Production function exhibit diminishing returns to capital

Question

Question 1. Suppose that the production function for an economy is given by

Y = A K^1/2 L^1/2

Where Y is output, A is the level of technology, K is capital and L is labor.

a. If the value of A is 10, and there are 100 units of K and 400 units of labor, what is the value of output equal to in this economy?  Show your work.

b. Given the values in part (a), what is output per worker?

c. Given the values in part (a), what is output per unit of capital?

d. What is the marginal product of labor equal to for this production function? Do not calculate a numerical value for this, but provide a general equation for MPL.

e. Does this production function exhibit diminishing returns to labor? (Assume capital and technology are constant when answering this question.) Explain your answer.

f. What is the marginal product of capital equal to for this production function? Do not calculate a numerically value for this, but provide a general equation for MPK.

g. Does this production function exhibit diminishing returns to capital? (Assume labor and technology are constant when answering this question.) Explain your answer.

h. What does the total wage bill equal for this economy given the values in part (a)?

i. What does the total return to capital equal for this economy given the values in part (a)?

j. What do you know about the ratio of labor-income to capital-income for this economy given the values in part (a)?