Question

So, lets say that there are 3 groups in a community with 3 respective demand curves for public television.

P1=200-Q1

P2=240-2Q2

P3=320-2Q3

Q₁, Q₂, and Q₃ are the quantities consumed of public television, measured in hours watched) by the three groups. P₁, P₂, and P₃ are “prices” or willingness-to-pay in dollars that each group would pay for hours watched.

Suppose public television is a pure public good that can be produced at a constant marginal cost of MC = 200.

1. What is the (socially) efficient number of public television hours to provide this community

2. What prices would you charge each group respectively if you followed a rule of charging based on willingness to pay?

Answer 1

Hi! Welcome to Chegg!

1.

In case of public good analysis, summation of demands are required to get total willingness to pay:

We have:

P1 + P2 + P3 = 760 - 5Q

Equilibrium:

P = MC

760 - 5Q = 200

5Q = 560

Q = 112 = The (socially) efficient number of public television hours to provide this community.

2.

Keeping different price, quantity for different group requires monopolist's outcome which maximizes profit in each group.

Group 1:

TR = P1Q1 = 200Q1 - Q1²

MR = 200 - 2Q1

Equilibrium:

MR = MC

200 - 2Q1 = 200

Q1=0

Market can't be serves as maximum willingness = MC.

Group 2:

TR = P2Q2 = 240Q2 - 2Q2²

MR = 240 - 4Q2

Equilibrium:

MR = MC

240 - 4Q2 = 200

4Q2 = 40

Q2 = 10

P = 240 - 2(10) = 220

Group 2:

TR = P3Q3 = 320Q3 - 2Q3²

MR = 320 - 4Q3

Equilibrium:

MR = MC

320 - 4Q3 = 200

4Q3 = 120

Q3 = 30

P = 320 - 2(30) = 260