4
The Firm’s Production and
Selling Decisions
Outline
● Production and Input Choice, with One
Variable Input
● Multiple Input Decisions: The Choice of
Optimal Input Combinations
● Cost and Its Dependence on Output
● Economies of Scale
Copyright© 2006 South-Western/Thomson Learning. All rights reserved.
Outline
● Price and Quantity: One Decision, Not Two
● Total Profit: Keep your Eye on the Goal
● Marginal Analysis and Maximization of
Total Profit
● Generalization: The Logic of Marginal
Analysis and Maximization
Copyright© 2006 South-Western/Thomson Learning. All rights reserved.
Production and Input Choice,
with 1 Variable Input
● Arkansas chicken farmer named Florence, who
owns a small poultry business.
♦ She knows Q corn she feeds her chickens will impact
Q meat.
♦ She could also buy more T, growth hormones, and L
to ↑Q meat. But for now, let’s focus on the
relationship between poultry meat and corn.
Copyright© 2006 South-Western/Thomson Learning. All rights reserved.
TABLE 1. TPP, MPP, and APP for Flo’s
Chicken Farm
Corn in bags
TPP in lbs.
MPP in lbs.
APP in lbs.
0
0.0
-----
-----
1
14.0
14.0
14.0
2
36.0
22.0
18.0
3
66.0
30.0
22.0
4
100.0
34.0
25.0
5
130.0
30.0
26.0
6
156.0
26.0
26.0
7
175.0
19.0
25.0
8
184.0
9.0
23.0
9
185.4
1.4
20.6
10
180.0
-5.4
18.0
11
165.0
-15.0
15.0
12
144.0
-21.0
12.0
FIGURE 1. TPP with Different
Quantities of Corn
Total Output of Poultry Meat
Total Physical Product (TPP) in lbs.
200
180
160
140
120
100
80
60
40
20
0
8
7
9
10
11
6
12
5
4
3
2
1
0
0
2
4
6
8
10
Quantity of Corn (bags per week)
12
14
Production and Input Choice,
with 1 Variable Input
● Total Physical Product (TPP) = amount of
output that can be produced as 1 input changes,
with all other inputs held constant.
♦ Table 1 shows TPP or how much chicken Flo can
produce with different Q corn, holding all other inputs
fixed.
♦ If Q corn = 0 → Q meat = 0. Each add. bag of corn
yields more poultry. 4 bags → 100 lbs. After 9 bags,
↑corn → ↓output –chickens are so overfed they
become ill.
Copyright© 2006 South-Western/Thomson Learning. All rights reserved.
Production and Input Choice,
with 1 Variable Input
● Average Physical Product (APP) = TPP/(Q of
input) = measures output per unit of input.
♦ E.g., 4 bags corn → 100 lbs meat, so APP = 25.
● Marginal Physical Product (MPP) = additional
output resulting from a 1 unit increase in the
input, holding all other inputs constant.
♦ E.g., ↑corn from 4 to 5 bags, the 5th bag yields an
add. 30 lbs of meat.
Copyright© 2006 South-Western/Thomson Learning. All rights reserved.
FIGURE 2. Flo’s MPP Curve
MPP
Rising
Falling
Negative
34
14
0
0
-21
MPP
0
4
9
12
Bags of corn
Graph of MPP
● Marginal returns to an input typically rise and
then fall.
● Area of ↑MPP (1 to 4 bags) → each add. bag of corn
adds more to TPP than previous bag. ↑TPP rapidly.
● Area of ↓MPP (between 4 and 9 bags) → each add. bag
of corn adds less to TPP than previous bag. ↑TPP at a
dim. rate.
● Area of (-)MPP (beyond 9 bags) → each add. bag of
corn reduces TPP by more than previous bag. ↓TPP.
Copyright© 2006 South-Western/Thomson Learning. All rights reserved.
The “Law” of Diminishing Marginal
Returns
● ↑ Q of any one input, holding Q of all other
inputs constant, leads to lower marginal returns to
the expanding input.
♦ E.g., Flo feeds chickens more and more, without
giving them extra water, cleaning up after them more,
or buying add. chickens. Eventually overfed and
become sick.
