will be a line, since it’s just price x quantity.
Want to know how a firm could find their profit maximizing output level given the
four dollar market price.
Difference between the two curves is profit. Want the quantity that makes the gap
between the two curves as wide as possible. (Where the arrow is pointing!)
Where revenue is steeper, we should ​increase​ production. (where the revenue
line is going up at a faster rate than the cost curve, produce more since the extra
unit will result in higher revenues than costs).
○ Can recognize this as the slope of the revenue is steeper.
If total cost is decreasing at a faster rate than revenue, we should lower/​decrease
quantity since the cost savings will more than offset the revenue losses.
○ If TC is steeper, decrease production!
The only place where there will be no incentive to raise or lower output is the
point where the slopes of these curves are identical. Thus, the revenue gain/loss
will exactly be offset by the cost gain/loss.
Thus, we will ​maximize profits at the quantity that ensures the slopes of these two
curves are identical.
Question​: What is the slope of the Total Revenue Line? What is the slope of the Total Cost Line?
Δ$
Slope: rise/run → ΔQ
● A: Slope of Total Revenue curve is the Marginal Revenue curve. A: Slope of the Total Cost curve is the Marginal Cost curve.
Profit-Maximization Rule:​ To maximize profits, produce the quantity level that ensures Marginal Revenue equals Marginal Cost.
Question​: In a perfectly competitive environment in which prices are fixed, what is the Marginal Revenue of any 1
unit of the good? MR = Price. In PC, it’s even simpler since MR = Price. Hence, if its PC then MR=MC ⇒ P=MC.
Perfectly Competitive Profit-Maximization Rule:​ In a perfectly competitive environment, to maximize profits produce the quantity level that
ensures Price equals Marginal Cost.
Optimal: MR = MC → Q*. This is the point where the gap between revenue and cost is largest and slope of both curves is the same.
23 October 2017
Perfect Competition Long Run Market Behavior
Left side is the cost structure an individual firm is facing. The right side is the
market supply/demand. Assume the market is barrier-free to entry.
● Market supply/demand dictates the price the firm on the left faces and
his behavior cannot affect market supply/demand since we are
assuming PC. Assume the market supply is made up of firms identical
to the firm on the left.
● Bad to assume this firm starts out as the only firm in the market b/c the
price-taking behavior is then shady. However, this is just illustrative
purposes.
● Note: if this is the only firm, then the profits this firm makes will be
identical to the market profits. Thus, the green areas will be identical
assuming fixed costs are zero. Note: at this high price, the firm will
make large profits.
● Areas are a bit different due to different scale and fixed costs.
● Q: What happens when outsiders see this firm making a profit?
Recognizing these high profits, more firms are going to enter the industry (since they are identical). This will shift the market supply curve
out, lowering the market price and reducing the profits either of the firms make. But there are still profits, so someone else will want to enter...
Goldstein 39
This logic will continue until there are no more profits to be made. In this case, this will occur at the minimum of the average total cost curve.
In other words, firms will produce as efficiently as possible (per-unit costs are as low as they can be), and none will make ECONOMIC
profits. In the long run, firms will produce at the bottom of the total cost curve. Econ profits will be zero.
● Zero economic profits could actually be very large accounting profits.
● So this really just means that profits here are exactly equal to what they would be in the next best industry.
● By #21 there are too many firms in the market, driving prices too low and there is now an incentive to leave the market. This will
shift the market demand curve in, again resulting in the same outcome.
Perfectly Competitive Long-Run Equilibrium: ​In a perfectly competitive environment with free entry/exit, firms will produce a level of
output such that the market price equals the minimum of the Average Total Cost curve. At this price, each firm will receive zero economic
profits.
● Economic profits: How much better off you are than if you instead invested in your next-best option
● Mature industries with free entry, when adjusted for risk, should all be equally profitable.
Rules about perfectly competitive markets
1. Firm should stop producing where price equals marginal cost
a. Don’t worry about fixed costs; fixed costs don’t change, so they shouldn’t be considered with choosing how much to
produce.
2. In the long run all firms make a zero economic profit.
Perfectly Competitive Markets - Shut Down
● Short-run:​ The time frame in which a firm is “stuck” with its fixed costs
● Long-Run​: The time frame it takes a firm to increase/decrease all factors of production
What do we do in the short-run if negative economic profits and cannot exit? Well we can “shut-down” which means to produce nothing.
Perfect Competition - Produce and earn negative profits - ​What does a firm do the SR when they are making a negative economic profit?
If we produce, still want to follow the P=MC rule.
● Total cost determined by ATC * Q
● Revenue determined by P*Q
● To find profits, subtract cost from revenue. In this case, profits are negative.
● Because it is the SR, exit is not possible, so they have 2 options: follow the profit maximizing
rule or shut-down and produce nothing.
● With a price of 11, profits are negative. We can see fixed costs are as follows.
● What will happen if we do not shut down?
○ In this case we produce according to the profit maximization rule and we do
generate some revenue, but total costs are greater. Thus, profits are negative by the
following amount.
● Remember that fixed costs are fixed (independent of production) so they must be paid.
Because there is no revenue, still have negative profit. Negative profit is the SR.
● IF price is below AVC the firm is getting a loss from every unit sold.
Goldstein 40
Moral of the story is that as long as the price is above the AVC curve, the firm should keep producing because they are able to recoup some of their fixed
costs. They are STILL losing money, but not as much as if they turned the lights off. If they do SHUT-DOWN, they still have to pay the fixed costs and they
don’t recoup any of the money. FOR SHUT DOWN FORGET ABOUT FIXED COSTS.
The Shut Down Decision
● If I shut down, I still have to pay all of my fixed costs, but my variable costs are zero.
● We need to know how much our fixed costs are. However, the typical graph does not influence AFC (or any other indication of
fixed costs)
● We know that ATC= AFC + AVC
● We know ATC and AVC
● ATC - AVC = AFC
● To convert an average cost to total cost, we just need to multiply by Q (find area of a rectangle)
Extra notes on shut down:
● When price is ​above​ the ATC, you are making profits even accounting for fixed costs
● When price is ​below​ the bottom of the ​AVC​ then the firm shuts down.
● For firms where price is above the AVC but still below the ATC, the firm is still making a profit not counting fixed costs. It’s making
positive profits when counting operating costs.
