Question

There are two individuals who are interested in having bird feeders put into their neighborhood. Suzie’s demand function is P = 10 – Q Mary’s demand function is P = 12 – 3Q The marginal cost of a bird feeder is $10

a) At the socially efficient outcome, how many bird feeders will be put into the neighborhood? _____ bird feeders

b) Suzie will pay _____________ and Mary will pay _________

c) Suzie’s surplus from the public solution is _________

d) How many bird feeders would there be if the planner relied on a private market solution? ________________

Answer 1

Demand for (public good) bird feeders = 10 - Q + 12 - 3Q or P = 22 - 4Q. Marginal cost is MC = 10

a) At the socially efficient outcome, we have P = MC or 22 - 4Q = 10. This gives Q = 3. Hence there will be 3 bird feeders into the neighborhood

b) Suzie pays 10 - 3 = $7 and Mary pays = 12 - 3*3 = $3 for each bird feeder

c) Suzie’s surplus from the public solution = 10 - 7 = $3 per bird feeder

d) Private demand is Q = 10 - P + 4 - P/3 or Q = 14 - 4P/3. This gives inverse demand P = 10.50 - 0.75Q. This will give a private solution at P = MC or 10.50 - 0.75Q = 10 or Q = 0.67 bird feeders.