4. a. b C. Assume a perfectly competitive firm with a strictly quasi-concave production function, q = f(L, K), which has the property that MPL exhibits increasing marginal returns and then diminishing marginal returns as L increases (holding K constant). Production also exhibits strict increasing returns to scale as production increases. Set up the long run cost minimizing optimization function and describe the resulting factor demand curves (what are they a function of). How would you use this to generate the firm long run supply function? Set up the long run profit maximizing optimization function (where the choice variables are L and K). What is the difference in the resulting factor demand functions for each optimization compared to part a above? How would you use this to generate the firm's long run supply function? Graph the long run cost function and include three short run cost functions all with different levels of capital. Also graph the long run average and marginal cost curves and add in a set of short run MC and ATC curves.
4. a. b C. Assume a perfectly competitive firm with a strictly quasi-concave production function, q = f(L, K), which has the property that MPL exhibits increasing marginal returns and then diminishing marginal returns as L increases (holding K constant). Production also exhibits strict increasing returns to scale as production increases. Set up the long run cost minimizing optimization function and describe the resulting factor demand curves (what are they a function of). How would you use this to generate the firm long run supply function? Set up the long run profit maximizing optimization function (where the choice variables are L and K). What is the difference in the resulting factor demand functions for each optimization compared to part a above? How would you use this to generate the firm's long run supply function? Graph the long run cost function and include three short run cost functions all with different levels of capital. Also graph the long run average and marginal cost curves and add in a set of short run MC and ATC curves.
Chapter2: Mathematics For Microeconomics
Section: Chapter Questions
Problem 2.8P
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