A common answer in micro and macro
This task consists of two parts. They are indirectly related, and the answers to them are somewhat similar. If you answer part (a) correctly, it'll be easier for you to come up with a correct answer to (b), and vice versa.
(a) (15 rp) It often happens that, under the threat of entry of a competitor, an incumbent monopolist lowers the price even before the entry actually occurs. But this monopolist's behaviour is, at first glance, irrational as the price before entry has no effect on the prices and quantities after entry and thus the pre-entry price cannot affect the entrant's decision to enter and eventually deter entry. Lowering the pre-entry price relative to the optimal price only causes the incumbent to lose the pre-entry profits. Propose a simple verbal model in which such monopolist's behaviour is nevertheless rational.
Short: signaling by the monopolist its low level of costs.
Long: The key is that the entrant doesn't have complete information about the monopolist's costs. Hence the entrant doesn't know how painful the price war or quantity competition will be in case of entry.
(b) (15 rp) Different individuals and firms have different inflation expectations. Research shows that when the expectations differ little, contractionary monetary policy (raising the interest rate by a central bank) leads to a decrease in inflation. However, when the inflation expectations differ a lot, raising the interest rate can paradoxically lead to an increase in inflation. Explain this phenomenon.
Short answer: raising the interest rate by a CB is a signal for the economic agents that the aggregate demand is high (because the tightening of monetary policy is only necessary when the aggregate demand is high). Upon realizing that the demand is high, the firms raise prices.
Long answer: Irrespective of the variance of inflation expectations, the classic monetary policy transmission mechanism is at work: when the interest rate grows, investment (and, possibly, consumption) contract (consumption through the effect of the interest rate on consumer loans). This lowers the aggregate demand and slows down inflation. However, when the differences in inflation expectations are large, there is a high level of uncertainty about the economy, and the agents are not likely to have right information about the aggregate demand. The CB, on the other hand, is likely to have better information as it sees the full picture and has overall better data, models, and economists. Thus, in times of high uncertainty, actions of the CB convey valuable information to the agents. In particular, raising the interest rate signals that the AD is high. Upon realizing that the demand is high, the firms raise prices. If this second informational effect is strong enough, it outweighs the classical transmission mechanism, and inflation increases.
Bibliographic note: The signaling explanation of the phenomenon in the first part of the problem (called "limit pricing") was proposed by Milgrom and Roberts in 1982. The second part is based on the recent work of Falck and coauthors.