Monday, November 16, 2009

Can you tell me how to get to Sesame Street?

There are three groups in Marietta. Their demand curves for public television in hours of programming, T, are given respectively by:

W1 = $200 - T
W2 = $240 - T
W3 = $320 - 2T.

Suppose public television is a pure public good that can be produced at a constant marginal cost of $200 per hour.

a) What is the efficient number of hours of public television? Explain how you determined the answer.

b) How much public television would a competitive private market provide? Explain how you determined the answer.

5 comments:

Xiaotian said...

a)since the efficient number of hours satisfies MC=W, then,
for W1, 200-T=200, T=0
for w2, 240-T=200, T=40
for w3, 320-2T=200, T=60

b) according to MC=200 and MR=MC,
a competitive private market would provide TVs at $200.

Yang Yang said...

A: public television is a pure public good that is both nonexcludable and nonrival in consumption.In the special case of the a public good,the marginal social benefit of a unit ofthe good is equal to the sum of the individual marginal benefits that are enjoyed by all consunmers of that unit.so the efficient number of hours satisfies the total of three group's W equal MC.
200-T=200,T=0 240-T=200, T=40
320-2T=200, T=60,60>40>0 when T =60, the Marginal marginal social benfefits=MC,so the efficient number of hours=60.
B:P=MC at the perfectly competitive firm's profit-maximizing quantity of output.
So P= 200.

Qi said...

Hi, Dr. Delemeester,
This is Qi Wu.
a) In order to get the efficient hours od public television, MC = MB = W.
W1 = $2OO - T = 200, T = 0
W2 = $240 - T = 200, T = 40
W3 = $320 - 2T = 200, T = 60
When T = 60, it can fits for all of the W.
So, the T = 60.

b) when the MC = P = $200, the public televison would be a competitive private market provide.

Thanks a lot.
Qi Wu

Molly said...

Dr. Delemeester,
This is Qi Wu, this is my answer.

a. Since this is pure public good and MC = MR, the quantity is optimal and benefit is maximum.
W1 + W2 + W3 = 760 - 4T = 200
T = 140 hours.

b. We know that all the Ws represent the demand of audience AND assume the price is the supply. Then, we can combine these two equations and get the supply surplus.
760 – 4T = P
P = 200
Supply surplus = (140 + 190)* 0.5*200 = 33,000

Molly said...

Dr. Delemeester,
This is Qi Wu, this is my answer.

a. Since this is pure public good and MC = MR, the quantity is optimal and benefit is maximum.
W1 + W2 + W3 = 760 - 4T = 200
T = 140 hours.

b. We know that all the Ws represent the demand of audience AND assume the price is the supply. Then, we can combine these two equations and get the supply surplus.
760 – 4T = P
200 = P
T ≤140
Supply surplus = 140 * 200 = 28800