○ The firm is operating on a slight loss due to the fixed costs, but the cost of shutting down would be higher b/c the firm
would lose the fixed costs too.
● The supply curve starts when the MC is greater than the AVC.
What does a firm do in the SR when they are making negative economic profit?
● Because it is the SR, exit is not possible, so they have 2 options: follow the
profit maximizing rule or shut-down and produce nothing.
● An example of this would be the picture on the right. With a price of 11, profits
are negative.
● Now lets first ask ourselves what will happen if we do not shut down? In this
case we produce according to the profit maximization rule and we do
generate some revenue, but total costs are greater. Thus, profits are negative
by the following amount.
● In the next picture, we will look at the same picture but now I want to ask what
will happen if the firm shuts down because they are making a negative profit.
The key here is to remember that fixed costs are fixed (independent of
production) so they must be paid. Because there is no revenue, we still have
negative profit.
The moral of the story is that as long as the price is above the AVC curve, the firm should keep producing because they are able to recoup
some of their fixed costs. They are STILL losing money, but not as much as if they turned the lights off. If they do SHUT-DOWN, they still
have to pay the fixed costs and they don’t recoup any of the money.
Notice that the price ($11) is greater than the AVC.
● Because the fixed cost has to be paid no matter what, it is a sunk cost.
● So, we just need to compare price with AVC
● Produce where Price=MC, find AVC at that quantity
● Notice that the price ($11) is greater than the AVC ($9.75).
● If we produce, the average unit will cost $9.75 and sell for $11.
● So, (ignoring sunk costs) we make money on each unit.
● Treat fixed costs as sunk costs. This is in the short run, of course!
○ In the long run all costs are variable.
What do you do when the price is ​lower​ than the AVC?
● Here, the firm is losing money over and above the fixed costs, which means they
need to turn the lights off & send everyone home.
Goldstein 41
Perfectly Competitive Short-Run Shut Down Decision: ​In a perfectly competitive environment, during the time frame in which a firm’s
expenditures are sunk, the firm should Shut Down (not operate) if the market price is below the Average Variable Cost curve.
Perfectly Competitive ​Short-Run​ Shut Down Decision:
IF...
● Perfectly competitive environment
● During the time frame in which a firm’s expenditures are sunk,
THEN...
● The firm should Shut Down (not operate) if the market price is below the Average ​Variable​ Cost curve.
Perfectly Competitive ​Long-Run​ Exit Decision:​ In a perfectly competitive environment, the firm should Exit the market if the market price
is below the Average Total Cost curve. Note no expenditures are sunk in the Long-Run.
● Q: Which firms will be able to “wait out” the market if the market price is below the Average Total Cost?
○ It’s harder to sell assets so long-run is longer time frame.
■ Shut down is also more expensive
○ Larger firms have large cash streams which allow them to eat negative profits for a longer period of time. Large firms
have savings and can get loans to be able to afford their fixed costs while they hold off on producing. Until price
rebounds to a point that they can make a profit.
25 October 2017
Relaxing the assumptions around Perfect Competition. A market in which:
1.
2.
3.
4.
5.
There exists many small identical firms (HHI very low). → ​breaking the “identical” part.
There exists many individual buyers.
Firms sell “identical” products.
Every buyer and every seller has full information about the price and quality of goods.
Transaction costs are very low.
No barriers to entry/exit. → Now we are doing Not-Quite Perfect Competition.
6.
Barriers to Entry: Assume there are costs over and above the standard fixed costs required to operate in an industry. For instance, suppose
there are 1-time legal fees, regulatory obstacles, or a necessary initial name-recognition advertising campaign.
● The reason we assume these are not “fixed costs” is because PC assumes all firms have identical cost structures (including fixed
costs). Thus, we’ll assume these are “extra” costs.
○ Ex. if Pepsi introduces a new product, we trust if. If a new company introduces a new product, we might not trust it &
additional advertising is different. This additional cost would be a barrier to entry.
●
●
Slide #5, firms will continue entering the market, but eventually the small available profits won’t be enough to justify the cost of entering the
market.
By slide #7 & #8, firms already in this market will want higher barriers to entry, as this ensures long run profits. At this point, profits aren’t big
enough to enter for those with a barrier to entry.
Goldstein 42
In a “not-quite perfectly competitive” environment without free entry/exit, firms will produce a level of output such that the market price is
above the Average Total Cost (i.e. a markup will exist). At this price, each firm in the market will receive positive economic profits. The
larger the barrier to entry, the ​more profit ​firms in the industry will receive and the ​higher the m
● One way that a firm in an industry might use this to their advantage is through lobbying FOR regulations. Specifically, firms already
in an industry might lobby for entry regulations (taxes, certifications, licensing, etc.) to create a barrier to entry for potential
competitors. This leads to higher profits for existing firms.
● Barriers to entry will hurt consumers, markup occur without improvements
Question:
● Large companies tend to have an advantage over small companies. Large firms already have name recognition, lobbyist, lawyers,
etc.
Cost Advantage: Assume a small firm in a large industry finds a method to reduce their total cost structure below the other firms.
Identical firms in this market make no profit. But if we assume that one firm finds a cost-saving mechanism that others cannot then
their average total cost curve will change. Assuming one firm can lower their costs. Since the market price is fixed, they are going
to make profits until other firms figure out what they did to lower costs (at which point price undercutting will happen again and
prices will drop down again). The lower MC, makes production more efficient. The lower ATC firm may be able to push the less
efficient firms out of the market in the long run.
Not-Quite Perfectly Competitive Long-Run Equilibrium with Cost Advantages​: In a “perfectly competitive” environment with cost advantages,
some firms will produce a level of output such that the market price is above the Average Total Cost (i.e. a markup will exist). At this price,
these firms will receive positive economic profits. The larger the cost advantage, the more profits low-cost firms in the industry will receive.
● Question: How much would a firm be willing to spend to obtain a cost advantage?
● A: The extra profits they would earn. They’d be willing to spend up to extra profits.
Monopolistic Competition:
​A market in which:
●
1.
2.
3.
4.
5.
6.
There exists many small identical firms (HHI very low).
There exists many individual buyers.
Firms sell slightly different products.
Every buyer and every seller has full information about the price and quality of goods.
Transaction costs are very low.
