Question

1. Suppose a firm is producing output according to Q=1001KL. A. Draw a sketch of this firm's isoquant map B. What equation do you use to find a cost-minimizing combination of inputs for a certain output level Q.? K C. The marginal products of labor and capital are given by MP, = 50, and L MPK = 50, L respectively. The price of labor is $5 per unit, and the price of K capital is $20 per unit. What is the cost-minimizing input combination if the firm wants to produce 2000 units? 2. Suppose the level of capital stock in the short run is fixed to K, and you want to produce Q. units of output produced according to Q=100 KL. A. Write down a formula for the cost-minimizing choice of labor in this case B. Draw a graph of the cost-minimizing choice of labor in A) as a function of Q. 3. Assuming the conditions in Problem 1 and your solution in Problem 2, derive a short- run total cost function for a fixed level of capital stock K.

Answer 1

As per the HomeworkLib policy guidelines answering the first four parts

1. Q = 100 VRT A. An B. Equation of Expansion Path' would be used to find cost- minimizing bundle , Below is the equilibrium condition - MRT SLK a Poice of Labor/price of Capital MP4/MPK = W/ 7 100x<* 100x<* 31+ » Ę = wo K= 니 - 0 C. & Using ean. .0 K= 54 S 10 l = 4 4 4 *L*:4k using production function, Q 100 x V x 4k Q = 200K at 0 = 2,000 JO K* = 2000/200 (* = 40 Ano 2. Q = 100 URL A. Q = » Put k=k 1000R XIL ri JOOVE 2 1L*= 10000