Three Prod Problems (Ch 7) - Here please find three...

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Here please find three additional problems on Ch. 7. (Solutions at the end.) Problem 1 A firm has the linear production function Q= K+L. Derive the cost-minimizing combination of Labour and Capital when w=1 and r=2 for the level of production Q 0 . Show your work Problem 2 Denote by w and r the price of labour (L) and capital (K) respectively. Consider the production function Q =4K (3/4) L (1/4) . The marginal product of labour and capital are MP L = (K/L) (3/4) and MP K = 3(L/K) (1/4) respectively. a. Find the expansion path, draw a graph to illustrate your answer. b. Are Capital and Labour normal or inferior inputs? c. Find the demand of labour Show your work Problem 3 Assume that a firm’s production line requires exactly one machine for three workers. Let the price of labour be 1 per unit and the price of capital be 3 per unit. Find the cost- minimizing bundle of inputs as a function of the budget B allocated to this production line.
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