No barriers to entry/exit.
Note: That all of the features are the same except #3, which is important b/c the product is slightly different giving the firm ​pricing power.
In monopolistic competition, the demand curve the individual firm faces is the
price line. The demand and the price line are the same!
● Obviously, they won’t sell for less since we assume they sell as many
as they want. They won’t sell for more because they would get any
sales. Thus, the price curve is nothing more than a perfectly elastic
demand curve. We know that with perfect elasticity, the optimal
pricing rule is to produce at the point where price = MC.
Goldstein 43
Firm doesn't have to take an external price. Instead, it’s facing individual
consumers with the following demand.
● No longer important for firm to produce P=MC
● Note: the “profit maximizing” output level when price was given is no
long profit maximizing. This firm could do much better by reducing
sales, but increasing prices.
● The firm has wiggle room in pricing due to product differentiation,
advertising, location etc.
● They won't want to go with the standard “go where supply =
demand”.
Compare Perfect Competition to Monopolistic Competition
●
●
In #23, revenue is straight line as there are fixed prices and perfectly elastic demand. Without perfectly elastic demand, we know
that as we move down the demand curve, we go from there having inelastic to elastic demand. Thus, raising quantity will lead to an
increase and then a decrease in revenues.
○ It’s perfect competition bc revenue is linear (a straight line)!
In #24, the firm has pricing power thus revenue has curvature, since you can only sell more by lowering the price and sell less by
raising the price. The firm has CONTROL over the price.
○ There's a sweet spot, specifical ​unit elasticity​.
○ As the curve rises, revenue is going up faster than cost, so the firm should produce more. If cost is dropping faster than
revenue, the firm should produce less.
○ As it is monopolistic, this is the only firm in the market producing that good. The optimality condition: ​MR = MC
○ Suppose the firm faces Q​D​ = ab − 1b P , where a,b > 0. Write: P=a - bQ​D​ → this is the ​inverse demand
Revenue:
● PC: Revenue = P * Q, P is set from Q​S​ = Q​D
● Monopoly: Revenue = P(Q) * Q = (a - bQ) * Q = aQ - bQ​2
**If the inverse demand is P = a - bQ, then MR = a - 2bQ**
Profit-Maximization Rule​: To maximize profits, produce the quantity level that ensures Marginal Revenue equals Marginal Cost.
E
● Mathematically equivalent to P = ( 1+E
)M C
Once again, MR=MC maximizes profits.
So profit maximizing condition still holds, but now, price does not equal marginal revenue (there is no market price here).
○ Why does price not equal MR? Because in order to sell more, price must drop (before this was not true).
%∆Q
E
P = ( 1+E
)M C ; E = %∆P
●
●
Perfectly Elastic: E = -∞
P = −∞−∞+ 1 M C → P = MC
Unit Inelastic: E = -1
P = −1−1+ 1 M C → P = ∞
Typical example: E = -3
P = −3−3+ 1 M C → P = 1.5 * MC
Firm will ​not​ price on the inelastic part of the demand curve, will never have E > -1
Goldstein 44
*If demand is linear, MR is linear with twice the slope of the demand.*
● To draw, use half of the x intercept.
● The profit maximizing output level is the point where MR = MC
● To choose the price, choose the higher price consumers are willing to
pay for that Q (will find this on the demand curve)
To determine all this you must first find the quantity level by MR = MC, then
figure out the price with the demand curve.
● This sucks for consumers and has a social cost. No market clearing
condition. Firms know what the optimal quantity is.
To determine the best P and Q in a non-PC environment (when demand is not a horizontal line):
1.
2.
3.
4.
Through graphical, analytical, data, or numerical methods, determine the ​marginal revenue​ schedule.
Through graphical, analytical, data, or numerical methods, determine the ​marginal cost ​schedule.
Find the ​quantity​ level that ​equates​ the marginal revenue and the marginal cost schedules.
Using the demand curve, determine the ​price​ that would cause that quantity level to be sold.
Monopolistic Competition Long Run Market Behavior
#12, the market is in a situation where there is a firm in the market that has market power and is making profits. B/c the firm is making profits,
other firms will create similar products and enter the market.
● Some of these firms will take the OG firm’s customers, shifting its demand in (remember, this is not the market demand curve but
demand for the ONE FIRM'S product). For any given price, people demand fewer. In addition, with increased substitutes, the
demand curve will become more elastic, meaning if I raise the price, the rate at which people stop purchasing is HIGHER.
● Once this happens, there will be a new demand that gives us a new MR, leading to a new profit maximizing output level that is
lower with lower profits (but still positive). However this continues, until Price = LRAC, so profits are zero.
○ This means there are no economic profits in the long run for a monopolistically competitive market.
● The firm will eventually produce at the bottom of its ATC curve. This is why no barriers to entry is great for consumers (leads to
lower prices!)
Monopolistically Competitive Long-Run Equilibrium:​ In a monopolistically competitive environment with free entry/exit, firms will produce
a level of output such that the price equals LRAC. At this price, each firm will receive zero economic profits.
● The “price exceeding ATC” because it makes for a nice comparison with PC market outcomes.
● Expect higher prices and lower quantities, relative to PC
● Advertising promotes competition, bc it makes consumers more informed.
27 October 2017
~MONOPOLY~
Analysis of monopoly is identical to monopolistic competition. The only difference is that no firms enter the market. Short term, it’s the same.
● Firms still face a downward sloping demand. MR is still half the demand curve (use half of the x intercept).
● Just like monopolistic competition, can find Q through the demand curve such that MR = MC
● The big difference between monopolistically competitive markets and a monopoly is that in the LR no firms can enter. This means
that there is nothing driving consumers to have more elastic demand.
○ Thus the SR and LR picture are the same and a monopoly can earn profits in the LR.
Monopolistic Long-Run Equilibrium: ​In a monopolistic environment, the monopoly firm will produce a level of output such that the market
price exceeds the minimum of the Average Total Cost curve. At this price, the firm will receive positive economic profits.
Goldstein 45
Monopoly Power
● Limited Resources​ as a Source of Monopoly Power: If a limited resource of a good exists, the firm that owns that resource will
have a monopoly.
● Legal Barriers​ as a Source of Monopoly Power: The government can grant a firm monopoly power. Any competition will be
deemed illegal.
