Chapter nineteen Profit-Maximization 利润最大化
Chapter Nineteen Profit-Maximization 利润最大化
Structure Economic profit Short-run profit maximization Comparative statics Long-run profit maximization Profit maximization and returns to scale Revealed profit maximization
Structure Economic profit Short-run profit maximization –Comparative statics Long-run profit maximization Profit maximization and returns to scale Revealed profit maximization
Economic profit A firm uses inputs j=1., m to make products i=1,n Output levels are y1.n nput levels are x1…,X Product prices are pis. ,pn. nput prices are w1…,Wm
Economic Profit A firm uses inputs j = 1…,m to make products i = 1,…n. Output levels are y1 ,…,yn . Input levels are x1 ,…,xm. Product prices are p1 ,…,pn . Input prices are w1 ,…,wm
The Competitive Firm The competitive firm takes all output prices p1,--,pn and all input prices as given constants
The Competitive Firm The competitive firm takes all output prices p1 ,…,pn and all input prices w1 ,…,wm as given constants
Economic profit The economic profit generated by the production plan(x1;…,xmy1…yn)is I=p1y1+…+Pnyn-W1X1-…WmXm
Economic Profit The economic profit generated by the production plan (x1 ,…,xm,y1 ,…,yn ) is = p1 y1 ++pn yn=− w1 x1 −wmxm
Economic profit Output and input levels are ty pically flows E.g. X, might be the number of labor units used per hour And y3 might be the number of cars produced per hour. Consequently, profit is typically a flow also; e.g. the number of dollars of profit earned per hour
Economic Profit Output and input levels are typically flows. E.g. x1 might be the number of labor units used per hour. And y3 might be the number of cars produced per hour. Consequently, profit is typically a flow also; e.g. the number of dollars of profit earned per hour
Opportunity Costs(机会成本) All inputs must be valued at their market value Labor Capital
Opportunity Costs (机会成本) All inputs must be valued at their market value. Labor Capital
Economic profit How do we value a firm? Suppose the firm's stream of periodic economic profits is Io, II1, ∏,∴ and r is the rate of interest. Then the present-value of the firm's economic profit stream is PV=IIo t l+r(1+r)
Economic Profit How do we value a firm? Suppose the firm’s stream of periodic economic profits is 0 , 1 , 2 , … and r is the rate of interest. Then the present-value of the firm’s economic profit stream is PV r r = + + + + + 0 1 2 1 2 (1 )
Profit maximization A competitive firm seeks to maximize its present-value How?
Profit Maximization A competitive firm seeks to maximize its present-value. How?
Short-Run profit maximization Suppose the firm is in a short-run circumstance in which X2= X2 Its short-run production function is y=f(x1,X2) The firms fixed cost is FC=W2X2 and its profit function is ∏=py-W1X1-W2X2
Suppose the firm is in a short-run circumstance in which Its short-run production function is The firm’s fixed cost is and its profit function is y = f(x ,x ~ ). 1 2 = py − w1 x1 − w2 x2 ~ . x2 x2 ~ . FC = w2 x2 ~ Short-Run Profit Maximization