● Law of dim. marginal returns should hold for most
activities.
Can you think of one?
Copyright© 2006 South-Western/Thomson Learning. All rights reserved.
Optimal Purchase Rule for a
Single Input
● How does a firm decide on the quantity of an input?
♦ Assume P corn = $10/40-lb bag and P chicken = $0.75/lb.
Consider purchasing just 1 bag of corn. Does this max profits?
● 1 bag produces 14 lbs of chicken.
TR: $0.75 x 14 = $10.50
TC: $10 x 1 = $10.00
Profit:
= $0.50
● Shouldn't stop at 1 bag because 2 bags yield more profit.
TR: $0.75 x 36 = $27.00
TC: $10 x 2 = $20.00
Profit:
= $7.00
Copyright© 2006 South-Western/Thomson Learning. All rights reserved.
Optimal Purchase Rule for a
Single Input
● Easier way to proceed. Until 9 bags, each add. bag of
corn ↑Q chicken. So each bag (1-9) raises TR, but also
costs $10. To max profit, Flo should compare revenue
that each bag generates against the cost of each bag.
● Marginal Revenue Product (MRP) = MPP x Price of
output.
● MRP = add. revenue generated from ↑input by 1 unit.
Copyright© 2006 South-Western/Thomson Learning. All rights reserved.
Table 2. Flo’s TPP, MPP, and MRP Schedules
Bags of
Corn
TPP
MPP
TR
(P*TPP)
MRP
(P*MPP)
P corn
Profit
0
0.0
-----
$0.00
-----
$10.00
$0.00
1
14.0
14.0
10.50
$10.50
10.00
0.50
2
36.0
22.0
27.00
16.50
10.00
7.00
3
66.0
30.0
49.50
22.50
10.00
19.50
4
100.0
34.0
75.00
25.50
10.00
35.00
5
130.0
30.0
97.50
22.50
10.00
47.50
6
156.0
26.0
117.00
19.50
10.00
57.00
7
175.0
19.0
131.25
14.25
10.00
61.25
8
184.0
9.0
138.00
6.75
10.00
58.00
9
185.4
1.4
139.05
1.05
10.00
49.05
10
180.0
-5.4
135.00
-4.05
10.00
35.00
11
165.0
-15.0
123.75
-11.25
10.00
13.75
12
144.0
-21.0
108.00
-15.75
10.00
-12.00
Optimal Purchase Rule for a
Single Input
● Rule: If MRP > P of an input → use more of the input.
If MRP < P of an input → use less of the input.
● Purchase an input where MRP = P of the input.
♦ E.g., Flo should purchase 7 bags of corn.
Can you explain why she should not buy the 8th bag?
● Note: ↓MPP (bag 4 to 9) → ↓MRP. At 7 bags, Flo is
producing where dim. MPP sets in. Flo should stop ↑corn
purchases when MRP falls to = P of corn.
Copyright© 2006 South-Western/Thomson Learning. All rights reserved.
Multiple Input Decisions
● Firms seek the method of production that is least
costly.
♦ Consider the choice between L and K in prod.
Compared with Mexico, in U.S., L is expensive and K
is cheap. So (K/L) U.S. > (K/L) Mexico
● One input can often be substituted for another in
production.
♦ E.g., shoes produced in Mexico are manufactured
using more L and less K than shoes in U.S.
Copyright© 2006 South-Western/Thomson Learning. All rights reserved.
Multiple Input Decisions
● A firm can produce same amount of a good with
less of one input (say L) as long as it’s willing to
use more of another input (like K).
● Actual combos of inputs (such as K and L)
depend on relative P of inputs. Firms strive to
produce a good using the least expensive method.
Copyright© 2006 South-Western/Thomson Learning. All rights reserved.
Marginal Rule for Optimal Input
Proportions
● E.g., Flo can feed chickens soymeal or cornmeal
–they are substitutes in production.
♦ Not perfect substitutes. Soymeal has more protein but
fewer carbohydrates than corn.
♦ Best to feed some combo of 2 meals. ↓Q poultry if Flo
relies too much on 1 input. There are dim. returns to
substitution among the inputs.
