Dr. Barry Haworth
University of Louisville
Department of Economics
Economics 301
Summer 2000

Exam #3

(Questions and Suggested Answers)

Section 1: Answer both questions 1-2 below
1. A monopolist faces a market demand (Q) and marginal revenue (MR) curve given by

Q = 70 - P
MR = 70 - 2Q

The monopolist produces at a constant short run average and marginal cost, whereby AC = MC = 20.

a. If this monopolist wants to maximize profits, how much output should the monopolist produce?

Set MR = MC
70 - 2Q = 20
Q* = 25

b. Calculate the profits, consumer surplus and deadweight loss associated with producing the output level you reported in part a.

First, find P*
Q* = 70 - P*
25 = 70 - P*
P* = 45

Now, let's consider what the graph would look like. The orange area is consumer surplus (CS), the yellow area is profits (p), and the blue area is deadweight loss (DWL).

We calculate these values as follows:

p = (45 - 20)(25) = $625
CS = (1/2)(70 - 45)(25) = $312.50
DWL = (1/2)(45 - 20)(50 - 25) = $312.50

c. Demonstrate how this monopolist can implement a two-part tariff to increase profits beyond those you reported in part b (this question requires actual numbers and an explanation for full credit, not discussion only).

A two-part tariff involves setting a fixed fee (e.g. for entry or hookup) and a per-unit fee. The fixed fee determines the size of the potential market and the per-unit fee determines how much is purchased.

Here, the monopolist can set any fixed fee it wants, except that the fee revenue does have a limit because the fee is "taken" from any existing consumer surplus and deadweight loss. If the monopolist leaves the per unit price at $45, then the most fixed fee revenue that can be obtained is $312.50 (i.e. the value of CS when P = $45). Therefore, by charging a fixed fee of $1 and a per-unit price of $45, the monopolist can earn the original profit of $625 as well as an additional dollar from every consumer in this market who wants to buy something.

2. Two firms (A and B) are engaged in an advertising game. Their strategies are: (i) to conduct a heavy advertising campaign, or (ii) conduct a light advertising campaign.

The payoffs relating to these strategies are as follows:

(a) if both firms choose heavy advertising, then firm A makes $5 million in profit and firm B makes $2 million in profit.

(b) if both firms choose light advertising, then firm A makes $2 million in profit and firm B makes $4 million in profit.

(c) if firm A chooses heavy advertising and firm B chooses light advertising, then firm A makes $3 million in profit and firm B makes $3 million in profit.

(d) if firm A chooses light advertising and firm B chooses heavy advertising, then firm A makes $4 million in profit and firm B makes $3 million in profit.

a. Construct a table (i.e. normal form game), similar to that in class, that illustrates the strategies and payoffs for each player.

b. Is this an example of the classic Prisoner's dilemma game discussed in lecture? Explain.

Yes. The Prisoner's dilemma involves a cooperative and noncooperative outcome. The dilemma is that, assuming players maximize their own benefit, the players end up with the noncooperative outcome, but at least one would be better off if they could just get to the cooperative outcome. That is, by cooperating (colluding) these firms could improve upon the Nash equilibrium attained under individual profit maximization.

Here, we see that the Nash equilibrium will be A - Heavy Advertising, B - Light Advertising (explained below), but by cooperating, these firms could achieve A - Light Advertising and B - Heavy Advertising. This would provide a gain for firm A with no change in firm B's result.

c. If it exists, then what is the (Nash) equilibrium of this game? Explain.

The Nash equilibrium is A - Heavy Advertising, B - Light Advertising. These choices reflect A and B's dominant strategies. That is, no matter what firm B (firm A) does, firm A (firm B) makes greater profits by choosing a strategy of heavy advertising (light advertising).

Section 2: Answer two of the three questions below.
1. Monopoly firms may choose linear or nonlinear pricing strategies. Linear pricing is said to distort the allocation of resources. During lecture, we discussed two "effects" relating to this misallocation (also including in the text): the allocation effect and the distribution effect.

a. Define/discuss each of these two effects and why they are problems?

The allocation effect concerns whether price is equal to marginal cost. When a monopolist sets a profit maximizing price, that price exceeds marginal cost. This is problematic from an allocational perspective because prices signal value and direct how resources are used. If P > MC, then the value of the monopolist's last unit of output is greater than the cost of the last resource used in producing that unit of output. Society would prefer more output, but doesn't get it. Consequently, output is too small.

The distribution effect concerns how surplus is distributed after a transaction is completed. In the case of monopoly, vs. perfect competition, there is some consumer surplus that is redistributed to the monopoly. Some consumer surplus is also lost to deadweight loss. To fully realize the extent of this problem, however, it is also necessary (as the text points out) to have some idea of how society views this redistribution. That is, a better understanding of "equity" is needed.

b. Does switching from a linear pricing strategy to a nonlinear pricing strategy like price discrimination eliminate the concerns associated with these two effects? Explain.

