Reference no: EM132482539

1. For the production function Q = (KL)^0.5, answer the following questions:

a. What are the equations for the Average Product of Labor and the Average Product of Capital?

b. What are the equations for the Marginal Product of Labor and the Marginal Product of Capital?

c. Does this function exhibit increasing, decreasing or constant returns to scale? Briefly explain.

2. A jeweler can potentially use two inputs in her handcrafted jewelry: copper or bronze. She finds that when she minimizes her costs, she uses either copper or bronze, but never both. What must her isoquants look like?

3. Miguel and Jake run a paper company. Each week they need to produce 1,000 reams of paper to ship to their customers. The paper plant's long-run production function is Q = 4K^0.75L^0.25, where Q is the number of reams produced, K is the quantity of capital rented, and L is the quantity of labor hired. For this production function, the MPL = K^0.75/L^0.75 and the MPK = 3L^0.25/K^0.25. The weekly cost function for the paper plant is C = 10K + 2L, where C is the total weekly cost.

a. What ratio of capital to labor minimizes Miguel and Jake's total costs? 

b. How much capital and labor will Miguel and Jake need to rent and hire in order to produce 1,000 reams of paper ?each week? 

c. How much will hiring these inputs cost them?