Question

2) Consider the following production function for shirts: q=13/4K1/4, where L is worker-hours, and K is sewing machine-hours. The cost of one hour of labor L is w The cost of renting a sewing machine for one hour is r. What type of returns to scale does this production function have? a) b) Compute the marginal product of labor L and marginal product of capital K. What is the marginal rate of technical substitution of labor for capital .e. how many units of capital are needed to make up for the loss of one unit of labor)? Are isoquants convex? c) Set the tangency condition for an interior solution to the cost minimization d) Solve the long run cost minimization problem .e. find optimal L and K as e) Use the input demand functions you derived at part (d) to compute the total cost f) problem. Now set the condition that output q is produced (i.e. write the production function) functions of q, w, and r: how much labor and how much capital does the firm use to produce q units of output at input prices w and r? TC as a function of q, w, and r Let w-$15/hour and r-$2/hour. What is the cost of producing 1 shirt? What about 2 shirts? 4 shirts? Draw the total cost curve. 3) Repeat problem 2, this time for the production function q 0.113/ K1/2

Answer 1

Constant relun to s 3/ リ le. 2. mex 2 L ㄥ 3と 34