Question

1. Let demand be P(Q) = 6-Q. What is the price elasticity of demand at Q = 4? a. E = - b. E= - 2 C. E = -4 d. ε = -2 2. Suppose we have 3 types of households each with private demand for a public good (like flood protection) of P1(Q) = 5, P2(Q) = 10 - Q, and P3(Q) = 20 – 2Q. What is the social demand curve for the range Q < 10? a. Ps(Q) = 30 – 30 b. Ps(Q) = 35 - 30 C. Ps(0) = 20 – 2Q d. Ps(Q) = 150 – 6Q 3. A perfect-price-discriminating monopoly's marginal revenue curve a. lies below the demand curve. b. is the demand curve. C. varies for each consumer. d. is the same as a single-price monopolist's marginal revenue curve. 4. Charging a higher price to ship corn than to ship soybean by covered hopper train car to the same destination is an example of a. Perfect price discrimination b. Group price discrimination C. Tiered price discrimination d. Actual cost differences

Answer 1

Solution:

1. Price elasticity of demand, ed = (dQ/dP)*(P/Q), where P is price and Q is quantity demanded

Given the inverse demand function P(Q) = 6 - 0.5*Q

Q = (6 - P)/0.5

Q = 12 - 2P

So, dQ/dP = -2

So, ed = (-2)*(6 - 0.5*4)/4

ed = -2*4/4 = -2

Thus, the correct option is (D) -2.

2. In case of a public good, the social demand function is found by aggregating the individual or private inverse demand curves (unlike a private good, where it is aggregation of demand functions and not inverse demand functions). Further note that for Q <10, all three are always willing to pay a maximum amount of greater than 0, that is they would be willing to pay a price for Q <10 (at Q >= 10, both second and third simply wish to pay 0 price, that is don't demand it). For first person, for any quantity, willingness to pay is $5.

So, social demand curve: Ps(Q) = P1(Q) + P2(Q) + P3(Q)

Ps(Q) = 5 + (10 - Q) + (20 - 2Q)

Ps(Q) = 35 - 3Q

Thus, the correct option is (B) 35 - 3Q

3. Under perfect price discrimination, the marginal revenue curve coincides with the demand curve, that is marginal revenue curve is the demand curve itself, as each consumer is charged their maximum willingness to pay, that is price at all levels of demand curve. This is why here the optimal condition of marginal revenue = marginal cost, occurs same as where price = marginal cost.

Thus, the correct option is (B) is the demand curve.