Copyright© 2006 South-Western/Thomson Learning. All rights reserved.
Marginal Rule for Optimal Input
Proportions
Price corn = $10 per 40 lb. bag
MPP bag corn = 30 lbs. meat
Price soy = $20 per 40 lb. bag
MPP bag soy = 50 lbs. meat
How much of each input should Flo purchase?
● Feed ↑corn and ↓soy. Soy costs twice as much, but yields only
67% more meat.
● If Flo ↓soy by 1 bag → saves $20. But ↓output by 50 lbs. So buy
1.67 (or 50/30) bags of corn to make up for ↓output, cost = $16.70.
She saves $3.30 while holding Q output fixed.
Copyright© 2006 South-Western/Thomson Learning. All rights reserved.
Marginal Rule for Optimal Input
Proportions
● Above: MPPsoy/Psoy < MPPcorn/Pcorn
i.e., 50/$20 < 30/$10
♦ Soy yields 2.5 lbs. meat per $1 while corn yields 3 lbs. per $1.
More output from corn rather than soy at the margin.
● MPP of an input/P of an input = add. output from
spending $1 on the input.
● By substituting input with lower output per $1 for input
with higher output per $1; firm can reduce costs while
holding Q output fixed.
Copyright© 2006 South-Western/Thomson Learning. All rights reserved.
Marginal Rule for Optimal Input
Proportions
● Rule: if MPPb/Pb > MPPa/Pa → spend less on
input a and more on input b.
♦ Optimally, MPPa/Pa = MPPb/Pb
● Above: MPPcorn/Pcorn > MPPsoy/Psoy
♦ These ratios will equalize at an optimum because of
dim. MPP. As Flo uses ↑corn and ↓soy → ↓MPP corn
and ↑MPP soy, until two ratios are equal.
Copyright© 2006 South-Western/Thomson Learning. All rights reserved.
Marginal Rule for Optimal Input
Proportions
● Changes in Input Prices and Input Proportions:
● Optimally, MPPcorn/Pcorn = MPPsoy/Psoy
● What if ↑P corn?
♦ Then ↑MPP corn to match ↑P corn. How? Flo will use ↓corn
and ↑soy until ratios are equal.
● As ↑P input → firms switch to cheaper inputs.
Copyright© 2006 South-Western/Thomson Learning. All rights reserved.
Cost Curves and Input
Quantities
● 3 different cost curves –Total Cost (TC), Average
Cost (AC), and Marginal Cost (MC).
● Flo’s costs depend on Q of inputs and on P of
those inputs.
● To calculate costs, assume:
♦ P corn is beyond Flo's control.
♦ Q of all other inputs (except corn) are fixed.
♦ P corn = $10 per 40 lb. bag
Copyright© 2006 South-Western/Thomson Learning. All rights reserved.
TABLE 3. TPP, TC, and AC for Flo’s
Chicken Farm
TPP of chicken
(lbs. per week)
Corn input
(bags per week)
Total Cost
(per week)
Average Cost
(TC/Q output)
0
0
0
0.00
14
1
10
0.71
36
2
20
0.56
66
3
30
0.45
100
4
40
0.40
130
5
50
0.38
156
6
60
0.38
175
7
70
0.40
184
8
80
0.43
185.4
9
90
0.49
Cost Curves and Input
Quantities
● TPP → Q output firm can produce given Q inputs. Q
inputs and P inputs → firm can determine TC of
producing any Q output.
● TC = P inputs x Q inputs
● AC = TC/Q output
♦ E.g., TC 100 lbs = $40 → AC = $40/100 = $0.40
● MC = TC when output increases by 1 unit
♦ E.g., if TC 100 lbs. = $40.00
TC 99 lbs. = $39.70
MC 100th lb. = $0.30
♦ Note: table above doesn’t show this because ↑output > 1.
Copyright© 2006 South-Western/Thomson Learning. All rights reserved.
FIGURE 3. Flo’s Total Cost Curve
Total Cost ($ / week)
Total Cost
100
90
80
70
60
50
40
30
20
10
0
0
50
100
150
Quantity of Chicken (lbs / week)
200
FIGURE 4. Flo’s Average Cost and
Marginal Cost Curves
AC and MC
MC
AC
0
Q of chicken
AC and MC
typically ↓ and
then ↑ as the
↑output level.
