Consider a production function for a firm:
Q = 2KL1/2
where Q is output, K is capital, and L is labor. 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? Round your answer to the nearest hundredth.
d. 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? (Hint: you can do this without a calculator - and, then you can check your answer with a calculator!)
e. Given the information in (d), what is the total cost for the firm of producing this level of output?
f. Given the information in (d) and (f), calculate the firm's average total cost of producing this new level of output.
g. Given your answer to the above set of questions, what can you conclude about returns to scale for this firm over the range of output you have considered?