12-706 and 19-702
MICROECON REVIEW
Scott Matthews
12-706/19-702
1
Discussion - “Willingness to Pay”
2

Survey of students of WTP for beer
 How
much for 1 beer? 2 beers? Etc.
Price
$4
Quantity
Price
1
$4
2
$3.75
3
$3
4
$2
$3.75
$2
0
1
2
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3
4
Quantity
WTP results
3

Economists also refer to this as demand

Does similar form hold for all goods?
 What
types of goods different?
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(Individual) Demand Curves
4


Downward Sloping is a result of diminishing marginal utility
of each additional unit (also consider as WTP)
Presumes that at some point you have enough to make you
happy and do not value additional units
Price
A
Actually an inverse
demand curve (where
P = f(Q) instead).
B
P*
0
1
2
3
4
Q*
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Quantity
Market Demand
5
Price
A
A
B
B
P*
P*
0
1
2
3
4
Q
0
1
2
3
4
5 Q
z If above graphs show two (groups of) consumer
demands, what is social demand curve?
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Market Demand
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P*
0
1
2
3
4
5
6
7
8
9 Q
z Found by calculating the horizontal sum of
individual demand curves
z Market demand then measures ‘total
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consumer surplus of entire
market’
Social WTP (i.e. market demand)
7
Price
A
B
P*
0
1
2
3
4
Q*
Quantity
z ‘Aggregate’ demand function: how all potential
consumers in society value the good or service
(i.e., someone willing to pay every price…)
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z This is the kind of demand
curves we care about
Demand Curve Shifts
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
Difference between change in demand and change
in quantity demanded
 Change
in just the price, all else equal, will just move
along same demand curve
 If other things change, eg preferences for eating meat,
demand curve shifts.
 Could
also happen from income changes, etc.
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First: Elasticities of Demand
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

Measurement of how “responsive” demand is to
some change in price or income.
Slope of demand curve = p/ q.
Elasticity of demand, e, is defined to be the percent
change in quantity divided by the percent change in
price.
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Elasticities of Demand
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Elastic demand:  > 1.
If P inc. by 1%, demand dec. by more than 1%.
Unit elasticity: v = 1. If P inc. by 1%, demand dec. by 1%.
Inelastic demand:  < 1
If P inc. by 1%, demand dec. by less than 1%.
P
P
Q
Q
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Elasticities of Demand
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P
Necessities, demand is
Completely insensitive
To price
Perfectly
Inelastic
P
Q
Perfectly
Elastic
A change in price causes
Demand to go to zero
(no easy examples)
Q
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Elasticity - Some Formulas
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Point elasticity = dq/dp * (p/q)
For linear curve, q = (p-a)/b so dq/dp = 1/b
Linear curve point elasticity =(1/b) *p/q =
(1/b)*(a+bq)/q =(a/bq) + 1
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Sorta Timely Analysis
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



How sensitive is gasoline demand to price
changes (in the short term)?
Historically, we have seen relatively little change
in demand.
New AAA report: higher gasoline prices have
caused a 3 percent reduction in demand from a
year ago.
Basic analysis - What was ∆p? q? ?
What does that tell us about gasoline?
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Maglev System Example
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


Maglev - downtown, tech center, UPMC, CMU
20,000 riders per day forecast by developers.
Let’s assume:
 price
elasticity -0.3;
 linear demand;
 20,000 riders @ average fare of $ 1.20.

Estimate Total Willingness to Pay.
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Example calculations
15

We have one point on demand curve:
 1.2

= a + b*(20,000)
We know an elasticity value:
 elasticity
for linear curve = 1 + a/bq
 -0.3 = 1 + a/b*(20,000)

Solve with two simultaneous equations:
a
= 5.2
 b = -0.0002 or 2.0 x 10^-4
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Types of Costs
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





Private - paid by consumers
Social - paid by all of society
Opportunity - cost of foregone options
Fixed - do not vary with usage
Variable - vary directly with usage
External - imposed by users on non-users
e.g. traffic, pollution, health risks
 Private decisions usually ignore external

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Making Cost Functions
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

Fundamental to analysis and policies
Three stages:






Technical knowledge of alternatives
Apply input (material) prices to options
Relate price to cost
Obvious need for engineering/economics
Main point: consider cost of all parties
Included: labor, materials, hazard costs
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Functional Forms
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

TC(q) = F+ VC(q)
Use TC eq’n to generate unit costs
 Average
Total: ATC = TC/q
 Variable: AVC = VC/q
 Marginal: MC = [TC]/ q
 but
F/
q = 0, so MC =
[VC]/ q
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Short Run vs. Long Run Cost
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
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Short term / short run - some costs fixed
In long run, “all costs variable”
Difference is in ‘degree of control of plans’
Generally say we are ‘constrained in the short run
but not the long run’
So TC(q) < = SRTC(q)
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From Cost to Supply
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
Given knowledge of costs to produce, producers
decide how much to produce
 As
price to sell at increases, incentivizes producers to
make more
 Also leads to more opportunities/methods to pay costs
required to produce
 (e.g., we would mine a lot more coal if the price were
$100 rather than $20 a ton)
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BCA Part 2: Cost
Welfare Economics Continued
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The upper segment of a firm’s marginal cost curve corresponds
to the firm’s SR supply curve. Again, diminishing returns occur.
Price
At any given price, determines
how much output to produce to
maximize profit
Supply=MC
AVC
Quantity
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Supply/Marginal Cost Notes
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Demand: WTP for each additional unit
Supply: cost incurred for each additional unit
Price
At any given price, determines
how much output to produce to
maximize profit
Supply=MC
P*
Q1
Q* Q2
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Quantity
Supply/Marginal Cost Notes
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Recall: We always want to be considering opportunity costs
(total asset value to society) and not accounting costs
Price
Area under MC is TVC - why?
Supply=MC
P*
Q1
Q* Q2
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Quantity
Firm Production Functions
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MC
What do marginal,
Average cost curves
Tell us?
Variable cost shows
Non-fixed components
Of producing the good
P
AVC
Marginal costs show us
Cost of producing one
Additional good
Q
Where would firm produce?
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Unifying Cost and Supply
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
Economists learn “Supply and Demand”

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

Equilibrium (meeting point): where S = D
In our case, substitute ‘cost’ for supply
Why cost? Need to trade-off Demand
Using MC is a standard method

Recall this is a perfectly competitive world!
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Example
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Demand Function: p = 4 - 3q
Supply function: p = 1.5q
Assume equilibrium, what is p,q?
In eq: S=D; 4-3q=1.5q ; 4.5q=4 ; q=8/9
P=1.5q=(3/2)*(8/9)= 4/3
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