Suppose that a firm's output (Q) is produced with the inputs capital (K) and labor (L) according to the relationship Q = K^0.6 L^0.3. ("A "is 1, is 0.6 and is 0.3 in the production function Q = AK L .) Suppose also that capital's per unit dollar price (R) is 10, labor's per unit dollar price (W) is 5 and the firm's product sells for a dollar price (P) of 18.

1. What is the profit-maximizing amount of output (Q*) to produce?

2. What is the dollar value of profit at that Q*?

3. The profit-maximizing amount of capital to use (K*) is____ and the profit-maximizing amount of labor to use (L*) is ____

4. With K at K*, what is the value of the marginal product of labor in going from L* - 1 to L* ?

5. What about in going from L* to L* + 1?

6. Where is W in relation to these two numbers (above, below, between)?

7. With L at L*, what is the value of the marginal product of capital in going from K* - 1 to K* ?

8. What about in going from K* to K* + 1?

9. Where is R in relation to these two numbers (above, below, between)?

10. What are returns to scale in production?

11. Are they increasing, constant, or decreasing?