Question

Maggie Miller is the town manager of Medfield, a town with 50,000 residents. At a recent...

Maggie Miller is the town manager of Medfield, a town with 50,000 residents. At a recent town meeting, several residents proposed building a large public recreation center in the center of town for all of the residents to enjoy. A survey of all 50,000 residents revealed that the recreation center would be worth $50 to each of them, or $2,500,000 total. The cost to build the recreation center is $1,000,000. Because the benefits to building the recreation center outweigh the costs, Manager Maggie arranges to have the recreation center built. (8 points)

a) Of the four main types of good described in class (private good, club good, common resource, public good), which type is this for the residents of Medfield, and why? (4 points)

b) Everyone in town enjoys using the recreation center but when Manager Miller asks for donations to pay for the center, she only collects $250,000, which is considerably less than the $2,500,000 value residents indicated previously. Who are the free-riders in this situation, and why are they free riding? (4 points)

Homework Answers

Answer #1

Answer to Part(a)

The public recreation centre at Medfield is non excludable in nature as there is no entry fee in practice and so, nobody can be denied access to the centre.

But on the other hand, use of the recreation centre by one person reduces the utility for someone else to use it as there might be overcrowding because of too many people using the centre.

Thus, the public recreation centre at Medfield is non excludable but rivalrous in nature. So, it can be classified as a common resource.

Answer to Part(b)

Total Amount required:- $1,000,000

Contribution per resident:- 1000000/50000 = $20

Amount collected is $250,000 after a contribution of $20 from one resident

Total number of residents who contributed:- 250,000/20 = 12500

So, the free riders are the other 37,500 residents who didnot contribute.

In order to understand why these people free ride, let's take help of Game Theory.

Suppose there are only two residents A and B in Medfield.

Each one has two options before them, to contribute or to free ride.

Benefit if the centre is establised:- $50 Contribution:- $20

The payoff matrix will be as follows:-

B Contributes B Free Rides
A Contributes (50-20, 50-20) (50-20, 50-0)
A Free Rides (50-0, 50-20) (50-0,50-0)
B Contributes B Free Rides
A Contributes (30, 30) (30, 50)
A Free Rides (50, 30) (50,50)

So, if B contributes, best strategy for A is to free ride. If B free rides, the best strategy for A is to free ride. The same applies to B as well.

Thus, the dominant strategy for both A and B is to free ride. This is why so many people were free riding.

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