Consider a used car market with 600 buyers each willing to buy exactly one used car, and 500 sellers each having exactly one used car. Out of the 500 used cars, 400 are of good qua... Consider a used car market with 600 buyers each willing to buy exactly one used car, and 500 sellers each having exactly one used car. Out of the 500 used cars, 400 are of good quality (peaches) and 100 are of bad quality (lemons). The monetary valuation of owning a peach is Rs. 100 for a buyer and Rs. 50 for a seller. On the other hand, the monetary valuation of owning a lemon is Rs. 10 for both a buyer and a seller. A seller knows whether the car she owns is a peach or a lemon, whereas a buyer only knows that there are 400 peaches and 100 lemons. Both the buyers and the sellers know the various valuations. (a) What outcome maximizes the aggregate surplus of the economy? Provide a clear explanation for your answer. (b) (i) Derive, with a clear explanation, the supply of used cars as a function of price. Draw this supply curve by plotting number of used cars on x-axis and price on y-axis. [You must label all the important points in the figure clearly.] (ii) Derive, with a clear explanation, the demand for used cars as a function of price. Draw this demand curve in the same figure as in part (i). [You must label all the important points in the figure clearly.] (iii) Use the demand and supply functions above to find out all possible competitive equilibria in the used car market mentioning clearly which types of car, lemon or peach, are bought and sold in each equilibrium. (c) Now suppose that buyers also know the identity of all cars, that is, whether any given car is a peach or a lemon. Use a similar demand-supply analysis as above to solve for all possible competitive equilibria in the used car market in this scenario. Read more

a) All 500 used cars (400 peaches and 100 lemons) should be sold. b) (i) Supply: 0 if P<10, 100 if 10≤P<50, 500 if P≥50. (ii) Demand: 600 if P≤82, 0 if P>82. (iii) Equilibria: Only lemons traded at 10≤P<50, or both traded at 50≤P≤82. c) Lemons at Rs. 10, Peaches at Rs. 50-100.

a) The outcome that maximizes the aggregate surplus of the economy would be when all 500 used cars (400 peaches and 100 lemons) are sold. This is because the buyers value both peaches (Rs. 100) and lemons (Rs. 10) higher than the sellers (Rs. 50 and Rs. 10 respectively).

b) (i) Supply of used cars as a function of price:

Sellers of lemons will be willing to sell if the price is greater than or equal to Rs. 10. Sellers of peaches will be willing to sell if the price is greater than or equal to Rs. 50. Therefore, the supply curve will be a step function:

-At price ( P < 10 ), the quantity supplied is 0. -At price ( 10 \leq P < 50 ), the quantity supplied is 100 (lemons). -At price ( P \geq 50 ), the quantity supplied is 500 (100 lemons and 400 peaches).

(ii) Demand for used cars as a function of price:

Buyers are willing to buy a car if the price is less than or equal to their expected valuation. Since buyers don't know whether a car is a peach or a lemon, they will value the car as the weighted average of the values of peaches and lemons. The expected value is:

[ E(V) = \frac{400}{500} \times 100 + \frac{100}{500} \times 10 = 82 ]

Therefore, the demand curve will also be a step function:

-At price ( P \leq 82 ), the quantity demanded is 600 (since there are 600 buyers). -At price ( P > 82 ), the quantity demanded is 0.

(iii) Competitive Equilibria:

To find the competitive equilibria, we need to find the prices at which the quantity demanded equals the quantity supplied. From the above analysis, we have:

-If ( 10 \leq P < 50 ), the quantity supplied is 100 (lemons). In this case, the equilibrium will be at a price between Rs. 10 and Rs. 50, and only lemons will be bought and sold. Since the quantity demanded at these prices is 600, but only 100 lemons are available, all lemons will be sold. -If ( P \geq 50 ), the quantity supplied is 500 (lemons and peaches). In this case, the equilibrium will be at a price between Rs. 50 and Rs. 82, and both lemons and peaches will be bought and sold. Since the quantity demanded at these prices is 600, but only 500 cars are available, all cars will be sold.

Therefore, there are two possible competitive equilibria:

1. Only lemons are traded at a price ( 10 \leq P < 50 ).
2. Both lemons and peaches are traded at a price ( 50 \leq P \leq 82 ).

c) If buyers know the identity of all cars, the analysis changes. Now there are two separate markets: one for peaches and one for lemons.

-For lemons: -The supply of lemons is 100 if ( P \geq 10 ), and 0 otherwise. -The demand for lemons is 600 if ( P \leq 10 ), and 0 otherwise. -The equilibrium price for lemons is Rs. 10, and 100 lemons are traded. -For peaches: -The supply of peaches is 400 if ( P \geq 50 ), and 0 otherwise. -The demand for peaches is 600 if ( P \leq 100 ), and 0 otherwise. -The equilibrium price for peaches is between Rs. 50 and Rs. 100, and 400 peaches are traded.

Therefore, the competitive equilibria in this scenario are:

1. Lemons are traded at a price of Rs. 10.
2. Peaches are traded at a price between Rs. 50 and Rs. 100.