【正文】 tion and the maximal isoprofit line are equal. ? ?? ??x1*y*2022/2/17 22 Profit Maximization ShortRun ProfitMaximization x1 y Slopes wp? ? 1At the shortrun profitmaximizing plan, the slopes of the shortrun production function and the maximal isoprofit line are equal. MPwpat x x y111 2?( , ~ , )* *? ?? ??x1*y*2022/2/17 23 Profit Maximization ShortRun ProfitMaximization MP w p p MP w1 1 1 1? ? ? ?p MP? 1 is the marginal revenue product 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. p MP w? ?1 1p MP w? ?1 12022/2/17 24 Profit Maximization ShortRun ProfitMaximization。 A CobbDouglas Example p x x w3 12 3 21/ 3 1( ) ~* /? ?Solving for x1 gives ( ) ~ .* /x wp x12 3 121/ 33? ?2022/2/17 26 Profit Maximization ShortRun ProfitMaximization。 A CobbDouglas Example p x x w3 12 3 21/ 3 1( ) ~* /? ?Solving for x1 gives ( ) ~ .* /x wp x12 3 121/ 33? ?That is, ( ) ~* /x p xw12 3 21/ 313?so xp xwpwx1 21/ 313 213 221/ 23 3*/ /~~ .? ???????? ? ??????2022/2/17 28 Profit Maximization ShortRun ProfitMaximization。 A CobbDouglas Example x pwx113 221/ 23*/~? ??????is the firm’s shortrun demand for input 1 when the level of input 2 is fixed at units. ~x2The firm’s shortrun output level is thus y x x pwx* *( ) ~ ~ .? ? ??????11/ 321/ 311/ 221/ 232022/2/17 30 Profit Maximization Comparative Statics of ShortRun ProfitMaximization ? What happens to the shortrun profitmaximizing production plan as the output price p changes? 2022/2/17 31 Profit Maximization Comparative Statics of ShortRun ProfitMaximization y wpx w xp? ? ?1 1 2 2?~The equation of a shortrun isoprofit line is so an increase in p causes a reduction in the slope, and a reduction in the vertical intercept. 2022/2/17 32 Profit Maximization Comparative Statics of ShortRun ProfitMaximization x1 ? ?? ?? ?? ??? ?? ???Slopes wp? ? 1y y f x x? ( , ~ )1 2x1*y*2022/2/17 33 Profit Maximization Comparative Statics of ShortRun ProfitMaximization x1 Slopes wp? ? 1y y f x x? ( , ~ )1 2x1*y*2022/2/17 34 Profit Maximization Comparative Statics of ShortRun ProfitMaximization x1 Slopes wp? ? 1y y f x x? ( , ~ )1 2x1*y*2022/2/17 35 Profit Maximization Comparative Statics of ShortRun ProfitMaximization ? An increase in p, the price of the firm’s output, causes ? an increase in the firm’s output level (the firm’s supply curve slopes upward), and ? an increase in the level of the firm’s variable input (the firm’s demand curve for its variable input shifts outward). 2022/2/17 36 Profit Maximization Comparative Statics of ShortRun ProfitMaximization x pwx113 221/ 23*/~? ??????The CobbDouglas example: When then the firm’s shortrun demand for its variable input 1 is y x x? 11/ 3 21/ 3~y pwx* ~ .? ??????3 11/ 221/ 2and its shortrun supply is 2022/2/17 37 Profit Maximization Comparative Statics of ShortRun ProfitMaximization The CobbDouglas example: When then the firm’s shortrun demand for its variable input 1 is y x x? 11/ 3 21/ 3~x1* increases as p increases. and its shortrun supply is x pwx113 221/ 23*/~? ??????y pwx* ~ .? ??????3 11/ 221/ 22022/2/17 38 Profit Maximization Comparative Statics of ShortRun ProfitMaximization The CobbDouglas example: When then the firm’s shortrun demand for its variable input 1 is y x x? 11/ 3 21/ 3~y* increases as p increases. and its shortrun supply is x1* increases as p increases. x pwx113 221/ 23*/~? ??????y pwx* ~ .? ??????3 11/ 221/ 22022/2/17 39 Profit Maximization Comparative Statics of ShortRun ProfitMaximization ? What happens to the shortrun profitmaximizing production plan as the variable input price w1 changes? 2022/2/17 40 Profit Maximization Comparative Statics of ShortRun ProfitMaximization y wpx w xp? ? ?1 1 2 2?~The equation of a shortrun isoprofit line is so an increase in w1 causes an increase in the slope, and no change to the vertical intercept. 2022/2/17 41 Profit Maximization Comparative Statics of ShortRun ProfitMaximization x1 ? ?? ?? ?? ??? ?? ???Slopes wp? ? 1y y f x x? ( , ~ )1 2x1*y*2022/2/17 42 Profit Maximization Comparative Statics of ShortRun ProfitMaximization x1 Slopes wp? ? 1y y f x x? ( , ~ )1 2x1*y*? ?? ?? ?? ??? ?? ???2022/2/17 43 Profit Maximization Comparative Statics of ShortRun ProfitMaximization x1 Slopes wp? ? 1y y f x x? ( , ~ )1 2x1*y*? ?? ?? ?? ??? ?? ???2022/2/17 44 Profit Maximization Comparative Statics of ShortRun ProfitMaximization ? An increase in w1, the price of the firm’s variable input, causes ? a decrease in the firm’s output level (the firm’s supply curve shifts inward), and ? a decrease in the level of the firm’s variable input (the firm’s demand curve for its variable input slopes downward). 2022/2/17 45 Profit Maxi