4. Suppose that your firm has a short run cost function of CSR = 250 + q3.
a) Calculate the marginal cost function (MC), the average variable cost function (AVC), and the average total cost function (AC).
b) Find the quantity at which MC=AC. Why is this an interesting point when thinking about the firm’s profits?
c) Suppose that the price of this firm’s output is P=$48. Calculate the profit maximizing level of production. Calculate the firm’s profit at this level of production, first by calculating total revenue and total cost, then by using price and the average cost function.
d) Should this firm shut down in the short run? Answer this question in two ways: first, compare the profit of producing q = 0 to the profit from 3c. Next, use the AVC function. In both cases, use these results to explain why the firm should shut down or stay in business. If you decide that this firm should stay open in the short run, how low would the price have to drop for the firm to shut down immediately?
e) Lastly, draw the cost curve diagram for this problem: P, AC, MC, and AVC. Since these are polynomials I won’t get picky – here’s the level of detail I expect.
- i) Draw your MC and AVC curves roughly to scale based on the coefficients.
- ii) AC, MC, and AVC curves need to obey the rules we discussed in lecture.
- iii) Label the following points: 1) q where MC=AC, and the associated MC. 2) Price of the good, and the profit maximizing quantity. 3) AC and AVC of the profit maximizing quantity. 4) The profit rectangle.
