1. Chapter 19 PROFIT MAXIMIZATION

2. Chapter 19 PROFIT MAXIMIZATION
The firm chooses a production plan so as to maximize its profits.
Competitive market
A market where the individual producer take the prices as given.

3. 19.1 Profits Profits: revenues minus cost. n outputs: (y1 …yn)
m inputs (x1 …xm)
The price of the outputs: (p1 …pn)
The price of the inputs: (w1 …wm)

4. 19.1 Profits
The economic definition of profit requires that we value all inputs and outputs at their opportunity cost.
Accounting profits are typically based on historical costs.
Price of labor: wage.
Price of capital: rental rate.
the rate at which you can rent a machine for the given time period.

5. 19.2 The Organization of Firms
Proprietorship
A firm that is owned by a single individual.
Partnership
A firm that is owned by two or more individuals.
Corporation
A firm that is usually owned by several individuals as well, but under the law has an existence separate form that of its owners.

6. 19.3 Profits and Stock Market Value
Present value of the firm
The present value of profits when a firm’s flow of future profits is publicly known.
Firm’s stock market value is its present value.
Firm maximizes its stock market value.
Equivalently a firm maximizes the present value of profit flows.

7. 19.4 Fixed and Variable Factors
Fixed factor
The factor of production that is in a fixed amount for the firm.
Must be paid for even if the firm decides to produce zero output.
Variable factor
A factor can be used in different amounts.
The division of factors depends on the question under concern.

8. 19.5 Short-Run Profit Maximization
The profit-maximization problem
output
Isoprofit lines
y=f(x1,x2’) y*
F.O.C.
π/p+w2x2’/p
x1* x1

9. 19.5 Short-Run Profit Maximization
Isoprofit lines
All combinations of the input good and the output good that give a constant level of profit.
Slope=w1/p.

10. 19.6 Comparative Statics y y
high w1
low p
high p
low w1 x1 x1 A B

11. 19.7 Profit Maximization in the Long Run
The long-run profit-maximization problem
F.O.C.s
pMP1(x1*,x2*)= w1
pMP2(x1*,x2*)= w2
Factor demand curves
Optimal choice as a function of the prices.

12. 19.9 Profit Maximization and Returns to Scale
Suppose a firm:
exhibits constant returns to scale;
makes positive profits in equilibrium.
Double inputs and output doubles.
Profit doubles.
Long-run profits must be zero.

13. 19.9 Profit Maximization and Returns to Scale
What happens when a firm expands indefinitely.
The firm may get too large to operate effectively.
Actually decreasing return to scale.
The firm may become a monopolist.
The monopolist won’t take output price as given.
Will be treated later.
Other firms enter the market for profits.
Eventually drives profits to zero.

14. 19.10 Revealed Profitability
Two choices under two price vectors
Choose (yt,x1t,x2t) when the price is (pt,w1t,w2t).
Choose (ys,x1s,x2s) when the price is (ps,w1s,w2s).
Technology remain unchanged.
Profit maximization requires that:
ptyt-w1tx1t-w2tx2t≥ptys-w1tx1s-w2tx2s
psys-w1sx1s-w2sx2s≥psyt-w1sx1t-w2sx2t

15. 19.10 Revealed Profitability
WAPM:
(pt-ps)(yt-ys)-(w1t-w1s)(x1t-x1s)-(w2t-w2s)(x2t-x2s)≥0
△p△y-△w1△x1-△w2△x2≥0
Suppose △w1=△w2=0
△p△y≥0
Suppose △y=△w2=0
△w1△x1≤0

16. 19.10 Revealed Profitability
We plot two isoprofit lines
πt=pty-w1tx1
πs=psy-w1sx1
WAPM requires that the choice in period t must lie below the period s is isoprofit line and that the choice in period s must lie below the period t isoprofit line.

17. 19.10 Revealed Profitability
Two isoprofit lines
πt=pty-w1tx1
πs=psy-w1sx1
The choice in period t must lie below the period s isoprofit line.
The choice in period s must lie below the period t isoprofit line. y
Isoprofit line for period s
Isoprofit line for period t
(yt,x1t)
Πt/pt
(ys,x1s)
Πs/ps x1

18. 19.10 Revealed Profitability
Isoprofit lines x

19. 19.11 Cost Minimization
If a firm is maximizing profits and if it chooses to supply some output y, then it must be minimizing the cost of producing y.
Breaking the profit-maximization problem into two stages:
First we figure out how to minimize the costs of producing any desired level of output y,
Then we figure out which level of output is indeed a profit-maximizing level of output.