资源描述
StructureuEconomic profituShort-run profit maximizationComparative staticsuLong-run profit maximizationuProfit maximization and returns to scaleuRevealed profit maximizationEconomic ProfituA firm uses inputs j=1,m to make products i=1,n.uOutput levels are y1,yn.uInput levels are x1,xm.uProduct prices are p1,pn.uInput prices are w1,wm.The Competitive FirmuThe competitive firm takes all output prices p1,pn and all input prices w1,wm as given constants.Economic ProfituThe economic profit generated by the production plan(x1,xm,y1,yn)isEconomic ProfituOutput and input levels are typically flows.uE.g.x1 might be the number of labor units used per hour.uAnd y3 might be the number of cars produced per hour.uConsequently,profit is typically a flow also;e.g.the number of dollars of profit earned per hour.Opportunity Costs(机会成本)uAll inputs must be valued at their market value.uLaboruCapitalEconomic ProfituHow do we value a firm?uSuppose the firms stream of periodic economic profits is P P0 0,P,P1 1,P P2 2,and r is the rate of interest.uThen the present-value of the firms economic profit stream isProfit MaximizationuA competitive firm seeks to maximize its present-value.uHow?uSuppose the firm is in a short-run circumstance in which uIts short-run production function isuThe firms fixed cost isand its profit function isShort-Run Profit MaximizationShort-Run Iso-Profit LinesuA$P P iso-profit line(等利润线等利润线)contains all the production plans that yield a profit level of$P P.uThe equation of a$P P iso-profit line isuI.e.Short-Run Iso-Profit Lineshas a slope ofand a vertical intercept ofShort-Run Iso-Profit LinesIncreasing profityx1Short-Run Profit-MaximizationuThe firms problem is to locate the production plan that attains the highest possible iso-profit line,given the firms constraint on choices of production plans.uQ:What is this constraint?uA:The production function.Short-Run Profit-Maximizationx1TechnicallyinefficientplansyThe short-run production function andtechnology set for Short-Run Profit-Maximizationx1Increasing profityShort-Run Profit-Maximizationx1yShort-Run Profit-Maximizationx1yGiven p,w1 and the short-runprofit-maximizing plan is Short-Run Profit-Maximizationx1yGiven p,w1 and the short-runprofit-maximizing plan is And the maximumpossible profitis Short-Run Profit-Maximizationx1yAt the short-run profit-maximizing plan,the slopes of the short-run production function and the maximaliso-profit line areequal.Short-Run Profit-Maximizationx1yAt the short-run profit-maximizing plan,the slopes of the short-run production function and the maximaliso-profit line areequal.Short-Run Profit-Maximization is the marginal revenue product(边际边际收益产量收益产量)of input 1,the rate at which revenue Increases with the amount used of input 1.If then profit increases with x1.If then profit decreases with x1.Short-Run Profit-Maximization;A Cobb-Douglas ExampleSuppose the short-run productionfunction isThe marginal product of the variableinput 1 isThe profit-maximizing condition isShort-Run Profit-Maximization;A Cobb-Douglas ExampleSolvingfor x1 givesShort-Run Profit-Maximization;A Cobb-Douglas ExampleSolvingfor x1 givesThat is,Short-Run Profit-Maximization;A Cobb-Douglas ExampleSolvingfor x1 givesThat is,soShort-Run Profit-Maximization;A Cobb-Douglas Exampleis the firmsshort-run demandfor input 1 when the level of input 2 is fixed at units.Short-Run Profit-Maximization;A Cobb-Douglas Exampleis the firmsshort-run demandfor input 1 when the level of input 2 is fixed at units.The firms short-run output level is thusComparative Statics of Short-Run Profit-MaximizationuWhat happens to the short-run profit-maximizing production plan as the output price p changes?Comparative Statics of Short-Run Profit-MaximizationThe equation of a short-run iso-profit lineisso an increase in p causes -a reduction in the slope,and -a reduction in the vertical intercept.Comparative Statics of Short-Run Profit-Maximizationx1yComparative Statics of Short-Run Profit-Maximizationx1yComparative Statics of Short-Run Profit-Maximizationx1yComparative Statics of Short-Run Profit-MaximizationuAn increase in p,the price of the firms output,causesan increase in the firms output level(the firms supply curve slopes upward),andan increase in the level of the firms variable input(the firms demand curve for its variable input shifts outward).Comparative Statics of Short-Run Profit-MaximizationThe Cobb-Douglas example:When then the firms short-rundemand for its variable input 1 isand its short-runsupply isComparative Statics of Short-Run Profit-MaximizationThe Cobb-Douglas example:When then the firms short-rundemand for its variable input 1 isincreases as p increases.and its short-runsupply isComparative Statics of Short-Run Profit-MaximizationThe Cobb-Douglas example:When then the firms short-rundemand for its variable input 1 isincreases as p increases.and its short-runsupply isincreases as p increases.Comparative Statics of Short-Run