Questions:
Q1. If the average variable cost curve is horizontal, what is the shape of the short-run marginal cost curve? What shape would the short-run average cost curve be?
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 longrun 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.
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. [6 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.
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.
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.