A linear pricing strategy involves setting one price. Nonlinear pricing involves setting multiple prices. With price discrimination, we get at least two different (per unit) prices, charged on the basis of consumer differences. The monopolist will consider differences in some demand-related characteristic that relates to willingness to pay for the product and charge prices accordingly. Of course, this information is not easy to get for all consumers and so the monopoly will be limited in some respects. If the monopoly can keep low price consumers from reselling to high price consumers, then this strategy will work. The monopoly will secure additional consumer surplus or possibly (by setting a price lower than the linear price) "take" some of the former deadweight loss. This makes it possible to resolve the allocation effect problem, but not the distribution effect because the monopolist uses price discrimination to possibly redistribute even more consumer surplus to profits.

2. The threat of potential entry in imperfectly competitive markets affects the behavior of existing firms. Discuss each of the following:

a. how the threat of entry affects the pricing behavior of (existing) firms

To best understand how firms react to entry, it is important to realize what entry means to existing firms. When products are homogeneous, or at least somewhat close substitutes, entry will decrease the profits of existing firms. Firms have a strong incentive to deter or prevent entry whenever possible.

A firm's pricing behavior may change in one of several ways. The most obvious response is a lowering of price. How low the price falls depends upon the intensity of price competition within the market. The more intense the price competition, the lower the price falls (and closer to marginal cost). For some firms, price may fall significantly, as these existing firms attempt to discourage entrants from coming into the market (or staying long). Limit pricing is one example of this. If entrants have higher costs than the existing firm(s), then the existing firms may set a price that is below the average cost of the entrant. This discourages the entrant from staying, and when the entrants exits, the price can rise to former levels. Quite often, however, it is difficult to know whether these entrants are less efficient. Firms engaging in this type of price war may find it more costly than simply accommodating the entry of these firms.

b. possible strategic actions by (existing) firms that are designed to deter entry

There are several strategies that firms can use to deter entry. One strategy, limit pricing, is discussed above. Other strategies include raising the cost of rivals, increasing the startup costs associated with producing a good, lowering one's own costs (to obtain a cost-advantage), etc. For the most part, these are all strategies focused upon developing natural barriers to entry. In some cases, e.g. process innovation, we may want to ask why the firm wouldn't be doing this already. That is, how likely is it that a firm will choose process innovation in response to entry rather than as an ongoing means of increasing profit. It is possible that firms may focus also on developing legal barriers to entry. One approach might be to develop a "wall of patents" that make it difficult for potential entrants to navigate through.

3. Solarmobile has a monopoly on the production of solar powered compact cars. Assume that the company is currently able to produce at zero cost but is capable of producing up to 25,000 of these cars per year.

The cars sell for either of two prices (Solarmobile decides which price).

If Solarmobile sets P = $10,000, then market demand is 25,000 cars

If Solarmobile sets P = $5,000, then market demand is 50,000 cars

A potential entrant is considering whether to enter this market, but to do so the firm must build a production facility. The fixed cost of the production facility would be the only costs incurred by the entrant. Depending on how much the firm needs to produce, the firm would choose one of two types of production facility:

  • to produce 20,000 or fewer cars the entrant would spend $100 million
  • to produce 20,001 - 25,000 cars the entrant would spend $120 million

(for simplicity, assume that these facilities can be built overnight) Furthermore, if the firm enters, then the entrant and Solarmobile will each serve half of the overall market demand.

a. If the entrant first decides whether to enter before Solarmobile chooses a market price, then draw this situation as a sequential game in extensive form (i.e. as a game tree) where the payoffs are the profits (for each firm) associated with each potential outcome.

This game is depicted below.

The entrant moves first, deciding whether or not to enter. Solarmobile moves second, deciding whether to set a price of $10,000 ($10K) or $5,000 ($5K). The profits/payoffs from each set of actions are given on the far right. Note that Solarmobile is constrained from producing the entire market demand of 50,000 cars if the price is $5,000 and the entrant doesn't enter.

b. If this game has a Nash equilibrium, then what is it? Explain.

If we assume that the firms do not interact directly, then this game does not have a unique Nash equilibrium. The outcome of this game can be where entry occurs and the price of $10,000 is set, or where entry occurs and the price of $5,000 is set. To find this, we look ahead to see what Solarmobile will do and then see what the entrant will do. That is, look ahead and work backwards. Solarmobile realizes that the entrant will come into the market no matter what happens because this firm makes positive profits by entering. Solarmobile receives the same profits no matter what price is set, and so this firm will be indifferent between the two possible prices. Therefore, two equilibria are possible.

c. Does the entrant have an incentive to "bribe" Solarmobile to choose a different price? Explain.

The entrant has a big incentive to bribe Solarmobile. If the price is set at $10,000, then the entrant will net an additional $20 million in profit ($25 mill vs. $5 mill). This firm should be willing to bribe Solarmobile up to this amount to set the higher price. As Solarmobile is indifferent between the two prices, the bribe would cause Solarmobile to suddenly prefer the higher price.