Comparative economic problem set
ECON 175 Problem Set 1 Instructor: Yang Xie∗ 1 Market for lemons Assume that a good second-hand car worths $10 to the seller and $12 to the buyer, an ordinary second-hand car worths $7 to the seller and $9 to the buyer, and a bad second-hand car worths $5 to the seller and $3 to the buyer. Assume that one third of the cars are good, one third are ordinary, and one third are bad. a. If the buyer can tell good or ordinary or bad, will the good cars sell? Will the ordinary cars sell? Will the bad cars sell? b. Now assume that the buyer cannot tell good or ordinary or bad but knows that the probabilities of a good, ordinary, and bad car are 1/3, respectively. How much will a risk neutral buyer be ready to pay? c. Will the seller keep the good cars in the market? d. Understanding this, now the buyer sees a car in the market. What are the probabilities that this car is good, ordinary, and bad, respectively? e. How much will the buyer be ready to pay now? f. Will the seller now keep the ordinary cars in the market? g. Understanding this, now the buyer sees a car in the market. What is the probability that this car is good, or ordinary, or bad? h. How much will the buyer be ready to pay now? ∗ Affiliation: Department of Economics, University of California, Riverside. 1 i. Will the seller now keep the bad cars in the market? j. Will any car be sold? 2 Hold-up problem Assume that an Indian firm is contacted by a multinational car company to produce brake systems. This requires an initial specific investment of I from the Indian subcontractor and a variable cost c per braking system. The car company plans to buy n braking systems from the subcontractor at price p per braking system. a. Looking from now, at what price, p = p0 , the Indian subcontractor would break even? b. Once the specific investment is made, at what minimum price, p1 , that the Indian subcontractor will just be willing to produce the braking systems? c. Which price is higher, p0 or p1 ? What is their difference? d. Understanding this potential situation, will the Indian subcontractor make the initial investment? e. The difference between p0 and p1 is a measure of the severity of the hold-up problem. If the initial investment increases, will the problem become more severe? f. Consider an extreme case in which I = 0. Will there still be a hold-up problem? g. Given some I > 0, will the variable cost, c, affect the severity of the hold-up problem? h. What can you conclude from this exercise? 3 Cooperation problem and coordination problem Consider Table 1, a payoff matrix for Player A and Player B. a. Under what condition will Option 1 be a dominant strategy for Player A? b. Under what condition will Option 1 be a dominant strategy for Player B? c. Under what conditions will “both players choosing Option 1” be a Nash equilibrium? 2 Table 1 A chooses Option 1 A chooses Option 2 B chooses Option 1 B chooses Option 2 (a, b) (e, f ) (c, d) (g, h) d. Under what conditions will “both players choosing Option 1” not be a Nash equilibrium? e. Under what conditions will “A choosing Option 2 while B choosing Option 1” be a Nash equilibrium? f. Now consider Table 2, another payoff matrix for Player A and Player B. Which situation will Player A like the best? Table 2 A chooses Option 1 A chooses Option 2 B chooses Option 1 B chooses Option 2 (4, 3) (−1, 2) (2, −1) (100, 200) g. Which situation will Player B like the best? h. Is “both players choosing Option 2” a Nash equilibrium? Why? i. Is “both players choosing Option 1” a Nash equilibrium? Why? j. Which problem do we see now, a coordination problem or a cooperation problem? k. Now consider Table 3, another payoff matrix for Player A and Player B. Which problem do we see now, a coordination problem or a cooperation problem? Table 3 A chooses Option 1 A chooses Option 2 B chooses Option 1 B chooses Option 2 (4, 3) (−1, 500) (500, −1) (400, 400) 3
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