1)If a production function is: Q= 250K^0.7L^0.3. Determine the marginal product of capital and the marginal product of labor when K = 50 and L= 150.

2)Suppose that a firm's production function is Q=7K^0.5L^0.5 where Q is units of output, K is machine hours, and L is labor hours. Suppose that the amount of K available to the firm is fixed at 144 machine hours.

A.What is the firm's total product of labor equation?

B.What is the firm's marginal product of labor equation?

C.What is the firm's average product of labor equation?

3)A firms production function is Q= 250K^0.7L^0.3 verify that AP_L=MP_L when AP_L is maximized.

4)If a production function is: Q=200KL-10KL². Verify that AP_L=MP_L when AP_L is maximized.

5)If a production function is: Q= 250K^0.7L^0.3. verify that this expression exhibits the law of diminishing marginal product with respect to variable labor input.

6)If a production function is: Q= 250K^0.7L^0.3. suppose that Q=1000.what is the equation of the corresponding isoquant in terms of L?

7)Suppose that the average product of labor is given by the equation AP_L=100+500L-5L²

A.What is the equation for the total product of labor (TP_L)?

B.What is the equation for the marginal product of labor (MP_L)?

C.At what level of labor usage is AP_L=MP_L?

8)Consider the following production function: Q= 300KL + 18L² + 3K² - 0.5L³ - 0.25K³ where Q is units of output per month, L is the number of workers, and K is units of capital. Assume that L=20 and K=10.

A.Calculate total output per month.

B.Calculate MP_L and MP_K

C.Calculate AP_L and AP_K

9)Consider the following production function:

Q = 225L + 100K - 7.5L² - 5K² + KL; where Q represents units of output per month, L is the number of workers, and K is units of capital.

A. how much K and L will maximize Q?

B. What is the maximum output per month?

10)Does the following production function have increasing, decreasing or constant returns to scale (show your workings)

A. Q =5K ²+ L²

B. Q =4K^1/3 L^1/3