Fixed and Variable Costs
● TC, AC, and MC can be divided into 2 parts –fixed costs
and variable costs.
● Fixed cost is the cost of an input whose Q does not ↑
when ↑output. Input that the firm requires to produce
any output. Any other cost is a variable cost.
♦ E.g., takes at least 1 taxi to run a cab co. and its cost is the
same whether 1 or 60 people ride in it. But gas use rises as
more people ride. Taxi is a fixed cost and gas is a variable cost.
What are the fixed and variable costs where you work?
Copyright© 2006 South-Western/Thomson Learning. All rights reserved.
Fixed and Variable Costs
● TC = TVC + TFC
● AC = AVC + AFC
♦ AC = TC/Q output
♦ AVC = TVC/Q output
♦ AFC = TFC/Q output
Copyright© 2006 South-Western/Thomson Learning. All rights reserved.
Table 4. Flo’s Total and Average
Fixed Costs
Output
(20 lb pack)
TFC
$ / week
AFC
$ / week
0
5.0
---
1
5.0
5.00
2
5.0
2.50
3
5.0
1.70
4
5.0
1.25
5
5.0
1.00
6
5.0
0.80
7
5.0
0.70
8
5.0
0.60
Flo pays rent of $5 per
week for her chicken coop.
FIGURE 5. Graph of Flo’s Total Fixed Cost
TFC
$5
0
TFC
6
8
10
Q (20 lb. packages)
FIGURE 6. Graph of Flo’s Average Fixed Cost
AFC
If Flo produces 1 package,
TFC is carried by 1. But if she
produces 4, TFC gets divided
between 4 packages. So
$5.00
↓AFC as ↑output.
$1.25
$0.70
AFC
0
1
4
7
Q (20 lb. packages)
FIGURE 7. Flo’s Total Variable Cost Curve
TVC
TVC
$125
$57
0
6
10
Q
TVC has same
shape as TC
because ↑variable
costs as ↑output.
Fixed and Variable Costs
● Marginal Cost = Marginal Variable Cost (MVC)
Why doesn't MC have a fixed component (i.e.,
MC = MVC + MFC)?
Copyright© 2006 South-Western/Thomson Learning. All rights reserved.
Shape of the Average Cost Curve
● AC is generally U shaped –it initially declines
and eventually rises with the level of output.
● AC declines for 2 reasons:
1. Changing input proportions: at first, Flo feeds
chickens more corn while holding all other inputs
constant. Output rises rapidly when ↑MPP corn,
which tends to ↓AC.
2. ↓Average fixed costs as ↑output.
Copyright© 2006 South-Western/Thomson Learning. All rights reserved.
Shape of the Average Cost Curve
● AC eventually rises for 2 reasons:
1. Dim MPP: ↑output more slowly as ↓MPP corn,
which tends to ↑AC.
2. Bureaucratic mess: as firms grow in size they lose
personal touch of management and become
increasingly bureaucratic, which drives up costs.
● Point where ↑AC varies by industry. AC in auto
industry begins ↑ after more units of output than
farming. Huge K investment → AFC↓ dramatically.
Copyright© 2006 South-Western/Thomson Learning. All rights reserved.
Short-run versus Long-run
Costs
● Cost of changing a firm's output level depends on period
of time under consideration. Many input choices are
precommitted by past decisions.
● Sunk cost = a cost to which a firm is precommitted for
some limited period of time.
♦ E.g., a 2-year-old machine with a 9-year economic life is a
variable cost after 7 years because the machine would have to
be replaced anyway.
Copyright© 2006 South-Western/Thomson Learning. All rights reserved.
Short-run versus Long-run
Costs
● SR = period of time when some of the firm's cost
commitments end.
● LR = period of time when all of the firm's cost
commitments end.
● There are no fixed costs in LR –all costs are variable.
♦ E.g., if # of workers can be altered daily, and # of machines
altered yearly, and size of plant every 10 years. Then 10 years
is the LR.
