2. Suppose a producer's production function is F(X,L) = 3KL The cost of K is 20 (r=20) and the cost of L is 80 (w = 80) The finn wants to produce 30 units of output. a. What is the cost-minimizing way for the firm to produce 30 units of output? How many units of capital and how many units of labor should be used? b. Suppose the firm has committed itself to 4 units of capital (K) and therefore is operating in the short run. What combination of inputs is the least costly way for it to produce 30 units now?

Suppose a firm with a production function given by Q = K0.4L0.6 produces 100 units of output. The firm pays a wage of $20 per units and pays a rental rate of capital of $40 per unit. (Note: MPL = 0.6K0.4L-0.4 and MPK = 0.4K-0.6L0.6 ) What is the minimum cost of producing 100 units of output?

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The production function for a product is given by q= 10K^(1/2)L^(1/2) where K is capital, and L is labor and q is output d)  Now suppose w =30 and r = 120. What is the minimum cost of producing q=1000. (You must show your work by clearly writing the equations that you use to derive the cost minimizing levels of L and K.) e)  Now suppose that the firm is in the short run and cannot vary the amount of capital. That is, it must use the same amount of capital as in part d). However, the firm wants to produce 1200 units of output. How much labor should it use to minimize its cost and what is the minimum cost of producing q =1200?

Question 2: Suppose a production function is given by F(K,L) = KL² the price of capital is $10 and the price of labor $15. What combination of labor and capital minimizes the cost of producing any given output?

Consider the following marginal cost function MC= 5 + 2qi. (a) Does the production process exhibits increasing returns? decreasing returns? constant returns? (b) If the price is $23. What’s the optimal production level? (c) If the price is $31. What’s the optimal production level?