Question

Suppose Tokyo is planning to construct a new public park. Based on some market research, they have determined that the town’s 50 residents can be divided into two types with respect to their benefit from this public good. 20 of the town’s residents are of Type 1 and the other 30 residents are of Type 2. Each resident's individual demand for acres of park space is given by:

Type 1: Q_D = 20 – P

Type 2: Q_D = 40 – 2P

a. Solve for the aggregate demand of Tokyo’s 50 residents as a function of the number of acres. Be sure to write down equations for each section of the aggregate demand curve, as well as the interval of quantities each section spans.

b. Graph the aggregate demand curve calculated in part a. Make sure to label both intercepts, slopes, and the intersection of the two sections.

c. Suppose each acre of public park has a marginal cost of MC = 200 + Q . Solve for the socially efficient number of acres for the town to construct.

d. Calculate the total surplus the 50 residents of Tokyo's gain from constructing this public park.

Answer 1

1)type 1:Qd=20-p

P=20-Q

Type B:Qd=40-2P

P=20-0.5Q

Aggregate demand of public good is sum of marginal benefit of individual CONSUMERs.

Aggregate demand of type 1:p=20*(20-Q)=400-20Q

Aggregate demand of type 2: p=20(20-0.5)=400-10Q

Aggregate Tokyo Demand;type 1 +type 2

P=800-30Q

B)

C ) Social efficient outcome will be that where aggregate marginal benefit is equal to marginal cost.

800-30Q=200+Q

600=31Q

Q=600/31=19.35

D) total surplus=1/2*(800-200)*19.35=300*19.35=5805