Question

5 Suppose the marginal willingness to pay for each of two individuals who will benefit from some public good is MWTP = 5 – 2Q and the marginal cost of providing the public good is MC = 3 + 3Q.

A. Determine the socially efficient quantity of this public good.Derive your answer algebraically and illustrate by graphing the aggregate WTP and the MC functions.

B. Calculate the total willingness to pay and the total cost of providing the socially efficient quantity of this public good. Is the total WTP enough to finance the costs of providing the socially efficient quantity of this public good? Would a voluntary agreement by both individuals to provide the public good be likely to succeed? Explain your answers.

C. Calculate the net gain if the socially efficient quantity of this public good was provided. Identify this area in your graph.

Answer 1

1. at equilibrium :

MC = MWTP

3+3Q = 5-2Q

=> 5Q = 2

=> Q = 0.4(see the graph at the bottom)

2.TWTP =

=

=

TC =

=

=

at Q = 0.4

TWTP = 5*0.4 - (0.4)^2 = 2 - 0.16 = 1.84

TC = 3*0.4 + 1.5*(0.4)^2 = 1.2 + 0.24 = 1.44

Voluntary agreement will be secured as Total WTP is more than the total cost.

3. Total Gains = TWTP - TC = 1.84 - 1.44 = 0.4

For the graph, refer the red triangle which has same area: