Question

In: Economics

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

  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?
  1. 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.)
  1. 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)
  1. 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.


Related Solutions

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 =...
21. A public park is a public good because: a. it is both excludable and rival...
21. A public park is a public good because: a. it is both excludable and rival good. b. it is excludable but non rival c. it is non-excludable but rival d. it is non-excludable and non-rival. 22. If there are 5 firms in the market each with 10% of the market share, and another 10 firms that have the remaining market split between them equally, we can say that C4 or Concentration Ratio is 55%. True or False 23. Regulated...
Provide an Example of a good that you think is a public good at least some...
Provide an Example of a good that you think is a public good at least some of the time. Is it publically or privately provided?
Is EPA providing a public good for US? What are some of the problem with public...
Is EPA providing a public good for US? What are some of the problem with public goods? What's the free rider problem? Does the free rider problem justify the existence of EPA? please try to be as detailed as possible. here is a short youtube video to watch https://www.youtube.com/watch?v=YHLSENkD6rk https://youtu.be/PV9Lm17yWN8
Discuss how public good are used for the betterment of the general public. Provide at least...
Discuss how public good are used for the betterment of the general public. Provide at least three examples and provide details on the general government’s expenditure on those goods.
1. Discuss how public good are used for the betterment of the general public. Provide at...
1. Discuss how public good are used for the betterment of the general public. Provide at least three examples and provide details on the general government’s expenditure on those goods.
Is public infrastructure a public good? Explain and provide clear logical arguments for your position.
Is public infrastructure a public good? Explain and provide clear logical arguments for your position.
Do you consider the public good provision problem as an externality problem? Explain.
Do you consider the public good provision problem as an externality problem? Explain.
To determine the right amount of a certain public good to provide, the government of Wakanda...
To determine the right amount of a certain public good to provide, the government of Wakanda decides to survey its residents about how much they value the good. It will then finance the public good provision by taxes on residents. Describe a tax system that woul lead residents to underreport their valuations. Describe an alternative system that could lead residents to overreport their valuations.
Vickrey-Clarke-Groves mechanism seems to be a good solution to the public good problem. But we do...
Vickrey-Clarke-Groves mechanism seems to be a good solution to the public good problem. But we do not see a frequent application of it in real world. What could be the reason(s) of this situation? Do some search, explain the weaknesses of the mechanism.
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT