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Chapter 19 PROFIT MAXIMIZATION

Chapter 19 PROFIT MAXIMIZATION. Chapter 19 PROFIT MAXIMIZATION. 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. 19.1 Profits. Profits: revenues minus cost.

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Chapter 19 PROFIT MAXIMIZATION

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  1. Chapter 19 PROFIT MAXIMIZATION

  2. Chapter 19 PROFIT MAXIMIZATION • 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 output Isoprofit lines • The profit-maximization problem 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 twoisoprofit 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 • Twoisoprofit 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 y 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.

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