Copyright© 2006 South-Western/Thomson Learning. All rights reserved.
Short-run versus Long-run
Costs
● Size of a firm may be fixed in SR because it has
purchased or leased a particular plant, but firm
can alter size of its plant in LR.
♦ E.g., Flo has already built a chicken coop, which
restricts her ability to ∆ output level in SR. In LR, Flo
can build a new larger coop to produce more.
Copyright© 2006 South-Western/Thomson Learning. All rights reserved.
Average Cost Curve in the Short
and Long Run
● LR AC curve differs from SR AC curve because
all inputs are variable in LR.
♦ E.g., In SR, Flo can only chose how many chickens to
squeeze into coop. In LR, she can chose among
different coop sizes.
Copyright© 2006 South-Western/Thomson Learning. All rights reserved.
FIGURE 8. Flo’s SR and LR Average Cost
Curves
AC (per package)
B
$16
L
S
$12
U
V
T
G
$9
40
100
Q (20 lb. packages)
Average Cost Curve in the
Short and Long Run
● If Flo expects to sell 40 → she buys a small coop with
AC of SL. If Q = 40 → AC = $12 (pt U).
● She is surprised by strong D and can sell 100 with AC =
$12 (pt V).
● Now she needs a bigger coop with AC of BG with its
lower AC of $9 for Q = 100.
● In SR, Flo is stuck with AC of SL. In LR, she can
replace coop and the relevant AC is STG.
● LR AC curve shows the lowest possible SR AC for each
output level.
Copyright© 2006 South-Western/Thomson Learning. All rights reserved.
Economies of Scale
● Returns to scale indicates how the output level
changes when all the firm's inputs are doubled.
1. Increasing Returns to Scale (IRTS): Q output more than
doubles.
● IRTS gives a cost advantage to larger firms. Found in
industries like telecommunications, electricity, automobiles,
and aircraft.
2. Constant Returns to Scale (CRTS): Q output doubles.
3. Decreasing Returns to Scale (DRTS): Q output less than
doubles.
● Gives a cost advantage to smaller firms. Most U.S. industries
have DRTS.
Copyright© 2006 South-Western/Thomson Learning. All rights reserved.
Economies of Scale
● Returns to scale impacts the shape of the AC
curve.
● AC = TC/Q output = (P input x Q input)/Q output
♦ E.g., if Q inputs doubles and Q output doubles, then
AC is constant.
Copyright© 2006 South-Western/Thomson Learning. All rights reserved.
AC
Quantity of Output
(a)
Constant returns
to scale
AC
Quantity of Output
(b)
Long-Run Average Cost
Increasing returns
to scale
Long-Run Average Cost
Long-Run Average Cost
FIGURE 9. 3 Possible Shapes for the AC Curve
Decreasing returns
to scale
Quantity of Output
(c)
AC
Economies of Scale
● Law of dim. marginal returns and IRTS may seem
contradictory, but they are unrelated.
● Dim. marginal returns refers to increasing a single
input. Returns to scale refers to a doubling of all
inputs.
● A firm with dim. returns to a single input could
have IRTS, CRTS, or DRTS.
Copyright© 2006 South-Western/Thomson Learning. All rights reserved.
Price and Quantity: One
Decision, Not Two
● Critical decision -when Apple decides how many ipods
to produce and P it will charge.
● P affects how consumers respond and Q affects K and L
costs.
● When firms chose P and Q to max profits → they can
pick only one –P or Q.
♦ Chose P → customers decide Q
♦ Chose Q → market determines P at which this Q can be sold
Copyright© 2006 South-Western/Thomson Learning. All rights reserved.
FIGURE 10. Demand Curve for Flo’s
Poultry Meat
Price per package
Flo faces a local D curve.
A
$19
If she picks P = $19 → Qd = 1.
If she picks Q = 9 → P = $11 to
find required # of customers.
B
$11
D
1
9
Quantity of Chicken (20 lb-packages per week)
Price and Quantity: One
Decision, Not Two
● Each pt on D curve corresponds to a (P,Q) pair. A firm
can pick 1 pair, but it can never pick P from 1 pt on D
and a different Q from another pt on D.
