Microeconomics Exam

Below is the final exam for my intermediate microeconomics course (by the way, just got the instructors evaluation result: I rank 6 out of 30 -- not too bad).

1. Think about a monopoly market.
1. A monopolist is a single player in its market. He/she can search for an optimal price. However, a rational monopolist can not set any arbitrary price. Why?
2. Imagine an apple monopolist in Medan. He told you that today he gained maximum profit. You know from his neighbor that his marginal cost of production is Rp 4,000. But he sells his apples at Rp 7,500 each. There is another monopolist selling apple in Jakarta. She prices at Rp 5,000 and produces at the same marginal cost as the Medan monopolist’s. A friend of yours claims that the price difference is due to “Medan people are more responsive to apple price changes than Jakarta people”. Is he right or wrong? Give me a proof (assume away arbitrage between Jakarta and Medan).
   

2. Following on # 2:
1. The Jakarta monopolist – let’s call her Patrice – turns to you. She complains that there are now new competitors coming in to Jakarta. The first competitor uses advertisement that goes: “New Kind of Apples: Redder!”. The second competitor goes: “Super Apples: They Smell Better!”. So do other competitors; all try to appear differently. You, however; know that actually consumers don’t care that much with color or smell of the apples. What kind of market is this now in Jakarta?
2. As it turns out, the new entrants put downward pressure to price. Now you can buy apple in Jakarta at Rp 4,500 each. Given the same marginal cost, is the market now efficient?
3. Threatened by the increasing competition, Patrice changes her strategy. She buys a new technology from Singapore that allows her to be more efficient. Too bad, one competitor named Patrick follows suit. Other competitors can not compete anymore against Patrice and Patrick; they quit. What kind of market is this now?
4. As they are the only players now, Patrice and Patrick become extra cautious. Meaning, one’s decision takes into account the other’s as given. What type of equilibrium do you expect?
5. Explain the interaction process between Patrice and Patrick if: i) Each assumes other’s output as given then act accordingly; ii) Each assumes other’s price as given then act accordingly; iii) Patrick observes Patrice’s output, then decides his own.
   

3. Exhausted from harsh competition, Patrice and Patrick agree to negotiate. They agree that profits will be joined, then shared proportional of outputs produced. Each may choose to produce 50, 75, or 100 apples. You are told that the total joint profits are Rp 3,200, Rp 3,500; Rp 3,000; Rp 2,100; and Rp 1,000 for total quantities of 100, 125, 150, 175, and 200 apples per day, respectively.
1. Find the Nash equilibrium.
2. Find the Stackelberg equilibrium, assuming Patrice as the first mover.