Question 1: (15 Marks) Rose's firm faces the following production function: q = K0.5(L-1)0.5. The rental cost of capital is 20 and the wage is 5.

a) In the short run, capital cannot be changed and is equal to 25. What is the amount of labor required to produce 25 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 25 to 26?. (1 Mark)

d) If the firm is in the long run and wants to produce 25 units, how much capital and labor will it hire?. (4 Marks)

e) What is the total cost of producing 25 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 25 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)