Question

The demand curve for a public park for two consumers who represent society is given by:

𝑃 = 150 − 𝑄𝐷1, 𝑃 = 250 − 𝑄𝐷2

Graph the two demand curves and show the marginal social benefit curve for this public

park. If the marginal cost of providing the park was €240, what would the optimum

provision of this park be? Explain why any quantity above or below this amount would

represent a less than efficient allocation.

Answer 1

$P=150-QD_{1}$

$P=250-QD_{2}$

$MC=\$240$

$TC=240Q$

Social marginal benefits of Q is;

$MB_{1}+MB_{2}=P_{1}+P_{2}$

The demand for consumer 1 is; $Q<150$

The demand for consumer 2 is; $Q<250$

For consumer 1, the marginal cost represents less than efficient allocation.

$TR=150Q-Q^2$

$TC=240Q$

$TR=TC$

$150Q-Q^2=240Q$

$Q=-90$

For consumer 2;

$TR=250Q-Q^2$

$TC=240Q$

$TR=TC$

$250Q-Q^2=240Q$

$Q=10$