The Firm and Profit Maximization

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The Firm and Profit Maximization Overheads
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Neoclassical firm -
A neoclassical firm is an organization that
controls the transformation of inputs (resources
it owns or purchases) into outputs (valued
products that it sells),
and earns the difference between what it
receives in revenue, and what it spends on inputs
3
We define the production function as
y represents output
f represents the relationship between outputs
and inputs
xj is the quantity used of the jth input
(x1, x2, x3, . . . xn) is the input bundle
n is the number of inputs used by the firm
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Returns (Profit)
The profit from a production plan is the revenue
obtained from the plan minus the cost of inputs
used to implement it
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Objectives of the firm
We typically assume that a firm exists in order
to make money
A firm that wants to make money is called a
for-profit firm, or a profit maximizing firm
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Given the profit max assumption
The firm maximizes the returns from
the technologies it controls taking into account
The demand for final consumption goods
Opportunities for buying and selling factors /
products
The actions of other firms in the market
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The profit max problem
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What is profit?
Profit is revenue minus costs or
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Explicit and implicit costs
Explicit costs
1. purchase of expendable inputs including labor
time
2. purchase of capital services (usually rent or
lease)
Implicit costs
1. value of produced expendables (feed for a
cattle producer)
2. value of services provided by owned
capital including financial capital and charges
such as implicit rent, depreciation,
compensation for operator labor, etc.
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Accounting profit
Accounting cost
depreciation on plant equipment
explicit costs
Accounting profit
total revenue - accounting cost
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Economic profit
Economic cost
all implicit costs
explicit costs
Economic profit
total revenue - economic cost
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Why do we use economic profit?
To reflect total costs and revenues for a decision
To account for all resources used in production
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Why do profits exist?
All factors of production receive a payment
Expendables receive their market price
Labor receives wages
Land receives rent
Capital receives interest
Firm owners receive profits
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What are profits?
Profits are the returns to
Risk
Innovation
production
delivery
new products
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The Profit Maximizing Output Level
Profit Revenue - Cost R - C
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Demand
The individual demand curve facing a firm tells
us, for different prices, the quantity of output
that customers will choose to purchase from the
firm
The demand curve facing the firm show us
the maximum price the firm can charge to sell any
given amount of output
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Example Inverse Demands
p 320 - 20y
p 1.85
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Total Revenue
Revenue is the total income that comes from
the sale of the output (goods and services) of a
given firm or production process
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Y Price FC VC C TR Profit 0.00 320 120 0.00
120.00 0 -120.00
1.00 300 120 64.00 184.00 300 116.00
2.00 280 120 130.00 250.00 560 310.00
3.00 260 120 204.00 324.00 780 456.00
4.00 240 120 292.00 412.00 960 548.00
5.00 220 120 400.00 520.00 1100 580.00
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Y Price FC VC C TR Profit 0.00 320 120 0.00
120.00 0 -120.00 1.00 300 120 64.00 184.00
300 116.00 2.00 280 120 130.00 250.00
560 310.00 3.00 260 120 204.00 324.00
780 456.00 4.00 240 120 292.00 412.00
960 548.00 5.00 220 120 400.00 520.00
1100 580.00 6.00 200 120 534.00 654.00
1200 546.00 7.00 180 120 700.00 820.00
1260 440.00 8.00 160 120 904.00 1024.00
1280 256.00 9.00 140 120 1152.00 1272.00
1260 -12.00 10.00 120 120 1450.00 1570.00
1200 -370.00 11.00 100 120 1804.00 1924.00
1100 -824.00 12.00 80 120 2220.00 2340.00
960 -1380.00 14.00 40 120 3262.00 3382.00
560 -2822.00 16.00 0 120 4624.00 4744.00
0 -4744.00
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Total cost
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Maximizing profit
Choose the level of output where the difference
between TR and TC is the greatest
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Y Price FC VC C TR Profit 0.00 320 120 0.00
