Chapter NineteenEconomic ProfitThe Competitive FirmSlide 4Slide 5Slide 6Slide 7Slide 8Slide 9Short-Run Iso-Profit LinesSlide 11Slide 12Slide 13Short-Run Profit-MaximizationSlide 15Slide 16Slide 17Slide 18Slide 19Slide 20Slide 21Slide 22Slide 23Short-Run Profit-Maximization; A Cobb-Douglas ExampleSlide 25Slide 26Slide 27Slide 28Slide 29Comparative Statics of Short-Run Profit-MaximizationSlide 31Slide 32Slide 33Slide 34Slide 35Slide 36Slide 37Slide 38Slide 39Slide 40Slide 41Slide 42Slide 43Slide 44Slide 45Slide 46Slide 47Long-Run Profit-MaximizationSlide 49Slide 50Slide 51Slide 52Slide 53Slide 54Slide 55Slide 56Slide 57Slide 58Slide 59Slide 60Slide 61Slide 62Slide 63Slide 64Slide 65Slide 66Slide 67Slide 68Slide 69Slide 70Slide 71Returns-to-Scale and Profit-MaximizationReturns-to Scale and Profit-MaximizationSlide 74Slide 75Slide 76Slide 77Slide 78Slide 79Slide 80Slide 81Revealed ProfitabilitySlide 83Slide 84Slide 85Slide 86Slide 87Slide 88Slide 89Slide 90Slide 91Slide 92Slide 93Slide 94Slide 95Slide 96Slide 97Slide 98Slide 99Slide 100Slide 101Slide 102Slide 103Slide 104Slide 105Chapter NineteenProfit-MaximizationEconomic 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,…,wm as given constants.Economic ProfitThe economic profit generated by the production plan (x1,…,xm,y1,…,yn) is      p y p y w x w xn n m m1 1 1 1  .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.Economic ProfitHow do we value a firm?Suppose the firm’s stream of periodic economic profits is  … and r is the rate of interest.Then the present-value of the firm’s economic profit stream isPVrr  01 2211( )Economic ProfitA competitive firm seeks to maximize its present-value.How?Economic ProfitSuppose the firm is in a short-run circumstance in which Its short-run production function isy f x x ( ,~).1 2x x2 2~.Economic ProfitSuppose the firm is in a short-run circumstance in which Its short-run production function isThe firm’s fixed cost isand its profit function isy f x x ( ,~).1 2   py w x w x1 1 2 2~.x x2 2~.FC w x2 2~Short-Run Iso-Profit LinesA $ iso-profit line contains all the production plans that provide a profit level $.A $ iso-profit line’s equation is   py w x w x1 1 2 2~.Short-Run Iso-Profit LinesA $ iso-profit line contains all the production plans that yield a profit level of $.The equation of a $ iso-profit line isI.e.   py w x w x1 1 2 2~.ywpxw xp 112 2~.Short-Run Iso-Profit Linesywpxw xp 112 2~has a slope ofwp1and a vertical intercept of  w xp2 2~.Short-Run Iso-Profit Lines   Increasing profityx1Slopeswp1Short-Run Profit-MaximizationThe firm’s problem is to locate the production plan that attains the highest possible iso-profit line, given the firm’s constraint on choices of production plans.Q: What is this constraint?Short-Run Profit-MaximizationThe firm’s problem is to locate the production plan that attains the highest possible iso-profit line, given the firm’s constraint on choices of production plans.Q: What is this constraint?A: The production function.Short-Run Profit-Maximizationx1TechnicallyinefficientplansyThe short-run production function andtechnology set for x x2 2~.y f x x ( ,~)1 2Short-Run Profit-Maximizationx1Increasing profitSlopeswp1yy f x x ( ,~)1 2   Short-Run Profit-Maximizationx1y   Slopeswp1x1*y*Short-Run Profit-Maximizationx1ySlopeswp1Given p, w1 and the short-runprofit-maximizing plan is  x1*y*x x2 2~,( ,~, ).* *x x y1 2Short-Run Profit-Maximizationx1ySlopeswp1Given p, w1 and the short-runprofit-maximizing plan is And the maximumpossible profitis x x2 2~,( ,~, ).* *x x y1 2 . x1*y*Short-Run Profit-Maximizationx1ySlopeswp1At the short-run profit-maximizing plan, the slopes of the short-run production function and the maximaliso-profit line areequal. x1*y*Short-Run Profit-Maximizationx1ySlopeswp1At the short-run profit-maximizing plan, the slopes of the short-run production function and the maximaliso-profit line areequal.MPwpat x x y111 2( ,~, )* * x1*y*Short-Run Profit-MaximizationMPwpp MP w111 1   p MP1 is the marginal revenue product ofinput 1, the rate at which revenue increaseswith the amount used of input 1.If then profit increases with x1.If then profit decreases with x1. p MP w 1 1p MP w 1 1Short-Run Profit-Maximization; A Cobb-Douglas ExampleSuppose the short-run productionfunction isy x x11/321/3~.The marginal product of the variableinput 1 isMPyxx x1112 321/313 /~.The profit-maximizing condition isMRP p MPpx x w1 1 12 321/313   ( )~.* /Short-Run Profit-Maximization; A Cobb-Douglas Examplepx x w312 321/31( )~* /Solvingfor x1 gives( )~.* /xwpx12 3121/33Short-Run Profit-Maximization; A Cobb-Douglas Examplepx x w312 321/31( )~* /Solvingfor x1 gives( )~.* /xwpx12 3121/33That is,( )~* /xpxw12 321/313Short-Run Profit-Maximization; A Cobb-Douglas Examplepx x w312 321/31( )~* /Solvingfor x1 gives( )~.* /xwpx12 3121/33That is,( )~* /xpxw12 321/313soxpxwpwx121/313 213 221/23 3*//~~.Short-Run Profit-Maximization; A Cobb-Douglas Examplexpwx113 221/23*/~is the firm’sshort-run demandfor input 1 when the level of input 2 is fixed at units. ~x2Short-Run Profit-Maximization; A Cobb-Douglas Examplexpwx113 221/23*/~is the firm’sshort-run demandfor input 1 when the level of input 2 is fixed at