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Externality_sol

Externality_sol - MSC = MC MEC = 2 0.2Q 0.05Q = 2 0.25Q At...

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UBC COMM 295 Externality Solutions Question #1 A food processing industry produces packaged fruit products, among other things, and this process produces wastes as by products. The (marginal) external cost caused by these waste products (to a third party) is expressed as: MEC = 0.05Q, where Q = number of packages produced per week (in thousands). The marginal cost of production, ignoring MEC, at the industry level is: MC = 2 + 0.2Q. The industry demand for the product is: P = 10 - 0.25Q, a. Determine the output rate and price that would be established by profit maximizing competitive firms (in the absence of government regulation). At profit-maximizing production rate, MC = P 2 + 0.2Q = 10 - 0.25Q Q = (10-2)/0.45 = 17.77 (thousands) The selling price is: P = 10 - 0.25(17.77) = $5.55 per package. b. Determine the efficient output rate and price. The marginal social cost of production
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Unformatted text preview: MSC = MC + MEC = 2 + 0.2Q + 0.05Q = 2 + 0.25Q At the efficient level of production, MSC = P 2 + 0.25Q = 10 - 0.25Q Q * = (10-2)/0.5 = 16 The efficient selling price P * = 10 - 0.25(16) = $6 per package. c. Find the tax rate that must be imposed on the production of the fruit packages so that the after-tax profit-maximizing output level is equal to the efficient level. Also determine the cost to society (deadweight loss) caused by the firms producing at the profit-maximizing rates. The tax rate that must be imposed to obtain the profit-maximizing solution as the efficient solution t * = MEC(Q * ) = 0.05* 16 = $0.8 per package. The deadweight loss DWL = 0.5 (MSC(Q m ) – P m )(Q m- Q * ) = 0.5(6.44 – 5.55)1.77 = 0.79. d. Illustrate your results from (a), (b) and (c) in a diagram. MSC = MC + MEC MC D $ Fruit Packets (Q in 6.0 5.55 16 17.77 2 MEC =0.05Q 10 40 t * DWL...
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