04 Jun Question Econ 2200 Assignment #4, Late assignments are not accepted. Assignments shoul
Question
Econ 2200
Assignment #4,
Late assignments are not accepted. Assignments should be stapled and neatly written in ink (pencil is not accepted) or typed. (Show all calculations)
Q1. Suppose a firm has the following production function: Q = L0.5 K0.5
a. Does the production function exhibit constant, increasing or decreasing returns to scale? Prove. What is the shape of the firm’s long-run average cost curve? [4 marks]
b. Derive the input demand curve for labour when wage = w and the rental cost of capital = r. [6 marks]
c. What are the optimal levels of L and K when w= 20 and r =80? What is the cost of production Q = 100? [4 marks]
d. If K is fixed in the short-run, what will the firm’s output expansion curve (path) look like? Explain. [2 marks]
Q2. The cost of a person-hour of labour is w and the cost of a machine-hour of capital is r. The firm’s long- run total cost equation is TC(Q) =w 1/2 r 4/5 . Given this information, which change would cause the greater upward rotation in the long-run total cost curve: a 10 percent increase in w or a 10 percent increase in r? Based on your answer, is the firm’s production operation more capital intensive or labour intensive? Explain. [4 marks]
Q3. The production function is given by Q = LK. With w = 1 and r = 1.
a. Derive the equation for the firm’s long-run total cost curve as a function of output Q. [4 marks]
b. Solve the firm’s short-run cost-minimization problem when capital is fixed at K = 5. Derive the equation for the firm’s short-run total cost curve as a function of quantity Q and graph it together with the long-run total cost curve. [4 marks]
Q4. A firm produces a product with labour and capital, and its production function is described by Q = 2L0.5K0.5. Suppose that the price of a person-hour of labour equals 4 and the price of a machine-hour of capital equals 1. Derive the equations for the long-run total cost curve and the long-run average cost curve. [4 marks]
Q5. A firm’s long-run total cost curve is TC(Q) = 100Q0.5 . Derive the equation for the corresponding long-run average cost curve. Does the firm’s marginal cost curve lie above, below or on the firm’s average cost curve? Explain. [4 marks]
Q6. Explain how an increase in the price of labor would affect the long-run average cost curve. [4 marks]
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