● Economists assume that firms pick (P,Q) pair that
maximizes profits.
Copyright© 2006 South-Western/Thomson Learning. All rights reserved.
Total Profit: Keep Your Eye on
the Goal
● Total profit (or economic profit) = TR – TC (including
opportunity cost)
♦ Opportunity costs include any K or L supplied by the firm’s
owners.
● Economic profit = Accounting profit – opportunity cost.
♦ E.g., if a talented attorney, gives up her salary of $120,000 to
start her own law firm and earns $150,000 after paying for all
operating costs → accounting profit = $150,000 but economic
profit = $30,000
♦ E.g., if you start a business and earn 6% on money you
invested but could have earned 4% in T-Bills → economic
profit = 2%.
Copyright© 2006 South-Western/Thomson Learning. All rights reserved.
Total Profit: Keep Your Eye
on the Goal
● Total, Average, and Marginal Revenue:
♦ Total Revenue (TR) = P  Q
■ Calculated from D curve
♦ Average Revenue (AR) = TR/Q = (P  Q)/Q = P
■ AR curve = D curve
♦ Marginal Revenue (MR) =  TR when ↑output by 1
unit.
■ Slope of TR curve
Copyright© 2006 South-Western/Thomson Learning. All rights reserved.
TABLE 5. Schedule of Flo’s Total,
Average, and Marginal Revenue
Chicken
(20 lb-pack)
Price (or AR)
($ per package)
Total Revenue
(P x Q)
Marginal
Revenue
0
-----
0
-----
1
$19
$19
$19
2
18
36
17
3
17
51
15
4
16
64
13
5
15
75
11
6
14
84
9
7
13
91
7
8
12
96
5
9
11
99
3
10
10
100
1
FIGURE 11. Flo’s Total Revenue Curve
Total Revenue
Total Revenue
$100
$80
$60
$40
$20
$0
0
2
4
6
8
Quantity of Chicken (20-lb packages)
10
Total Profit: Keep Your Eye
on the Goal
● Total, Average, and Marginal Cost:
♦ TC = P inputs x Q inputs
♦ AC = TC/Q output
■Per unit costs
♦ MC = ∆TC when ↑output by 1 unit.
■Slope of TC curve
Copyright© 2006 South-Western/Thomson Learning. All rights reserved.
TABLE 6. Flo’s Total, Average, and
Marginal Cost
Chicken
(20 lb-pack)
Total Cost
Marginal Cost
Average Cost
0
$0.0
-----
-----
1
17.0
$17.0
$17.0
2
26.0
9.0
13.0
3
33.0
7.0
11.0
4
40.0
7.0
10.0
5
48.0
8.0
9.6
6
57.0
9.0
9.5
7
67.2
10.2
9.6
8
80.0
12.8
10.0
9
99.0
19.0
11.0
10
125.0
26.0
12.5
FIGURE 12(a). Flo’s Total Cost Curve
Total Cost
$120.00
Total Cost
$100.00
$80.00
$60.00
$40.00
$20.00
$0.00
0
2
4
6
8
Quantity of Chicken (20-lb packages per week)
10
FIGURE 12(b). Flo’s Average and
Marginal Cost Curves
Average and marginal cost
Average and Marginal Cost
30
25
20
MC
15
AC
10
5
0
1
2
3
4
5
6
7
8
9
10
Quantity of Chicken (20-lb packages per week)
11
Total Profit: Keep Your Eye
on the Goal
● Maximization of Total Profits:
♦ Profits typically increase with output, then fall.
♦ Some intermediate level of output generates
max profit.
Copyright© 2006 South-Western/Thomson Learning. All rights reserved.
TABLE 7. TR, TC, and Profit for Flo
Chicken
(20 lb-pack)
Total Revenue
(P x Q)
Total Cost
Total Profit
0
$0
$0.0
$0.0
1
19
17.0
2.0
2
36
26.0
10.0
3
51
33.0
18.0
4
64
40.0
24.0
5
75
48.0
27.0
6
84
57.0
27.0
7
91
67.2
23.8
8
96
80.0
16.0
9
99
99.0
0.0
10
100
125.0
-25.0
Total Profit: Keep Your Eye on
the Goal
● In our example:
♦ Total profit (Π) is max at 5 or 6 packages,
where farm earns its highest profits of $27 per
week.
