Question 1: A plant's production function is Q=L1/3K2/3. The price of labor services w is $4 and of capital services r is $5 per unit. (15 Marks)

a) In the short-run, the plant's capital is fixed at K=8. Find the amount of labor it must employ to produce Q=10 units of output. (2 Marks)

b) What is the total cost of producing this output in the short run?. (1 Mark)

c) What will happen to the MPL as capital increases from 8 to 10?. (1 Mark)

d) If the firm is in the long run and wants to produce 10 units, how much capital and labor will it hire?. (4 Marks)

e) What is the total cost of producing 10 units in the long run?. (1 Mark)

f) Mathematically, using the cost minimization condition, explain why in the long run the firm will not hire 8 units of capital and the amount of labor you found in part (a). (2 Marks)

g) Graph the isoquant and isocosts associated with the short run and the long run on the same graph (clearly show the optimal labor and capital combination in both the cases). (3 Marks)

h) From your answer in part (b) and (e), what do you observe about the costs in both the short run and the long run?. (1 Mark)