Question

1. The Public Good Problem

A national park that costs MC = 80 dollars to provide to society has been

privatized and handed over to a private firm; the firm is mandated to price at

marginal cost. There are two types of consumers, a group of high demand

consumers (group A) that have an aggregate demand function equal to MB = 100 –

Q, and a low demand group of consumers (group B) with aggregate demand equal to

MB = 50 – Q, where Q is thousands of acres.

1. How many acres will be provided by the firm when pricing at MC, assuming that the low-demand group will free-ride on the high-demand group?

2. What is the aggregate demand curve for the national park? (Hint: the aggregate demand curve for a public good is the vertical aggregation of the individual demand curves.)

3. Calculate the aggregate consumer surplus for the two types of consumers when the firm prices at M (Hint: in this case, the group B is free riding, and they can gain extra consumer surplus)

4. If the national park is provided by the government, how many acres SHOULD be provided?

Answer 1

A.) Given, MC = 80
MB = 100 – Q
Since low demand group is free riding on high demand group, their demand function is not considered (as their demand in not effective economic demand).
Equilibrium point is where MC = MB. Therefore solving the above functions we get:
80 = 100 - Q
or Q = 20 acres

B.) Aggregate demand curve is determined by adding the given two demand functions:
MB = 100 – Q (High demand consumers)
MB = 50 – Q (Low demand consumers)
MB = 150 - 2Q (equilibrium point 35 Acres @ MC or MB of 80)

C.) Calculation of consumer surplus for group A :-
Equilibrium point as calculated above in part A), MC=MB=80 and Q = 20
Using the same demand function, when Q1 = 0, MC1 = 100
Surplus = 1/2 X (MC1 - MC)(Q-Q1) = 1/2 X 20 X 20 = 200
(graphically, area of triangle above equilibrium point = 1/2 X base X height).
Similarly using the total demand function; equilibrium point in part B) above and plotting another point on that demand curve, we get MB1=150 and Q1 = 0, therefore consumer surplus = 1/2 X 70 X 35 = 1225

D.) The government should provide 35 acres on the basis of total demand of both groups to maximise consumer surplus.