Profit-MaximizationuWhat happens to the short-run profit-maximizing production plan as the variable input price w1 changes?Comparative Statics of Short-Run Profit-MaximizationThe equation of a short-run iso-profit lineisso an increase in w1 causes -an increase in the slope,and -no change to the vertical intercept.Comparative Statics of Short-Run Profit-Maximizationx1yComparative Statics of Short-Run Profit-Maximizationx1yComparative Statics of Short-Run Profit-Maximizationx1yComparative Statics of Short-Run Profit-MaximizationuAn increase in w1,the price of the firms variable input,causesa decrease in the firms output level(the firms supply curve shifts inward),anda decrease in the level of the firms variable input(the firms demand curve for its variable input slopes downward).Comparative Statics of Short-Run Profit-MaximizationThe Cobb-Douglas example:When then the firms short-rundemand for its variable input 1 isand its short-runsupply isComparative Statics of Short-Run Profit-MaximizationThe Cobb-Douglas example:When then the firms short-rundemand for its variable input 1 isdecreases as w1 increases.and its short-runsupply isComparative Statics of Short-Run Profit-MaximizationThe Cobb-Douglas example:When then the firms short-rundemand for its variable input 1 isdecreases as w1 increases.decreases as w1 increases.and its short-runsupply isLong-Run Profit-MaximizationuNow allow the firm to vary both input levels,i.e.,both x1 and x2 are variable.uSince no input level is fixed,there are no fixed costs.uThe profit-maximization problem isuFOCs are:Long-Run Profit-MaximizationFactor Demand FunctionsuDemand for inputs 1 and 2 can be solved as,Inverse Factor Demand FunctionsuFor a given optimal demand for x2,inverse demand function for x1 isuFor a given optimal demand for x1 inverse demand function for x2 isInverse Factor Demand Curvesx1w1Example:C-D Production FunctionThe production function isFirst-order conditions are:uSolving for x1 and x2:Plug-in production function to get:Example:C-D Production FunctionReturns-to-Scale and Profit-MaximizationuIf a competitive firms technology exhibits decreasing returns-to-scale then the firm has a single long-run profit-maximizing production plan.Returns-to Scale and Profit-Maximizationxyy*x*Decreasingreturns-to-scaleReturns-to-Scale and Profit-MaximizationuIf a competitive firms technology exhibits exhibits increasing returns-to-scale then the firm does not have a profit-maximizing plan.Returns-to Scale and Profit-Maximizationxyy”xIncreasingreturns-to-scaleyx”Increasing profitReturns-to-Scale and Profit-MaximizationuSo an increasing returns-to-scale technology is inconsistent with firms being perfectly competitive.Returns-to-Scale and Profit-MaximizationuWhat if the competitive firms technology exhibits constant returns-to-scale?Returns-to Scale and Profit-Maximizationxyy”xConstantreturns-to-scaleyx”Increasing profitReturns-to Scale and Profit-MaximizationuSo if any production plan earns a positive profit,the firm can double up all inputs to produce twice the original output and earn twice the original profit.Returns-to Scale and Profit-MaximizationuTherefore,when a firms technology exhibits constant returns-to-scale,earning a positive economic profit is inconsistent with firms being perfectly competitive.uHence constant returns-to-scale requires that competitive firms earn economic profits of zero.Returns-to Scale and Profit-Maximizationxyy”xConstantreturns-to-scaleyx”P P=0Revealed ProfitabilityuConsider a competitive firm with a technology that exhibits decreasing returns-to-scale.uFor a variety of output and input prices we observe the firms choices of production plans.uWhat can we learn from our observations?Revealed ProfitabilityuIf a production plan(x,y)is chosen at prices(w,p)we deduce that the plan(x,y)is revealed to be profit-maximizing for the prices(w,p).Revealed Profitabilityxy is chosen at prices so is profit-maximizing at these prices.Revealed Profitabilityxy is chosen at prices so is profit-maximizing at these prices.would give lowerprofits,soRevealed Profitabilityxy is chosen at prices so(x”,y”)is chosen at prices(w”,p”)so(x”,y”)is profit-maximizing at these prices.Weak Axiom of Profit Maximizationxy is chosen at prices so is chosen at prices soRevealed ProfitabilityandsoandAdding givesRevealed ProfitabilitysoThat is,is a necessary implication of profit-maximization.Revealed Profitabilityis a necessary implication of profit-maximization.Suppose the input price does not change.Then D Dw=0 and profit-maximizationimplies ;i.e.,a competitivefirms output supply curve cannot slopedownward.Revealed Profitabilityis a necessary implication of profit-maximization.Suppose the output price does not change.Then D Dp=0 and profit-maximizationimplies ;i.e.,a competitivefirms input demand curve cannot slopeupward.供娄浪颓蓝辣袄驹靴锯澜互慌仲写绎衰斡染圾明将呆则孰盆瘸砒腥悉漠堑脊髓灰质炎(讲课2019)脊髓灰质炎(讲课2019)供娄浪颓蓝辣袄驹靴锯澜互慌仲写绎衰斡染圾明将呆则孰盆瘸砒腥悉漠堑脊髓灰质炎(讲课2019)脊髓灰质炎(讲课2019)
展开阅读全文