♦ Any other Q level → ↓Π
■E.g., if Q = 3 → Π = $18 or if Q = 8 → Π = $16
Copyright© 2006 South-Western/Thomson Learning. All rights reserved.
Marginal Analysis and
Maximization of Total Profit
● Use marginal analysis to find Q that max profits.
● Marginal profit = ∆ total profit when ↑Q by 1 unit.
♦ Slope of total profit curve
● Rule: if marginal Π > 0 → ↑Q
if marginal Π < 0 → ↓Q
♦ Profit-max Q is reached when marginal Π = 0.
● Graphically, only reach top of total profit “hill” when
marginal profit (its slope) = 0.
Copyright© 2006 South-Western/Thomson Learning. All rights reserved.
FIGURE 13(a). Profit Maximization
Total Profit per week ($)
Total Profit “hill”
27
20
0
–20
1
2
3
4
5
6
7
8
9
10
–30
Output, Packages per week
Total profit has a “hill” shape. At Q = 0, Π = 0. At larger Q levels, firm
floods the market, and ↓Π. Only at intermediate Q levels is Π > 0.
Marginal Analysis and
Maximization of Total Profit
● Like marginal Π, MR and MC can guide us to Q output
where total profit is maximized.
● MR = slope of TR and MC = slope of TC
● Total profit is max when TR and TC are farthest apart.
♦ Occurs when their slopes are equal, so they are not growing
closer together (Π↓) or growing further apart (Π↑).
● Rule: if MR > MC → Q
if MR < MC → Q
♦ Profit maximizing Q is where MR = MC.
Copyright© 2006 South-Western/Thomson Learning. All rights reserved.
FIGURE 13(b). Profit Maximization
Total Revenue, Total Cost per week ($)
Total Π = vertical distance between TR and TC curves
TC
125
99
84
TR
57
Profit
20
$27
0
1
2
3
4
5
6
7
Output, packages per week
8
9
10
TABLE 8. Maximization of Flo’s Total
Profits
Output
(packages)
Marginal
Revenue
Marginal
Cost
Marginal
Profit
Total
Profit
0
-----
-----
-----
$0.0
1
$19
$17.0
$2.0
2.0
2
17
9.0
8.0
10.0
3
15
7.0
8.0
18.0
4
13
7.0
6.0
24.0
5
11
8.0
3.0
27.0
6
9
9.0
0.0
27.0
7
7
10.2
-3.2
23.8
8
5
12.8
-7.8
16.0
9
3
19.0
-16.0
0.0
10
1
26.0
-25.0
-25.0
Marginal Analysis and
Maximization of Total Profit
● Finding the Optimal P from Optimal Q:
● Optimal Q is where MR = MC (and marg. Π = 0).
♦ E.g., at Q = 6; MR = MC = $9.
● Producer picks Q then demand curve  P
buyers will pay to purchase that level of output.
♦ E.g., at Q = 6 → P = $14 –only P at which this Q is
purchased by consumers.
Copyright© 2006 South-Western/Thomson Learning. All rights reserved.
Logic of Marginal Analysis &
Maximization
● Decision makers constantly faced with problem of
choosing the magnitude of some variable.
♦ E.g., how many cars to produce; how many workers to hire, or
how many pints of ice cream to buy.
● Generally, larger the number selected → higher the total
benefit. However, costs ↑ as number chosen ↑.
● Optimally, decision makers chose Q of some variable
where difference between total benefit and total cost is
greatest.
Copyright© 2006 South-Western/Thomson Learning. All rights reserved.
Logic of Marginal Analysis &
Maximization
● Decide about Q of some variable, then max net benefit =
total benefit – total cost by choosing the Q where
marginal benefit = marginal cost.
● Rule is true regardless of who the decision maker is.
Decision
maker
Marginal
benefit
Marginal
cost
Choice
variable
Objective
consumer
MU
P good
Q of good
Max CS
firm
MRP input
P input
Q of 1 input
Max Π
firm
MR output
MC output
Q of output
Max Π