1. (10 points) Show on a diagram how commitment to a technology with low marginal cost shifts the reaction curves in a market where firms sell differentiated products and compete by setting prices. Would this be a wise move for the firm? Is the proper strategy here Top Dog, Puppy Dog, Lean and Hungry Look, or Fat Cat?
ANSWER. Firm 1's reaction curve shifts to the left when it invests in a low-cost technology. The price of Firm 1 then falls, and Firm 2's falls in response. By being Tough, Firm 1 induces Firm 2 to reduce its price. This is a bad outcome for Firm 1, so the Puppy Dog strategy of not committing to low costs is the appropriate strategy.
2. (20 points) There are two types of managers. Fifty percent are high quality and the rest are low quality. High quality managers are worth $100,000 per year to a company and low quality are worth $50,000. The company cannot tell the difference, but it can verify whether a job candidate can speak Classical Greek.
(a) If the job only lasts one year, and it costs a high quality manager $20,000 to learn Greek and a low quality manager $60,000, what is the signalling equilibrium?
ANSWER. In equilibrium, Highs learn Greek and Lows do not. Companies
pay $100,000 for managers who know Greek and $50,000 to managers who
do not.
This is an equilibrium because nobody would deviate. Companies
break even. Highs have payoffs of 100-20 = 80, compared to 50 if they
deviate. Lows have payoffs of 50, compared to 100-60=40 if they
deviate. Firms cannot cut wages without losing their managers to
other firms. (If there were just one firm, with no competition, then
it would pay managers $0 regardless of whether they knew Greek or
not-- or if not zero, whatever was the minimum a
manager would accept.)
Note that the Low's payoff from deviating and learning Greek is not 50-60 = -10. If he deviates and learns Greek, the employers will believe he is High ability and pay him 100. Given that his cost of learning Greek is 60, however, he is still better off settling for 50 without having to learn Greek.
Nor is it an equilibrium for companies to pay $90,000 for Greek- speakers and $50,000 for others. One company could profitably deviate by offering $71,000 regardless of linguistic accomplishments. That company would get all the Highs, because their payoff there would be 71 instead of 90-20=70. It would also get all the Lows, but overall it would make more profit, because it would get all the Highs, instead of just as miniscule number.
There also exists another equilibrium, a pooling one like the equilibrium in part (b). What happens depends on expectations.
(b) If it only costs the low quality manager $40,000 to learn Greek, what is the equilibrium?
ANSWER. In
equilibrium, nobody learns Greek. Companies pay $75,000 for
managers who know Greek and the same to managers who do not.
Companies do not believe that learning Greek conveys any information.
This is an equilibrium because nobody would deviate. Companies
break even. Highs have payoffs of 75, compared to 75-20=55 if they
deviate. Lows have payoffs of 75, compared to 75-40=35 if they
deviate.
The behavior in part (a) of this question is no longer an equilibrium. A Low could deviate from it and learn Greek for a payoff of 100-40=60, higher than the 50 he would get not learning Greek.
In some signalling games, there is also a pooling equilibrium where everybody acquires the signal, and they acquire it because if they do not, they are believed to be the undesirable type. Here, that equilibrium would be: High and Low both learn Greek, companies pay Greek speakers $75,000 and other people $50,000, and companies believe that anybody who deviates by not learning Greek is a Low type. But that is not an equilibrium, because the Low types would deviate and refrain from learning Greek, for a payoff of 50 instead of 75-40=35.
3. (10 points) You sell high-quality, speedy computer printers. You believe that there are two kinds of customers in the marketplace. Type 1 consumers place a high value on quality generally, and they also tend to be customers who are price insensitive and would pay a higher price for any given quality level. Type 2 consumers, while also valuing quality, do not value it as much, and would, in any case, not be willing to pay as high a price as Type 1 consumers for any given quality.
One of your staffers says,``We should sell at a high price, and forget about the Type 2 consumers.'' Another staffer says, ``We should sell at a low price, and sell to all consumers, even if the profit margin is lower.'' A third staffer says, ``We should sell our regular printers at a high price, but purposely damage some of them and sell the damaged ones at low prices.
Evaluate the advice of the third staffer. Could he be correct under any circumstances whatsoever?
ANSWER. Yes, he could be correct. His hope is that the company can sell the printers at a high price to Type 1 consumers and a low price to Type 2 consumers. The tricky part is to keep the Type 1 consumers from wanting to buy the low-priced printers. The only way to achieve that is to damage the low-priced printers. The big question is whether the Type 2 consumers will still be willing to buy the damaged printers at a price greater than the marginal cost to your company of producing and damaging them.
The main difficulty people had in answering this question was in explaining why purposely damaging the printers would be helpful. Just mentioning price discrimination was not enough to get full credit. Nor is it a good answer to say that the third staffer is correct "if his suggestion would result in increased profits"--- that is like saying that the weather will be cold tomorrow if the temperature will be low. The key is to recognize that unless some printers are damaged, the seller will not be able to keep charging a high price to the Type 1 consumers-- that the big danger is cannibalizing sales at high prices to the Type I consumers.
Note that it is quite wrong to say that if the firm can tell Type I from Type II consumers, it should price discriminate and sell regular printers at a high price to Type I consumers and damaged printers at a lower price to Type II consumers. If the firm can tell Type I from Type II, it should not damage any printers. Rather, it should price discriminate and sell regular printers at a high price to Type I consumers and the same printers at a lower price to Type II consumers. The only possible reason to damage printers is to keep the Type I consumers from wanting to buy them at the low price, an unnecessary trick if the firm can simply forbid the Type I consumers to buy at the low price.