Question

Exercise 2: Public Goods Provision (25 points) Consider three consumers indexed by i = {1,2,3} with the following demand functions for a public good G: P = 10 – 2oC, P = 20 – 26, Ps= 20 - hoc where pi is the price consumer i is willing to pay for G. (a) (10 pts) If marginal cost is contant at $15, what is the private provision of public good G? (b) (15 pts) If marginal cost is contant at $15, what is the optimal level of public good?

Answer 1

Answer:

Given that:

Considered three consumers indexed by i= {1,2,3} with the following demand functions for a public good G:

In private provision , for each person PMB =PMC for 1 as Max WTP (willingness to pay )=10 ,so he will not by

P2 = 15, 20 - 6 = 15, G = 100

p3 = 15, 20 - 4 = 15, G = 50

so total private provision =

G2+G3 = 100 + 50 = 150

b) Market curve for public good is vertical summation of individual dd curves $\rightarrow$

1 1 1 P= P1 + P2 + P3 = 10 + 20+20 – G 1 + 20+

P = 50 - G(2) = 50 – G/5

at equation P= Mc

50 – G/5 = 15

35 = G/5

G/5 = 175