Question

The seller’s utility function is given by: Us = Pn j=1 Xj + M and the buyer’s utility function is given by UB = Pn j=1 3 2Xj + M, where Xj is the value from j th car-quality, and M are other goods. Let’s for a moment consider that this is a market of symmetric information.

1. Given symmetric information, which of the following will happen?

(a) The cars will be sold at once same price, leading to welfare loss

(b) Pareto optimal trade will take place, where each cars of different quality will be sold at different prices.

(c) All cars will be in the market.

(d) Good cars will leave the market.

(e) Both (b) and (c).

2. Now let’s say there is asymmetric information at place, i.e. the sellers know more about the cars they are selling compared to the buyers. In this case, good cars will leave the market since the buyers will be willing to pay only one given price (P) for any car.

(a) True

(b) False

3. In the case of assymetric information, let’s assume that the buyers know the distribution of car quality, such that Xj ∼ U(0, 100). This means the following:

(a) Buyers know that there are same number of cars of different quality in the lot, i.e. P(Xi) = P(Xk) where i 6= k and both i, j(0,100).

(b) Buyers know that there are more average cars compared to the good or bad ones.

(c) Buyers know that there are more good cars compared to other quality cars.

(d) Both (a) and (b) are likely.

4. In another case, let’s assumer that the buyers know the distribution of car quality. In this case, Xj ∼ N(50, 2). This means the following:

(a) Buyers know that there are same number of cars of different quality in the lot, i.e. P(Xi) = P(Xk) where i 6= k and both i, j(0,100).

(b) Buyers know that there are more average cars compared to the good or bad ones.

(c) Buyers know that there are more good cars compared to other quality cars.

(d) Buyers typically have more information compared to the case of Xj being uniformly distributed.

(e) Both (b) and (d) are likely.

Answer 1

The seller’s utility function: Us = Pn j=1 Xj + M

Buyer’s utility function is given by UB = Pn j=1 3 2Xj + M

Where, Xj is the value from j the car-quality, and M are other goods.

1. Given symmetric information,

Both b and c will take place,

Where information is symmetric, Pareto optimal trade will take place, where each cars of different quality will be sold at different prices and All cars will be in the market.

However, symmetric data does not denote that all cars will sold once at one price nor that Good cars will leave the market.

2. If there is asymmetric information at place, sellers know more about the cars, in this case, the answer is true, because sellers might take undue advantage of the knowledge about the cars and may deteriorate the quality of the cars.

If the quality of cars will deteriorate, the consumers will not pay higher prices and the sellers will try their best to charge from consumers. This will make the buyers to pay only one given price for any car.

3. In the case of assymetric information, if we assume that the buyers know the distribution of car quality, Xj ∼ U(0, 100), this means that:

(b) Buyers know that there are more average cars compared to the good or bad ones.

As buyers become more aware, they know that there are cars of different quality and also decide the prices accordingly.

4. In another case, let’s assume that the buyers know the distribution of car quality.

Ans. (a) Buyers know that there are same number of cars of different quality in the lot, i.e. P(Xi) = P(Xk) where i 6= k and both i, j(0,100).

As buyers, become aware about the distribution of the quality of the cars they know that in the lot which are good and which are bad cars.