Theory of Production:
problem 1: Suppose a firm’s budget were large enough to employ 100 units of either labor or capital, the cost of a unit of labor being the same as a unit of capital. The production function is X = KL . Given that output must be at least 20, what is the maximum number of people the firm could employ?
problem 2: The production function of a small shop that frames pictures is Q = 5 √LK where Q is the number of pictures framed per day, L is labor hours and K is the machine hours. Suppose 9 labor hours and 9 machine hours, are used every day, what is the maximum number of pictures that can be framed in a day? find out the marginal product of labor when 9 labor hours are used each day together with 9 machine hours. Suppose the firm doubles both the amount of labor and machine hours used per day, find out the increase in output. Comment on the returns to scale in the operation.
problem 3: Suppose you are an efficient expert hired by a manufacturing firm that uses two inputs, labor (L) and capital (K). The firm produces and sells a given output. You have the following information: P_{L} = Rs 4, P_{K} = Rs 100, MP_{L} = Rs 4, MP_{K} = Rs 40.
a) Is the firm operating efficiently? Why or Why not?
b) What should the firm do?
problem 4: Suppose that in an isoquant mapping, you should consider three isoquants with 1000, 2000 & 3000 units of output. The price of capital is Rs 2 a unit, and the price of labor is Rs 1 per unit.
a) Construct an expansion path.
b) How many units of each input are used to produce each level of output efficiently?
c) What is the minimum cost of producing each level of output?
d) Answer each problem under the assumption that the price of labor is now Rs 2 a unit and the price of capital is Re 1 a unit.
problem 5: The production function of the personal computers for DISK Company is given by Q = 10 √KL where Q is the number of computers produced per day, K s the hours of machine time, and L is hours of labor input. Disk’s competitor, FLOPPY Company is using the production function Q = 10 K^{.6} L^{.4} .
a) If both companies use equal amounts of capital and labor, which will generate more output?
b) Assume that capital is 9 machine hours, but labor is unlimited in supply. In which company is the marginal product of labor the greater? describe.
Theory of Cost:
problem 6: A firm producing hockey sticks has a production function given by X = 2 √KL In the short-run, the firm’s amount of capital equipment is fixed at K = 1000. The rental rate for capital (PK) is PK = v = Re 1.00; and the wage rate for L is PL = w = Rs 4.00.
a) find out the firm’s short-run total cost curve. find out the short-run average cost curve.
b) What is the firms short-run marginal cost function? What are the STC, SATC & SMC for the firm if it produces 25 hockey sticks?
problem 7: Assume that input prices are constant at r = 1, w = 1, with technology which consists of 5 processes having the following properties:
A producer can purchase labor without limit, but can purchase machine-hour only up to a total of 75. find out
a) The producer’s total and average cost of producing 100, 200, 300, 400 and 500 tons.
b) At what output levels will marginal cost change?
c) Give the marginal costs and output ranges over which each level of marginal cost is relevant.
problem 8: A firm is employing 100 hours of labor and 50 tons of cement to produce 500 blocks. Labor costs Rs 4 per hour and cement costs Rs 12 per ton. For the quantities employed MP_{L} = 3 and MP_{C} = 2. Show this situation in an isoquant-isocost diagram. describe and show in the diagram, how the firm can produce the same output at a lower total cost.
problem 9: If the marginal product of L is MP_{L} = 10K – L and the marginal product of K is MPK = 10L – K, then what is the maximum possible output when the total amount that can be spent on K and L is Rs 1000 and the price of K is Rs 5 and the price of L is Rs 5.
problem 10: Is a firm minimizing its costs, if the marginal product of labor is six, the marginal product of capital is five, the wage rate is Rs 2.00 and the interest on capital is Rs 1.00? If not what must the firm do to minimize its costs?