1. (40 marks) Consider a production function for a firm:

Q = 2K^1/2L^1/2

where Q is output, K is capital, and L is labor. MP_K= K^-1/2L^1/2 and MP_L= K^1/2L^-1/2. Suppose initially K is equal to 25 units and L is equal to 16 units. You also know that the price of K, Pk, is $10 per unit of K and the price of L, Pl, is $4 per unit of L.

a. Given the above information, what is the value of output?

b. What is the total cost of producing the output you calculated in (a)?

c. What is the average total cost of producing this level of output?

d. What is the marginal revenue product of K? Can you tell whether K=25 maximizes the profit? Why?

e. What the MRT?

f. Suppose the amount of labor increases to 32 units and the amount of capital increases to 50 units. Given this information, what level of output can the firm now produce?

g. Given the information in (f), what is the total cost for the firm of producing this level of output?

h. Given the information in (f) and (g), calculate the firm's average total cost of producing this new level of output.

i. Given your answer to the above set of questions, what can you conclude about returns to scale for this firm?

h. Find the optimal input bundle for Pk=10 and Pl=4.

e. What the MRT? f. Suppose the amount of labor increases to 32 units and the amount of capital increases to SI] units. Given this information, what level of output can the firm now produce? [Hint: you can do this without a calculator and, then you can check your answer with a calculator!]| g. Given the information in If], what is the total cost for the rm of producing this level of output? h. Given the information in if} and [g], calculate the firm's average total cost of producing this new level of output. 1. Given your answer to the above set of questions, what can you conclude about returns to scale for this firm? it. Find the optimal input bundle for Pk=1 and PI=L 3. [40 marks} Consider a production function for a firm: [1 = EKWLL'? where [1 is output, K is capital, and L is labor. MPF K'lszm and MPL= KmL'm. Suppose initiall1_.Ir K is equal to 25 units and L is equal to 16 units. You also know that the price of K, Pk, is Sit] per unit of K and the price of L. PI, is $4 per unit of L. a. Given the above information, vvhat is the value of output? I]. What is the total cost of producing the output vou calculated in {a}? c. What is the average total cost of producing this level of output? d. What is the marginal revenue product of K? Can you tell whether K=25 maximizes the profit? Whv