● Natural Monopoly​ (Economies of Scale): If there are two firms in a market with extremely high fixed costs, the ATC is very steep
and it would be more beneficial for there to be just one firm to produce to good. ​(ON EXAM II)
○ Ex. Power, water, cable…Up-front costs are so high that it would be crazy to have multiple firms competing for business.
○ Once one firm pays cost, other firms are at huge disadvantage and don’t even try. Government often regulates these.
○ Note: that natural monopolies are based on cost structure and demand.
■ If the demand gets high enough (huge population growth so demand for power grows by a bunch), it might be
the situation where 1 firm cannot make a profit since costs are so high.
○ If economics of scale exist in a given market, then 1 firm might be able to produce the good more cheaply than multiple
firms. In such a case, a “natural monopoly” is a reasonable outcome.
■ Typically, natural monopolies are heavily regulated.
○ The ability for economies of scale to lead to a natural monopoly is based on economies of scale AND demand
conditions.
● Economies of Scope:​ If economics of scope exist between markets, then 1 firm producing multiple goods might be able to produce
the good more cheaply than multiple firms each producing 1 good. In such an environment, a large multi-product monopoly is a
reasonable outcome.
○ If you can charge a lower price than your competitors, you can drive them out of the market. One way to do this is
through economies of scope. Note that this isn’t very common, but it’s possible.
○ Large companies with large cash flow are at a big advantage and capable of doing this. Think P&G. They have enough
capital to make multiple goods.
Practice problem:
● Q​D​ = 200 - 1/2P; Monopolist: MC = 20; Inverse demand: P = 400 - 2Q (bc price is on the y-axis & Q is on the x-axis)
● Remember: optimality condition: MR = MC, if P = a - bQ then ​MR = a - 2bQ
○ MR = 400 - 4Q
○ 400 - 4Q = 20 → 66.6 = Q*
○ P = 400 - 2 (66.6)
○ P* = 266.6
-- END OF EXAM II --
Goldstein 46
30 October 2017 - Advanced Pricing Strategies
Constant MC Markup Rule: ​If your Marginal Costs are roughly constant in a relevant range, the profit maximizing price is:
● If given single price, but have pricing power (& the MC is constant) the optimal price is:
● This is simple, but analytically is​ not the best pricing strategy.
●
●
●
Money is still left on the table! (see orange triangle)
There is a gap between price and MC.
When we price in this manner, note the consumer still ends up with a surplus.
We’d like to take that surplus as firms and turn it into profit.
First Degree Price Discrimination: ​Charging different customers different prices for the same good. Charging each customer the maximum
price they would be willing to pay.
● This is the best case scenario. The firm can actually pin down what is ​each​ individual's
willingness to pay.
○ This means each consumer pays a different price!
● This effectively pulls out all surplus as profit.
● If we could price discriminate at every fraction of quantity, we could theoretically get all
the surplus as profits.
● Note that the old profit maximizing level and price are still optimal if only one price can be charged. Note how much bigger this
profit is.
● So this begs the question, why don’t all firms do this with their products? Most every retailer has some degree of market power.
Why don’t we see more examples of first-degree price discrimination?
○ Seller must know the individual’s demand curve. This is hard. Consumers lie.
○ Consumers hate this. We put up with it with cars and homes because they are large rare purchases. What if we had to
haggle for our groceries? Another firm could potentially earn higher profits by setting a fixed cost and offering consumers
a more pleasant experience.
First Degree Pricing Rule: If you can charge each individual different prices ​and​ you can ​determine​ each consumer’s ​willingness​ ​to pay​, you
can achieve maximal profits.
Second Degree Price Discrimination​: Offering a schedule of declining prices for different ranges of quantities.
● Charge a lot for the first unit, much less for the second unit. A pricing rule that depends on how many units the consumer is willing
to buy.
● Second degree price discrimination involves setting a menu that every customer can select from.
● Customers will then self-select on how much they want to buy.
● For the individuals that will purchase more, you are getting a higher level of surplus for the
first units.
● Note that this one is more realistic and there are a couple of ways that it can be done:
○ iPad story (Charge a premium to people who want to get the latest and greatest
tech)
○ Buy one pair of shoes get one half off
○ Parking garage (in big cities often times first hour is the most expensive).
Second Degree Pricing Rule: If you can estimate the market demand curve, you can implement a staggered price schedule that can increase
your profits over a single-price. *So it’s not as good as FDPD, but it's easier to implement.
Third Degree Price Discrimination:​ Charging different customer segments different prices.
● Customers have (1) an exogenous, verifiable, legal characteristic and
● (2) it’s not easy to resell the good between markets. i.e. age, students, faculty
● A change in prices in different markets. I.e. student prices vs. regular
Question: What is the arbitrage opportunity?
● Same good being sold for different prices in different markets
○ Can buy in cheaper market and sell in higher priced market → the firm needs to protect against this!
Goldstein 47
Third Degree Pricing Rule: If you can accurately (and legally) identify the market in which an individual resides and prevent cross-market
resale, offering different consumer groups different prices can increase your profits over a single-price.
● Ex. Coupons
Type
Different Prices for…
Example
First Degree
Everyone
Car dealer; college
Second Degree
Different quantities
Supersized meal
Third Degree
Different groups
Theater discounts
Two-Part Pricing
● If we lowered the price, we’d have more units sold & more consumer surplus generated. We could then charge an up-front fee
equal to the consumer surplus, the consumers would be willing to pay it, and we’d get all the profits.
● This way the entire CS becomes the PS. Figuring out what the highest fee you can
charge is hard tho…
● Firm w/ market power prices at perfect competition price then charges for the CS.
○ Charge a fixed fee to equal to the CS under perfect competition
○ Choose P, Q under PC conditions.
Two-Part Pricing Rule: Charging a fixed fee on top of a low per-unit cost can increase your profits
over a single, higher price.
Note: Figuring out the demand curve is (1) hard and (2) a bit of hocus pocus because most
people have different willingness to pays. Want to set prices so that make money on average
Block Pricing: Take it or Leave it.
● Firm is extracting all of the comunser surplus.
● Think large bundles of goods (like razors in packs of 5). Also can point out that multiple
pricing strategies can be used in the same place. Like Sam’s Club charging an up-front
cost AND selling items in bulk.
