The private and social marginal cost (MC) of producing squibs is MC = 2.5 + 0.0375Q, where Q is quantity of squibs in thousands of cases per month, and MC is measured in dollars per case. The market is competitive and firms would supply at marginal cost, except for a distortionary tax they have to pay to government in the amount of $0.50 per case. Define Pf to be the price received by firms net of the tax and Pc to be the (tax inclusive) market price (in dollars per case) at which the squibs are sold. The private (non project) inverse demand curve for squibs is given by Pc = 18 – 0.025Q, and this remains true with or without the project. A proposed project will need 22,000 extra cases of squibs per month, acting as a price-taker at the new equilibrium price. [For all parts of this question, please show and briefly explain all of your calculations. Be sure to express any numerical answers in the correct units of measure, such as $/month, or $/case.]
(a) Illustrate the market equilibria (i.e., Q, Pc) with (E1), and without (E0) the project using a graph or sketch. Label your axes and any curves drawn. Find each of the following:
(b) The expression for the new (with-project) demand function.
(c) The without-project equilibrium price paid by consumers (Pc0) and quantity exchanged in the market. (Label as E0 on your diagram).
(d) The with-project equilibrium price paid by consumers (Pc1) and quantity exchanged in the market. (Label as E1 on your diagram).
(e) The budgetary cost to the project of purchasing the squibs.
(f) The initial and final levels of tax revenues in the market, and the gain or loss in taxes due to the project.
(g) The initial and final levels of (private, non-project) consumers’ surplus and the gain or loss due to the project.
(h) The initial and final levels of producers’ surplus and the gain or loss due to the project.
(i) The per-period social opportunity cost of squibs acquired by the project and the social opportunity cost per case. Relate this result to your answers to (e) through (h). Show (and label) the per-period opportunity cost of squib purchases as one or more shaded areas on your diagram from (a).
(j) The percentage of project materials acquired that is due to an expansion of output and the percentage which is due to displacing the purchases of others.
(k) Use these proportions (from (j)) and Harberger’s weighted average formula to approximate the social opportunity cost per case of squibs used by the project.