Microeconomics Asdsignment
1. Expect one question from any post midterm discussion and none from any pre midterm discussion.
2. Assume a one output production function which we know very little about. But over a period of three years we see that (1) with p = 1, w = 1 the firm choose x = 2, y = 5 (2) with p = 3, w = 0.5, the firm will choose x = 4 and y = 8 and (3) with p = 4, w = 2, the firm will choose x = 3, y = 7. Graph the isoprofit lines associated with each pair of prices and quantity choices. Show on your graph what we have learned about the firm's technology.
3. Assume we have a perfect substitute technology so that y = x1 + x2. Assume that w1 = 1 < 2 = w2. Graph the short run average total cost curve if x2 is fixed to be 1, 2, or 3 respectively. Graph the long run average total cost curve. Repeat the same exercise if the technology is perfect compliments, i.e. y = min(x1, x2).
4. Suppose that the firm's total cost function is of the form C(y) = 100 + 10x + x2. Where does the average cost function reach a minimum? Consider the following demand curves:
(a) D(P ) = 100 - 3P (b) D(P ) = 90 - 3P (c) D(P ) = 100 - 2P
For which of these examples is the firm a natural monopoly?
5. Suppose there are two firms in a market with demand D(p) = 100 -P . Assume that there are two possible firms who can serve this market. One has a total cost function of C1(y) = 100 + y. The other firm has a cost function of C2(y) = 12y. Suppose that Firm 1 serves this indus- try as a monopoly. What will be the outcome (price and quantity)? Suppose the same for Firm 2? Which maximizes total surplus?
(a) Now assume that the right to be a monopolist will be "auctioned by price?" That is each firm will submit a price that they will charge if they are a monopolist and the lowest price will win the firm the monopoly. [Hint: For those of you who have game the- ory experience you can probably predict how firms will behave in equilibrium. But as a general hint. Find the prices that will give each firm zero profits. The lowest price a firm will bid is this price. Take the firm that has the lowest break even price you just found. Look at all the prices between the two average costs and pick the one that maximizes their profit. This is the outcome. Pay special care to the endpoints.]
(b) Repeat the above example but assume a different model for auc- tioning off the right to be a monopolist. Suppose instead that they must bid a flat payment up front to be the monopolist. Assume that the firm that would earn more profits bids a fee equal to the profits of the less profitable potential monopolist and wins. Who wins this auction?
Of the two auction methods, which maximizes:
i. Consumer surplus
ii. Government revenue
iii. Output
iv. Total surplus (assuming that gov't revenues are part of total surplus)?
6. Assume a monopolist with total cost C(y) = 500+20y. Market demand is Q = 100 - P .
(a) If price is set equal to marginal cost, what will the firm's profits be?
(b) If price is set equal to average cost, what will the loss be in terms of output and total surplus from the first part? [Your answer should be a number.]
(c) Suppose all consumers are identical. What will be two-tariff sched- ule (membership fee + marginal price) that maximizes total sur- plus while assuming zero profits?
(d) Let's divide the demand into ten individual demands. Assume six "rich" consumers with demand functions: P (y) = 100 - 6.3y and four "poor" consumers with a demand function: P (y) = 100-80y.
i. What is the highest fixed fee that poor consumers will be willing to pay for the right to purchase at marginal cost?
ii. In this model the fixed fee necessary for efficiency is 50. How does this compare to the above number?
iii. Suppose the monopolist is restricted to marginal cost pricing and they must charge a fixed fee to the 6 rich consumers who will be the only ones to participate in the market? What will be the deadweight loss in this outcome?
iv. Suppose they charge a fixed fee necessary for everyone to par- ticipate and a per unit price necessary to achieve zero profits. What will be the deadweight loss to this outcome?
7. Consider the above problem and let's consider an optimal pair of two- tariff prices. One will be the solution to the last part of the previous problem. The next will involve a fixed fee of F = 51 and a per unit price, p = 20.50. Show that offering this pair of schedules Pareto dominates just offering the uniform two-tiered schedule we found above. [Hint Remember what it means for the two groups (rich and poor) for a new policy to Pareto Dominate a status quo policy. Note that this schedule will lead to poor consumers choosing the original tariff. Note also that it is important to show that this policy does not lower profits for the monopolist.]
8. Show either graphically or through an argument the difference in effects of a profit tax and a revenue tax.
9. Show how that in a period of high inflation, previous outcomes with low inflation might be useful in helping analyzing the effects of a ceiling on nominal interest rates.
10. Remember that when we restrict ourselves to linear prices (no fixed fees), economic theory says that efficiency is maximized by charging a higher marginal price to consumers (or markets) with more inelastic demand. Can you give a real world example where this result can be seen in current policy? Can you give an example where the real world policies do not satisfy this? What, in your opinion is (was) the reason that such non-efficient policies were chosen? [Points will be rewarded for originality]
11. Consider an industry with marginal cost of 10 and a demand of D(p) = 100 - p. What would be the deadweight loss of having this industry convert from competitive to monopoly? Suppose that to become a monopoly the firm must undertake an additional 15 units of advertising per unit sold. What is the deadweight loss of permitting such adver- tising (assuming that it leads to a monopoly)? Assume that market demand is unaffected by advertising. Lets say that there is a wasteful expenditure x such that if the firm spends x upfront, they will become a monopoly. What is the maximum the firm will be willing to spend on x? What are the implications for such a theory on the DWL of monopoly?
12. Show that a monopolist always sets price above MC.
13. Assume an industry with a cost function of c(y) = 49+2y and a demand of 100 -y. Assume there is an entrant and an incumbent. Assume that the incumbent announces their price before the incumbent decides to enter the industry, what is the highest price (lowest quantity) that the incumbent can offer which keep the entrant outside the market? Finally assume that if the incumbent is forbidden to make an announcement, there will be entry and both firms will adopt average cost pricing. Does it maximize social surplus to ban announcements?
14. Explain, with the aid of a graph, how deadweight losses from monopoly may be more trapezoidal than triangular.