The market for donuts is competitive and has the following s

The market for donuts is competitive and has the following supply curve, QS(P) = max{0, 60 + 4P}. The government plans to place a $5 tax on each donut sale (collected from sellers).
(a) What is the private marginal cost schedule of producing donuts (private

marginal cost as a function of the quantity produced)? (2 points)
(b) How does the tax aect the private marginal cost of donuts (i.e., sellers’ marginal cost schedule)? The social marginal cost schedule? Explain. (3 points)
Calculate the deadweight loss of this tax and shade in the corresponding area in a diagram when:
(c) The demand for donuts is QD(P) = 20 (for all P 0). (2 points) (d) The demand for donuts is QD(P) = max{0, 240 6P}. (4 points) (e) Why is the deadweight loss dierent in these two cases? (2 points) (f) Suppose that demand is as in part (c). How much revenue would the
government raise from a tax of $30 per donut? What is the deadweight loss from implementing this tax? (4 points)

Solution

(a) What is the private marginal cost schedule of producing donuts (private marginal cost as a function of the quantity produced)?

It is =

MC = 5Q

b) How does the tax aect the private marginal cost of donuts (i.e., sellers’ marginal cost schedule)? The social marginal cost schedule? Explain.

Social Marginal Cost = Same as Private marginal cost
Calculate the deadweight loss of this tax and shade in the corresponding area in a diagram when:
c) The demand for donuts is QD(P) = 20 (for all P 0).

5Q = 20

Q = 4 units