1 Profit Maximization
14.01 Principles of Microeconomics, Fall 2007
Chia-Hui Chen
October 19, 2007
1
1. Chap 8: Profit Maximization
2. Chap 8: Short Run Supply
3. Chap 8: Producer Surplus
4. Chap 8: Long Run Competitive Equilibrium
For perfect competition in a product market, we make some assumptions:
•
Price taking: either individual firms or consumers cannot affect the price.
•
Product homogeneity: product of all firms are perfect substitutes.
•
Free entry and exit: no special cost to enter or exit the market.
Firms choose the level of output to maximize their profits. Profit equals total revenue minus total cost, namely
π ( q ) = R ( q )
−
C ( q ) = P ( q ) q
−
C ( q ) .
To maximize the profit, the following condition must hold: dπ ( dq q )
= dR dq
− dC dq
= M R ( q )
−
M C ( q ) = 0 , and thus
M R ( q ) = M C ( q ) .
Since
R ( q ) = P q, we have
M R ( q ) = dR ( q ) dq
= P, and
M R = AR,
Cite as: Chia-Hui Chen, course materials for 14.01
Principles of Microeconomics, Fall 2007.
MIT
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2 Short Run Supply 2 thus
M C ( q ) = P = M R = AR is the maximization condition. Note that the condition is not sufficient. In
Figure 1), if the price is
maximizes the profit.
P
2
, q
2 and q
3 both satisfy the condition, but only q
3
10
9
6
5
8
7
P
1
4
3
2
P
2
1
0
0 1 q
2
2
MC
3 4 5 q q
3
6 7
Figure 1: Profit Maximization.
8 q
1
9 10
Assume the firm has production costs shown in Figure 2, let us discuss its
behavior under different prices.
•
When P = P
1
, the firm is making profits, so it will continue to produce;
•
When P = P
2
, the firm has losses but still continues to produce, because if it shuts down, the profit is is R
−
T V C
−
F C >
−
F C .
−
F C , and if continuing to produce, the profit
•
Since R < SV C , when P = P
3
, the profit if the firm shuts down, more than the profit if it continues, R
−
T V C
−
F C
−
F C , is
, so it will shut down.
When the firm produces, it chooses the output level where M C ( q ) = P . There­ fore, the firm’s supply curve when it produces is just the part of M C above
T V C . When P < AV C , the firm shuts down and q = 0.
We can derive market supply from an individual firm’s supply (see Figure 3).
Define elasticity of market supply as follows:
E
S
= dQ/Q dP/P
.
Figure 4 and 5 stand for inelastic and elastic supply curves, respectively.
Cite as: Chia-Hui Chen, course materials for 14.01
Principles of Microeconomics, Fall 2007.
MIT
OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology.
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2 Short Run Supply
10
9
8
7
P
1
6
5
4
3
P
2
2
P
3
1
0
0 1 2 3
AVC
MC
4 5 q
6 7
ATC
8 9 10
Figure 2: Individual Firm’s Supply in Short Run.
10
9
8
7
6
5
4
3
2
1
0
0 1
MC
1
MC
2
Market Supply
2 3 4 5 q
6 7 8 9 10
Figure 3: Market Supply in Short Run.
Cite as: Chia-Hui Chen, course materials for 14.01
Principles of Microeconomics, Fall 2007.
MIT
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3

2 Short Run Supply
10
9
8
7
6
5
4
3
2
1
0
0 1
MC
2 3 4 5 q
6 7 8 9 10
Figure 4: Inelastic Market Supply Curve.
10
9
8
7
6
5
4
3
2
1
0
0 1
MC
2 3 4 5 q
6 7 8 9 10
Figure 5: Elastic Market Supply Curve.
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Principles of Microeconomics, Fall 2007.
MIT
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4

2 Short Run Supply
7
6
5
4
3
10
9
8
2
1
0
0 1 2 3 4 5 q
6 7 8 9
Figure 6: Perfectly Inelastic Market Supply Curve.
10
5
7
6
5
4
3
10
9
8
2
1
0
0 1 2 3 4 5 q
6 7 8 9
Figure 7: Perfectly Elastic Market Supply Curve.
10
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Principles of Microeconomics, Fall 2007.
MIT
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3 Producer Surplus 6
Similarly, we have perfectly inelastic market supply (see Figure 6) and perfectly elastic market supply (see Figure 7).
Perfectly elastic market supply happens when
M C = const .
Producer Surplus is the difference between the firm’s revenue and the sum of the total variable cost of producing q
(see Figure 8):
P S = R
−
T V C = R
−
T V C
−
F C + F C = P rof it + F C.
Thus, producer surplus is the sum of profit and fixed cost.
2
1
4
3
0
0
6
5
8
7
1 2
MC
AVC
3 4 q
5 6 7 8
Figure 8: Producer Surplus.
Cite as: Chia-Hui Chen, course materials for 14.01
Principles of Microeconomics, Fall 2007.
MIT
OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology.
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YYYY].