● Think about paper towels here:
○ Buy 1 for 2 bucks, or buy 6 for 8.00. This averages 1.30 per roll, so you are
overpaying… but it’s better than buying 6 individual rolls for 12 bucks.
○ Note that this is used a lot (tv packages, car-wash packages, cell phone
minutes)
Block Pricing Rule: Forcing your consumers into a take-it-or-leave-it offer can increase your profits over a single, higher price.
Practice Problem:
Linear demand: P=400-2Q
MC = 2Q
MR = 400 - 4Q
a). Price of a block
b). Fee in 2 part pricing
a). Q*pc : Q​S​ = Q​D​ → P = MC
400 - 2Q = 2Q → 4Q = 400 → Q*pc = 100
P*pc: P = 2 * Q*pc → P*pc = 200
Block: Want to find P such that:
P : Q*pc - C(Q*pc) (profit under block pricing) = CS + PS (target profit)
CS= ½ (400-200)100 = 10,000 → C(Q*pc) = area below MC curve ; c(Q*pc) = 10,000 ; PS = 10,000
P * 100 - 10000 = 20000
P *100= 30000 → P =300
1 November 2017
Commodity Bundling ​→ This is very similar to 2nd degree price discrimination.
● 2nd degree price discrimination is when firms offer bulk discounts. Bulk discounts give you a discount on the goods you value less.
● Commodity bundling also gives you a discount on the good you value less. Transfers value from one good to another.
Commodity Bundling Pricing Rule:​ If different consumers have ​different tastes​ concerning your product offering, offering commodity
bundle discounts can increase your profits over a single, higher price per good. (i.e. internet, phone, and tv bundles)
Goldstein 48
Peak Load Pricing​: Charging different prices at times during which demand is sufficiently different.
● Similar to 3rd degree price discrimination: Segment the market into two groups, then
charge the optimal price for each group.
● The firm charges different prices according to seasonal preferences
● MR = MC for the two different set of prices.
Peak-Load Pricing Rule:​ If demand for your good differs throughout time, offering
time-dependant pricing can increase your profits over a single, higher price.
Cross-Subsidies:
● By lowering the price of burgers & driving up consumption, the demand for
soft-drinks significantly increases.
● This is actually the business strategy of a lot of fast food places. Soft-drinks are just boxes of sugar-water and carbonated water.
Marginal cost is almost nothing. Thus, offer cheap food & hope people buy the drinks.
Cross-Subsidization Pricing Rule​: If two goods are complements, lowering the price of one ​might​ increase the demand for the other by
enough that overall profits are increased.
● Might depends, on how good the firm is at determining preferences.
3 November 2017
Game Theory → My decision affects your payoff; your decision affects my payoff.
● All you need for a game: plays, strategies, actions & payoff.
Normal-Form Game:
● A set of players
● Moves each player can make
● Payoffs the players might receive under each combination of moves
● Played simultaneously; the whole point is to figure out what likely outcome will happens given the incentives.
○ Maximizing profit is best guess my opponents choices.
6 November 2017
Dominant Strategies: ​A move that provides a higher payoff (than any other possible move) regardless of how a player’s opponents play.
● It is the best strategy is the best regardless of what other player is doing
● Start by asking the question “if the other player is playing ______, then what
should I do”?
○ If your SO goes to Franklin, your best response is to go to Franklin
○ If your SO stays home, your BR is to go to Franklin.
■ Thus you have a dominant strategy
● Dominant Strategy Solution Concept:
○ All players will play a dominant strategy, if it exists. Otherwise, All
players without a dominant strategy will assume their opponents are playing dominant strategies (if they exist) and will
respond accordingly.
● A reasonable way for a game with a dominant strategy to end is to have each player play their dominant strategy, and each other
player respond accordingly. In this case, that would make (Franklin, Franklin) a dominant strategy equilibrium.
Goldstein 49
IESDS
●
Dominant Strategy​: A move that provides a higher payoff (than any other possible move) regardless of how a player’s opponents
play.
○ Dominant strategy equilibrium is based on the concept of “I’ll play what’s always best for me, or I’ll respond to what’s
always best for my opponent”
○ Never yield highest pay off regardless of what the other player does. → Never best strategy
● Strictly Dominated Strategy​: A move that will never provide the highest payoff regardless of how a player’s opponents play.
● IESDS is based on the concept of “I won’t play what’s worse, and I’ll assume my opponent will do the same”. We first need to
introduce the concept of a strictly dominated strategy. Instead of “always best”, it’s “never best”.
Iterated Elimination of Strictly Dominated Strategies (IESDS) Solution Concept:
1. If I have a strictly dominated strategy, I will never play it.
2. Knowing this, my opponents will determine if they have a strategy that is never the best strategy regardless of the strategy I select
from those I have not eliminated. If so, they will never play it.
3. Knowing this, I will determine if I have a strategy that is never a best strategy regardless of the strategy my opponents select from
those they have not eliminated. If so, I will never play it…
4. And so on…
In other words, I only consider the strategies you might play, assuming you’ll never play a strictly dominated strategy. Then I only play those
strategies that are never best responses to these strategies. You, in turn, do the same, only considering those strategies I might play.
● Top​ for player 1 is dominated strategy, center is strictly better than top.
○ Can get rid of ​top​. So right becomes dominated for player 2.
○ (14,7) → single outcome.
● Can do this for starting with player 2. IESDS will always result in the same answer,
regardless of which player you start with. Good way to check answers on tests!
Critique of IESDS:
The other problem is that IESDS, while providing more concrete answers than dominant
strategy equilibrium, still doesn’t give us tight predictions. In many cases, there is no
predicted outcome, which means our game theoretic response to “how will this game resolve
itself” will be “anything’s possible”
Nash Equilibrium (NE) Solution Concept:
● If a set of strategies is such that no player has an incentive to unilaterally
deviate, it is a Nash Equilibrium.
● “Unilaterally” just means that each player is acting on their own
● In a NE, the following is true for both players:
● “Given your strategy, I’m doing the best I can.” & “No regrets”
In particular, a NE says “IF we happen to play a Nash equilibrium, we will have no reason to deviate”. It’s agnostic about how this happens,
and there are different explanations for why this might be the case. Nash is nice because it doesn’t require us to assume
the other players are thinking through a large number of steps in the game. Instead, it just says “if we happen to find
ourselves in a situation where neither of us want to deviate, we won’t”.
