The production function is given by: Q = 50K^1/2 L^1/2

w = $5; r = $10

a. Find the cost-minimizing combination of inputs to produce 10,000 units. You must show the Lagrangian equation

b. The firm has now decided that it wants to produce 12,000 units of output.

1. Assuming that capital is fixed at the level you chose in a., what will the firm do in the short run? What will it cost to produce the 12,000 units?

2. What will it cost to produce this in the long run, and what is the cost-minimizing input choice?

c. Show graphically what you have found in parts a and b of this problem on an isoquant map.

Now suppose that the wage rate rises to $10.

Use a graph and discuss how this will change this firm's LONG RUN input and output choice. Please include a discussion of hypothetical scale and substitution effects.