Question

6. A lake has three commercial resorts along with a public access area. All users of the lake benefit from improvements to water quality of the lake (still polluted from earlier industrial use). q is a measure of the water quality. Each commercial resort has demand for quality, Qc = 1000-5p and the public demand for quality is Qp = 1000-20p. The marginal cost of providing an additional unit of water quality is $90.

a) Find the demand function for water quality when it is a public good.

b) What is the efficient level of water quality

c) what is the willingness to pay of each type of user (commercial or public) at the optimal level of water quality?

d) What is the total willingness to pay (summed over all units of water quality)?

Answer 1

(a) Willingness to pay for commercial resorts : p = 1000/5 - 1/5 q  

p = 200 - 1/5 q

and there are total 3 resorts so, the demand function: p = 3(200- 1/5 q)

Willingness to pay for ublic access : p= 1000/20 - 1/20 q

p = 50 - 1/20 q

Total willingness to pay = 3(200 -1/5 q ) + 50 - 1/20 q

= 650 - 13/20 q

(b) Efficient level of water quality is when MSB (marginal social benefit ) is equal to Marginal cost (MC):

650 - 13/20 q = 90

560 = 13/20 q

q = 861.5

(c) Willingness to pay of each commercial user = 200 - 1/5 (861.5) = 200 - 172.3 = $27.70.

Willingness to pay of public access = 50 - 1/20 (861.5) = 50 - 43.07 = $6.93.

(d) Total willingness to pay = 3(27.70) + 6.93 = 83.1 + 6.93 = $ 90.03