NASH → all players are playing their best response
In example 1, (8,2) is a NASH equilibrium & player 1 has a dominant strategy in B. →
Example 2: (14,7)
Goldstein 50
Prisoner’s Dilemma:​ The category of games in which players have a dominant strategy to “cheat”, preventing beneficial cooperation from
occurring.
● (-6,-6) is the Nash equilibria. The better choice would be to choose -1, -1, but b/c the players have an
incentive to deviate they play A,a
● The problem (and the key to the prisoner’s dilemma) is that each individual has an incentive to deviate
from the “better” outcome. In particular (in this case), each individual has a dominant strategy to play A.
Example: 2 criminals are arrested under suspicion of committing a crime. The DA has enough evidence to convict on a smaller charge, but
needs a confession to get the larger charge. They take the two prisoners, put them into different cells, and tell each the following:
● If you confess & your partner doesn’t, you’ll go scott free.
● If neither of you confess, we’ll charge you both with the lesser crime.
● If you both confess, you’ll get the larger crime punishment, but with some leniency.
● If you don’t confess and your partner confesses, we’re throwing the book at you
In the business world, an ex is price wars. Both players have an incentive to play an outcome that is not beneficial.
To Prevent the Prisoner’s Dilemma: Increase the punishment for deviating
● If we’re in a situation where we know we’re going to end up in a situation that’s worse for both players BECAUSE of the incentive
to deviate, then we need to “change the game” by increasing the punishment or reducing the benefit of cheating.
● Consider how the mob handles the “confess, confess” problem. In particular, they kill you and your family. That’s an increase in the
punishment.
**This is also why we see price guarantees, with a price guarantee, you’re reducing the benefit of the other firms from deviating (offering low
prices). In particular, it will cut into their profits, but they won’t actually get any new customers. Also, if you respond with a price war across all
products, you can make their incentive to deviate even weaker.
15 November 2017
Coordination Games: ​The category of games in which multiple Nash Equilibria exist, each corresponding to each
player doing what the other players are doing.
● (11,11) & (0,0) are Nash. If everyone is going to invest, you should invest. However, if other people aren’t
investing, you shouldn’t. This is exactly what happens in markets.
● Note that when this game is played in the lab we find that more times than not people choose not to invest. Psychologists and
behavior economists have found that many people have a large aversion to losing than desire to gain.
Other coordination games:
● Union strikes​: If everyone walks out, so will you. If no one walks out, neither will you.
● Cheating​: If everyone in the class is cheating, you might as well. If no one in the class is cheating, neither should you.
● Technology Standards:​ If everyone is using Blu-Ray, so should you. If everyone is using HD DVD, so should you.
● Social Norms​: If a company’s employees all value honesty and punish cutthroat actions, you should too. If a company’s
employees are all cutthroat, you should be too.
● Peer Pressure:​ If everyone else is binge drinking, so will you. If no one else is, you won’t either.
● Bank Runs:​ If everyone is taking their money out of a bank (so it will likely fail), I should too. If everyone is keeping their money in
a bank, I should too.
Managing Coordination Games: “Pushing” a coordination game into a “good” equilibrium can be achieved through costless expectations.
However, your employees must believe you are willing to pay if the equilibrium does not occur; your threat must be credible.
● Examples: Businesses must be sincere in their desire to punish dishonest employees
● From a managerial perspective, the key is that you have to have individuals believe you’ll live up to your promise in order to push a
coordination game into a “good” equilibrium. Sometimes, this means that no matter how good a manager is, a new one needs to
be brought in simply to make employees think a new sheriff is in town.
● Consider coaches in sports. When one “loses his team”, a new one is brought in and you tend to see immediately better results like
“smarter play”.
Hawk/Dove Games:​ Games with multiple Nash Equilibria, where corresponds to one player being “strong” and the other being “weak.” aka
game of chicken.
● Payoff is highest when you don’t do what everyone else is doing.
● The equilibria is that one person yields and the other doesn’t. You don’t want to go to full-out combat & if the
other person yields, you want to be the strong one.
● Show that we have two Nashes & that they occur where one is good for one individual and the other is good
for the other individual (no agreement). Commit to being the ​strong​ player to win.
Managing Hawk/Dove Games: ​To be the “Hawk” in a Hawk/Dove game, ​commit irreversibly to the strong position.​ If the game is
repeated and both players are stubborn, consider a compromise.
Goldstein 51
Mixed Strategy NE → ​No pure strategy nash equilibria exist. (Pure strategy is yield or don’t yield)
Question: What if you knew I was perfectly randomizing between rock, paper, and scissors. (playing each
1/3 of the time) What would your best response be?
● Play Rock always: win 1/3, lose 1/3, tie 1/3
● Play Paper always: win 1/3, lose 1/3, tie 1/3
● Play each 1/3 of the time: win 1/3, lose 1/3, tie 1/3
Every strategy I choose gives the same results. So, every strategy is a best response.
Mixed Strategy Nash Equilibrium​: A Nash equilibrium in which one or both players are randomizing their strategy. Every pure strategy is
also, technically, a mixed strategy, where you play one strategy 100% of the time.
● This does not mean randomizing with equal weight on every option! It just means that I play each option with some probability.
● Note then that every pure nash is also mixed.
Managing Using Mixed Strategies:​ If your competitor can gain a competitive advantage by knowing your strategy, randomize to keep them
guessing.
Quick note about Strictly Dominated Strategies:
● Strictly Dominated definition: Strategy A is strictly dominated by Strategy B if the payoff for B is greater than the payoff for A for
every possible strategy of the opponent.
● Strictly Dominated => Never Best Response (NBR), but NBR ≠> Strictly Dominated.
● Using IESDS, eliminating NBR may eliminate mixed strategy Nash equilibria.
17 November 2017
Normal Form Games:​ Set of strategies is discrete (countable) and finite.
Continuous Form Games: ​Set of strategies is a continuum.
Duopoly:​ Two firms produce an identical good; Barriers to entry ensure they keep their market power.
● Market supply: Q = q​1​ + q​2​ (two firms!)
● P= a - bQ → P = a - b(q​1​ + q​2​)
● GOAL: Max P(Q) - q​1​ - C(q​1​) given q​2​ → this is maximizing profit!
