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1、Chapter Nineteen,Profit-Maximization,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 w1
2、,wm as given constants.,Economic Profit,The economic profit generated by the production plan (x1,xm,y1,yn) is,Economic Profit,Output and input levels are typically flows.(流量） E.g. x1 might be the number of labor units used per hour.（每小时劳动投入量） And y3 might be the number of cars produced per hour.（每小时
3、产出量） Consequently, profit is typically a flow also; e.g. the number of dollars of profit earned per hour.,Economic Profit,How do we value a firm?如何为一个公司订价？ Suppose the firms stream of periodic economic profits is P0, P1, P2, and r is the rate of interest. Then the present-value of the firms economic
4、 profit stream is,Economic Profit,A competitive firm seeks to maximize its present-value.一个竞争性企业为最大化利润流现值。 How?,Economic Profit,Suppose the firm is in a short-run circumstance in which（假定公司处于短期的生产环境） Its short-run production function is,Economic Profit,Suppose the firm is in a short-run circumstance
5、 in which Its short-run production function is The firms fixed cost is and its profit function is,Short-Run Iso-Profit Lines 短期等利润线,A $P iso-profit line （等利润线）contains all the production plans that provide a profit level $P . A $P iso-profit lines equation is,Short-Run Iso-Profit Lines,A $P iso-prof
6、it line contains all the production plans that yield a profit level of $P . The equation of a $P iso-profit line is I.e.,Short-Run Iso-Profit Lines短期等利润线,has a slope of,and a vertical intercept of,Short-Run Iso-Profit Lines,Increasing profit,y,x1,Short-Run Profit-Maximization 短期公司利润最大化,The firms pro
7、blem is to locate the production plan that attains the highest possible iso-profit line, given the firms constraint on choices of production plans.（给定公司的生产计划约束，使生产计划尽可能地达到最高的等利润线上。） Q: What is this constraint?（生产计划约束？）,Short-Run Profit-Maximization,The firms problem is to locate the production plan
8、that attains the highest possible iso-profit line, given the firms constraint on choices of production plans.（生产计划的选择约束） Q: What is this constraint?（技术约束） A: The production function.（生产函数）,Short-Run Profit-Maximization,x1,Technically inefficient plans,y,The short-run production function and technolo
9、gy set for,Short-Run Profit-Maximization,x1,Increasing profit,y,Short-Run Profit-Maximization,x1,y,Short-Run Profit-Maximization,x1,y,Given p, w1 and the short-run profit-maximizing plan is,Short-Run Profit-Maximization,x1,y,Given p, w1 and the short-run profit-maximizing plan is And the maximum pos
10、sible profit is,Short-Run Profit-Maximization,x1,y,At the short-run profit-maximizing plan, the slopes of the short-run production function and the maximal iso-profit line are equal.,Short-Run Profit-Maximization,x1,y,At the short-run profit-maximizing plan, the slopes of the short-run production fu
11、nction and the maximal iso-profit line are equal.,Short-Run Profit-Maximization,is the marginal revenue product of input 1, the rate at which revenue increases with the amount used of input 1（要素1的边际产品收益）. If then profit increases with x1. If then profit decreases with x1.,Short-Run Profit-Maximizati
12、on; A Cobb-Douglas Example,Suppose the short-run production function is,The marginal product of the variable input 1 is,The profit-maximizing condition is,Short-Run Profit-Maximization; A Cobb-Douglas Example,Solving,for x1 gives,Short-Run Profit-Maximization; A Cobb-Douglas Example,Solving,for x1 g
13、ives,That is,Short-Run Profit-Maximization; A Cobb-Douglas Example,Solving,for x1 gives,That is,so,Short-Run Profit-Maximization; A Cobb-Douglas Example,is the firms short-run demand,for input 1 when the level of input 2 is fixed at units.,Short-Run Profit-Maximization; A Cobb-Douglas Example,is the
14、 firms short-run demand,for input 1 when the level of input 2 is fixed at units.,The firms short-run output level is thus,Comparative Statics of Short-Run Profit-Maximization,比较静态分析 What happens to the short-run profit-maximizing production plan as the output price p changes?,Comparative Statics of
15、Short-Run Profit-Maximization,The equation of a short-run iso-profit line is,so an increase in p causes - a reduction in the slope, and - a reduction in the vertical intercept.,Comparative Statics of Short-Run Profit-Maximization,x1,y,Comparative Statics of Short-Run Profit-Maximization,x1,y,Comparative Statics of Short-Run Profit-Maximization,x1,y,Comparative Statics of Short-Run Profit-Maximization,An increase in p, the price of the firms output, causes an increase in the firms output level (the firms supply curve slopes upward), and an increase in the level of the firms variable input (the
