Question

In: Economics

1. The Public Good Problem A national park that costs MC = 80 dollars to provide...

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.

A. 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?

B. 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.)

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

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

Solutions

Expert Solution

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.


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