120.00 0 -120.00
1.00 300 120 64.00 184.00 300 116.00
2.00 280 120 130.00 250.00 560 310.00
3.00 260 120 204.00 324.00 780 456.00
4.00 240 120 292.00 412.00 960 548.00
5.00 220 120 400.00 520.00 1100 580.00
6.00 200 120 534.00 654.00 1200 546.00
7.00 180 120 700.00 820.00 1260 440.00
8.00 160 120 904.00 1024.00 1280 256.00 9.00
140 120 1152.00 1272.00 1260 -12.00 10.00
120 120 1450.00 1570.00 1200 -370.00 11.00
100 120 1804.00 1924.00 1100 -824.00 12.00
80 120 2220.00 2340.00 960 -1380.00
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Y Price FC VC C TR Profit 0.00 320 120 0.00
120.00 0 -120.00 1.00 300 120 64.00 184.00
300 116.00 2.00 280 120 130.00 250.00
560 310.00 3.00 260 120 204.00 324.00
780 456.00 4.00 240 120 292.00 412.00
960 548.00 5.00 220 120 400.00 520.00
1100 580.00 6.00 200 120 534.00 654.00
1200 546.00 7.00 180 120 700.00 820.00
1260 440.00 8.00 160 120 904.00 1024.00
1280 256.00 9.00 140 120 1152.00 1272.00
1260 -12.00 10.00 120 120 1450.00 1570.00
1200 -370.00 11.00 100 120 1804.00 1924.00
1100 -824.00 12.00 80 120 2220.00 2340.00
960 -1380.00 14.00 40 120 3262.00 3382.00
560 -2822.00 16.00 0 120 4624.00 4744.00
0 -4744.00
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Marginal cost (MC)
Marginal cost is the increment, or addition, to
cost that results from producing one more unit of
output
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y Price FC VC C AFC AVC ATC MC TR MR Profit 0.00
320 120 0.00 120.00 0 -120.00 64.0
0 300.00 1.00 300 120 64.00 184.00 120.00
64.00 184.00 300 116.00 66.00
260.00 2.00 280 120 130.00 250.00 60.00
65.00 125.00 560 310.00 74.00
220.00 3.00 260 120 204.00 324.00 40.00
68.00 108.00 780 456.00 88.00
180.00 4.00 240 120 292.00 412.00 30.00
73.00 103.00 960 548.00 108.00
140.00 5.00 220 120 400.00 520.00 24.00
80.00 104.00 1100 580.00 134.00
100.00 6.00 200 120 534.00 654.00 20.00
89.00 109.00 1200 546.00 166.00
60.00 7.00 180 120 700.00 820.00 17.14
100.00 117.14 1260 440.00 204.00
20.00 8.00 160 120 904.00 1024.00 15.00
113.00 128.00 1280 256.00 248.00
-20.00 9.00 140 120 1152.00 1272.00 13.33
128.00 141.33 1260 -12.00 298.00
-60.00 10.00 120 120 1450.00 1570.00 12.00
145.00 157.00 1200 -370.00
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y Price FC VC C AFC AVC ATC MC 3 260 120 204.00
324.0 40.00 68.00 108.00 88.00 4
240 120 292.00 412.0 30.00 73.00
103.00 108.00 5 220 120 400.00 520.0
24.00 80.00 104.00
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Marginal Revenue (MR)
Marginal revenue is the increment, or
addition, to revenue that results from
producing one more unit of output
Marginal revenue is the change in total
revenue from producing one more unit of output
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y Price FC VC C AFC AVC ATC MC TR MR Profit 0
320 120 0.00 120.0 0 -120.0 64.00
300.0 1 300 120 64.00 184.0 120.00 64.00
184.00 300 116.0 66.00 260.0 2
280 120 130.00 250.0 60.00 65.00 125.00
560 310.0 74.00 220.0 3
260 120 204.0 324.0 40.0 68.0 108.0
780 456.0 88.00 180.0 4
240 120 292.0 412.0 30.0 73.0 103.0
960 548.0 108.00 140.0 5
220 120 400.00 520.0 24.00 80.00 104.00
1100 580.0 134.00 100.0 6
200 120 534.00 654.0 20.00 89.00 109.00
1200 546.0 166.00 60.0 7
180 120 700.00 820.0 17.14 100.00 117.14
1260 440.0 204.00 20.0 8
160 120 904.00 1024.0 15.00 113.00 128.00
1280 256.0
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y Price TR MR Profit 3.00 260 780 456.0 180.
0 4.00 240 960 548.0 140.0 5.00
220 1100 580.0 100.0 6.00 200 1200 546.0
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Another example
Increase output from 4 to 5 units
y Price TR MR Profit 3.00 260 780 456.0 180.0
4.00 240 960 548.0 140.0 5.00 220 1100 580.0
100.0 6.00 200 1200 546.0
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A note on marginal revenue and price
Marginal revenue is always less than price
WHY?
The firm must lower price in order to sell more
units
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1
2
3
4
5
Marginal Revenue p0
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p
MR A - B
B
q
The lower price applies to all units and so the
revenue per unit will be less than the price
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Profit Max Using MR and MC
An increase in output will always increase
profit if MR gt MC
An increase in output will always decrease
profit if MR lt MC
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The rule is then
Increase output whenever MR gt MC
Decrease output if MR lt MC
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Example
y Price C MC TR MR Profit 3.00
260 324.00 780 456.00 88.00 180.00
4.00 240 412.00 960 548.00 108.00
140.00 5.00 220 520.00 1100 580.00 134.
00 100.00 6.00 200 654.00 1200 546.00
Yes
Should we increase output from 3 to 4?
Yes
Should we increase output from 4 to 5?
No !
Should we increase output from 5 to 6?
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Profit Maximization Using Graphs
Profit is positive if TR gt TC
2000
1800

