5a. Chris Carpentry uses capital (K) and labor (L) to produce two different prod

Question

5a. Chris Carpentry uses capital (K) and labor (L) to produce two different products, doors (D) and windows (W). Assume that the marginal product of capital in producing doors is 10 and the marginal product of labor in door production is 5. Further assume marginal product of capital in window making is 15 and the marginal product of labor is 9. Assume that Chris Carpentry is a price-taking firm and that doors sell for $100 each while windows sell for $50 each. Is Chris Carpentry technically efficient? If not, what adjustments does Chris need? 5b. Is Chris Carpentry allocatively efficient? If not, what adjustments does Chris need?

Explanation / Answer

Technical efficiency implies that given output (of doors and windows) is being produced at minimum cost. In order for output to be produced at minimum cost (and hence be on the cost function as well as on the PPF) the GOLDEN RULE of cost minimization requires that ratio of marginal products of K and L in producing doors must equal the ratio of the marginal products of K and L in producing windows. Let's check on Cutrate Carpentry. MPKDoors/MPLDoors= 10/5 = 2, and MPKWindows/MPLWindows= 100/50 =2 . Thus the ratio of marginal products of the inputs in producing output is equal for all outputs so there is no reallocation of capital and labor that can produce more doors without producing fewer windows and Cutrate Carpentry is technically efficient!6b. Is Cutrate Carpentry allocatively efficient? Please justify your response. Allocative efficiency requires that production take place where the ratio of marginal costs is equal to the price ratio. But how can we know the ratio of the marginal costs if we don't know the wage of labor or price of capital? Here's the trick - if you got it give yourself a gold star. Marginal cost of producing doors using capital = MCKDoors= R/MPKDoors= R/2 . Marginal cost of producing windows using capital is MCKWindows= R/Mp= R10

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