Monopoly: Optimal quantity is the peak of the profit curve given consumers tastes
Duopoly: Optimal quantity is the peak of the profit curve given consumers tastes ​and​ q​2​.
● When we maximize profit give what the opponent is doing... remember P(q​1​ + q​2​)q​1​, aka firm 2 affects firm 1’s revenues through
price.
○ P = a - b(q​1​ + q​2​)
● q​1​*: Best response to q​2
● q​2​*: Best response to q​1​ → q​2​*: Best response (q​1​*) → here is a nash equilibria. (this is game theory!)
Isoproftis​:
● Firm 1’s profits: π​1
● Firm 1 and firm 2 face inverse demand P= a - bQ. Since Q=q​1​ + q​2​, firm 1’s profits are given by
○ Π​1​ = [a - b(q​1​ + q​2​)] + q​1​ - c(q​1​)
○ Π​1​ = aq​1​ - bq​1​,q​2​ - bq;​2​ - c(q​1​)
● FC or VC doesn’t matter for C bc Q* doesn’t change! Just P*.
If q​2​ increases quantity. Profit for q1 is falling →
● *Profits decrease as curve shifts up!!
● If curve shifts down π1 increases!
● The closer you get to the x-axis, π increases.
π​1​* is where π is tangent to q 2​​ →
Isoprofit lines, which are just like Isoquants, but with profits.
● In particular, they are the Firm 1 & Firm 2 combinations that give Firm 1 the same level
of profits. With a few assumptions we’ll ignore (but are reasonable), the isoprofit lines
will look something like “hills”.
It’s important to recognize that isoprofit lines represent higher profits for Firm 1 the lower the are.
The reason is that a lower isoprofit line indicates that Firm 2 is producing less. Thus, Firm 1 has
more flexibility & is guaranteed to be better (it’s like having a small competitor in a market).
Goldstein 52
Again, we can map out the BEST RESPONSE function. It tells us that GIVEN a Firm 2 quantity level (in this case, 23), then the BEST RESPONSE for Firm
1 can be read off the graph. In this case, 8.
● We can do the exact same exercise for Firm 2. Note if we flipped the paper then turned it,
we would have Firm 2 on the X axis, Firm 1 on the Y axis, and the isoprofit lines would look
identical.
● Note in this case isoprofit lines represent larger profits as we move to the left.
Ultimately, the only point where neither Firm will deviate is the point where the BEST RESPONSE
functions intersect. This is where both firms are choosing optimally conditional on what the other firm is
producing.
● Note if we have more than 2 players, graphical techniques would be very difficult, which is
where we need the math. In this case, it’s just finding a solution to a set of equations.
● Verify this is a NE. In particular, what’s the best thing Firm 2 can do if Firm 1 plays 14? What’s the best thing Firm 1 can do if Firm 2 plays 16?
To find a Nash Equilibrium in a continuous game:
1. Through graphical, analytical (calculus), data, or numerical
methods, determine Player 1’s Best Response function as a
function of the other players’ actions.
2. Repeat the process for every Player in the game.
3. Find the points that lie on the intersections of all Best
Response functions. These are the Nash equilibria.
MISSING 27 NOVEMBER 2017
29 November 2017
Continuous Games: ​Need some new techniques (because a game matrix will no longer work) and these are much more in line with the
techniques game theorists actually use (with graphs instead of math).
Cournot Game: ​Firms choose quantity simultaneously. Each firm chooses ​quantity​ & price adjusts to market clearing price.
● Firms simultaneously select the quantity to produce.
● Once all firms select a quantity, the market price is dictated by the market demand curve (specifically, the price will ensure all the
units will sell).
● These are the types of games we’ve been looking at. In particular, firms compete in QUANTITIES. Assumptions that make this
reasonable are:
○ Firms cannot quickly produce a larger number of units
○ It’s fairly expensive to produce a larger number of units
○ Once a product is produced, it’s irreversible.
Question: How will the Nash equilibrium change if Player 1 develops a technology that lowers its marginal cost? Q1 increase, Q2 decreases.
Goldstein 53
A neat remnant of the Cournot model (we won’t get into the details) is that if there
are N identical firms competing in this way, the optimal price for each firm will be.
○ Note when N=1, this is the exact monopoly condition we’ve found.
○ Note when N=∞, this is P=MC, the perfect competition condition.
● Thus, Cournot oligopoly bridges the gap between everything we’ve done (all of it
has been some form of Cournot).
One thing to note in Cournot games is that the NE isn’t the best possible outcome for each
player.
● Much like the prisoner’s dilemma, both firms could do better if they agreed to
reduce production (driving up prices).
● In particular, they could act like one monopoly firm, then split the profits. This is what OPEC does.
Collusion in a Cournot Game:​ If firms competing in quantity (Cournot) can agree to limit their production, thereby increasing the market
price, they can achieve higher profits. The firms are effectively acting “as a monopoly”, splitting the monopoly profits.
● Much like the prisoner’s dilemma, there’s always an incentive to deviate. If your competitor is under producing, you’ll want to flood
the market.
● Both firms are at a higher profit level
○ Each firm has an incentive to expand production to increase market share
○ Agreement by firms to produce at a lower produce and quantity → firms at as a monopoly
Question: Why don’t all firms participate in collusion?
Collusion Failure in a Cournot Game:​ The temptation to deviate from a collusive agreement can make sustaining collusion difficult.
● This is just like prisoners dilemma. Two people cannot agree to lie because there is always an incentive to deviate.
● Note that collusion is against the law in the US. Justice Department.
● Still happens though. Not always purposeful and often the government doesn’t get involved.
● Example: sometimes a large firm that possesses a majority of the market will set high prices then all small firms don’t undercut
because they do not have the capacity to produce with the increase in sales.
Stackelberg game: Firms choose quantity sequentially.
1. Firm 1 (the leader) selects a quantity to produce.
2. Firm 2 (the follower), seeing Firm 1’s decision, selects its quantity to produce.
3. Once all firms select a quantity, the market price is dictated by the market demand curve (specifically, the price will ensure all the
units will sell).
Question: Who has the advantage in the Stackelberg Game?
● The Leader has an advantage in the Stackelberg game, since they can “control” the behavior of the Follower. We call this
advantage the “First-Mover Advantage”.