1600
1400
1200
1000
800
600
400
200
0
0
2
4
6
8
10
12
14
16
18
Output
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Profit Maximization Using MR and MC
Profit on a given unit is positive if MR gt MC
400

350
300
250
200
150
100
50
0
0
2
4
6
8
10
12
14
16
18
Output
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Two intersections of MC and MR
300

250
200
150
100
50
0
0
2
4
6
8
10
12
14
16
18
20
Output
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The optimal output level occurs where MC
intersects MR from below
300

250
200
150
100
50
0
0
2
4
6
8
10
12
14
16
18
20
Output
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Why average costs are irrelevant in the short-run
The short-run decision is whether to produce one
more unit or not
Only marginal cost and marginal revenue are
relevant for this decision
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Marginal Decision Making and Short-run Decisions
The marginal approach to profit states that a
firm should take any action that adds more to its
revenue than to its cost
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Examples where marginal decision making is
relevant
advertising
cost efficiency consultant
adding a salesperson
sprucing up sales area
adding a two-year warranty to product
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The shutdown rule
Do we keep producing if we are losing money?
It depends on what we mean by a loss
It depends on whether we are in the short-run or
in the long run
It depends on which costs are fixed, which are
variable, and which are sunk
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Case 1 - TC gt TR at all Q
TR gt TVC where MR MC
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Total Cost Revenue Curves
200
TC gt TR at all Q
175
Cost
150
125
100
75
50
25
0
0
1
2
3
4
5
6
7
8
9
10
Output - y
Marginal Cost Revenue Curves
40
35
TR gt TVC where MR MC
Cost
30
25
20
15
10
5
0
0
1
2
3
4
5
6
7
8
9
10
Output - y
48
In the short-run fixed costs must be
paid independent of the level of output
At 6 units of output, total revenue more
than covers total variable costs,
leaving a residual to help cover fixed costs
So the firm should produce 6 units in the short
run
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The shutdown rule
In the short-run, the firm should continue to
produce if total revenue exceeds total variable
costs
otherwise, it should shut down
50
Case 2 - TC gt TR at all Q
TR lt TVC where MR MC
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Total Revenue and Cost Curves
90
80
Cost
70
60
50
40
30
20
10
TR lt TC at all Q
0
0
1
2
3
4
5
6
7
Output - y
Marginal Revenue and Cost Curves
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28
Cost
TR lt TVC where MR MC
24
20
16
12
8
4
0
0
1
2
3
4
5
6
7
Output - y
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The shutdown rule
In the short-run, the firm should continue to
produce if total revenue exceeds total variable
costs
otherwise, it should shut down
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Shutdown in the long-run
In the long-run the firm should exit the industry
if it has any size loss
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Shutdown and fixed costs that are not sunk
In the short-run, if some of the fixed costs are
not sunk, the firm may be better off to not
operate when TR gt TVC, if it can recover most of
its sunk costs that are fixed costs, by shutting
down
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Suppose at 6 units of output, TFC 50, TVC 60
and TC 110
Suppose at 6 units of output, that total revenue
is equal to 95.
By operating the firm can make 35 over variable
costs
(95 - 60)
This will help cover the the fixed costs of 50
The firms net loss is then just 15.00
(35 - 50 or 95 - 110)
But suppose that only 10 of the fixed costs are
sunk, so that by shutting down the firm can
recover 40.00 of fixed cost
The firm's net loss by shutting down is only
10.00
The firm is better off by shutting down
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Asset Fixed Variable Total Sales
Disposal Total Profit/ Cost Cost Cost
Revenue Revenue Revenue Loss Operate 50 60 110 95
0 95 -15 Shut-down 50 0 50 0 40 40 -10
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The End