Question

Given the following production functions:
F(L,K) = L + K
F(L,K) = (L + K)^2
F(L,K) = (L + K)^1/2

1. Determine the returns to scale for each function.

2. For the rest of this exercise assume that the price of labor, w, and the price of capital, r,
equal 1: w = r = 1. Find the conditional input demand functions of labor and capital (the
cost-minimizing combinations of labor and capital).

3. Now find the cost functions for each of the production functions.

4. For each of the above production functions, functions, plot the cost function on the same
graph with Q on the horizontal axis and total cost on the vertical axis.

5. Find and plot the average and marginal cost functions with Q on the horizontal axis and
average cost on the vertical axis. Related these graphs with your answers to the returns to
scale of the production function you found in subquestion 1.

Answer 1

Graphs

Green : for crs production function

Purple : for DRS , 3rd production function

Black : for IRS, 2nd production function

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