○ This ability to “control” what the 2nd-mover does gives the first-mover an advantage. At worst, the NE can be achieved
because if Firm 1 selects his NE strategy, by definition of NE we know Firm 2 will also select his NE strategy. However,
now there are additional possibilities.
○ It is very important to realize it’s not always better to go first. For instance, if there is a large cost to innovate a market,
then a second mover might be able to piggyback on the efforts of the first-mover. This is beyond the scope of this course,
but they should consider the implications.
●
Assume you’re Firm 1. Because you can calculate Firm 2’s BR function as easily as Firm 2 can, you know exactly what Firm 2 will do given any output level
you select. Thus, when selecting your output level, you’re effectively selecting Firm 2’s output level as well. By doing this, you can produce an output level
that will maximize your profits, recognizing that Firm 2 will be responding per their BR function. Can someone find a strictly better point?
● If Firm 1 increases output, it will end up with higher profits (lower isoprofit) at the expense of Firm 2 (more right isoprofit). Firm 1 essentially
crowds the market and Firm 2 can only take what’s left over.
By choosing first F1 can force F2 to produce at a certain level. As F2 has no incentive to choose a different production level. (both firms have same MC)
P(Q) = a - SQ → a - b (q​1​ + q​2​*(q1))
Goldstein 54
Bertrand Games: ​Firms choose price. Can be a concentrated industry, but firms compete on price i.e. produce at P = MC. Price wars!!
● Each firm chooses a price
● Consumers choose who to buy from
● Quantity produced and sold by each firm adjusts to meet demand
Firms simultaneously select the price of an identical good & The firm with the lowest price sells their good to the entire market. All other firms
do not sell their good.
● Different class of continuous games. Firms compete in PRICES. Assumptions that make this reasonable are:
○ Firms can quickly produce a large number of units
○ It’s fairly inexpensive to produce a larger number of units
○ Firms can sell as few or as many units as they want at any given price
○ Products are effectively the same, and consumers shop only based on price
○ Each firm is able to supply the entire market
● Examples include software, telephone service, cable service, etc.
Use the exact same technique, but forming the BR functions will require some consideration. First, draw the 45 degree line. As before, ask
the question “If Firm 1 offers to sell the good at $10, what is Firm 2’s best response?”
● Firm 2 should sell the price at $9.99, undercutting Firm 1 just enough to get all the customers. If Firm 1 prices at $15, Firm 2 should
sell at $14.99 etc.
● Note this is why we have the 45 degree line, because immediately under that will be a price slightly lower that Firm 1’s price.
● Recalling MC=0, what is Firm 2’s BR if Firm 1 offers the good at $0? Should also offer it at $0 (or above), since any less would
have them losing money.
● As before, if we did this at every price level, could map out Firm 2’s BR.
● We can then do the same for Firm 1’s BR given every possible Firm 2 price level. Now a slightly lower price will be a point
immediately to the left of the 45 degree line. The question then becomes “where is the NE?”
Question: In a Bertrand Game, what is the Nash equilibrium price level if each firm has Marginal Costs of $0?
● Answer: Both firms charge $0 and receive no profits.
● Even in the case of only 2 firms, could actually have an outcome identical to the PC result. That’s one of the reasons why PC is
viewed as a baseline case. It also why the FTC needs to be so thorough. Just bc an industry is highly concentrated doesn’t
necessarily mean it will be anticompetitive.
Question: How can a firm avoid the zero-profit Bertrand outcome?
● Differentiate its product
● Collude
● Impose switching costs: Costs associated with switching suppliers. Can be very important in maintaining customers.
○ If you can make it costly for customers to switch companies, that allows you to retain profits as well.
○ Example: What if a rival firm charges $2 less than you, but it costs customers $3 to switch firms?
■ Effort needed to tell friends/families/employers your new phone number.
■ Time required to convert all Microsoft documents to Apple formats.
■ Penalty for early DirecTV contract cancellation.
■ Training necessary to learn a new software.
1 December 2017
Cournot Duopoly
Q = q​1​ + q​2
Suppose firm 1 maximizes profits given q2.
● P(Q) = a - bQ → P(Q) = a - b(q​1​ + q​2​)
● P(Q) = a - bq​2​ - bq​1
○ a - bq​2​ → intercept
Compute best response to q​2​ → need to maximize profit given q​2
Goldstein 55
● Assume MC = C. MR = MC ⇒ a = bq​2​ - 2bq​1​ = C
1
● Q​1​ = 2b
[a − bq 2 − c]
1
c
Best response: q *1 * (q 2 ) = 2b
(a − bq 2 ) − 2b
1
● 2b
(a − bq 2 ) ⇒ external factors (consumer tastes, opponents choice etc.)
c
● 2b ⇒ internal factors + input prices
Example: a = 200 ; b = ½ ; c = 40
Best response q​2​:
● Q​1​ = 200 - ½ q​2​ - ½ q​2​ - 40
● Q​1​ = 160 - ½ q​2
Best response q​1​:
● Q​1​ = 160 = ½ q​2
● Q​2​ = 160 - ½ q​2
q​1​* = 320/3 ; q​2​* = 320/2
Stackelberg Duopoly:
A = 200 ; b = ½ ; q​2​ = 160 - ½ q​1
● Q = q​1​ + q​2​, firm 1 moves first.
● Q = q​1​ = 100 - ½ q​1​ → 160 + ½ q​1
Inverse demand: P(Q) = a - bQ
● P(q​1​) = a - b (160 + ½ q​1​)
● P(q​1​) = 120 - ¼ q​1​ → MC = MR
● MR = 120 - ½ q​1​ , MC = 40
● 120 - ½ q​1​ = 40 ⇒​ q​1​* = 160
○ Once F1 choses its q​1​*, q​2​* for F2 is already chosen!
○ Choose an isoprofit that still touches q​2​*
● Q​2​ = 160 - ½ (160) = ​q​2​* = 80
What is the point of this course? To maximize profit!
Step 1 (this determines MC): Choose K, L to produce q units of output at the lowest possible cost.
Step 2 (Optimality condition is always MR = MC): Choose Q to maximize profits.
● PC, monopoly, duopoly, cournot, Stackelberg & Bertrand.
Goldstein 56