Hw 5 #2

# Hw 5 #2 - P T = PMC 100 – q T= 10 q 100 – 30 – T = 10...

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Hw 5 #2 a) Socially optimal output P =100 – q PMC = 10 +q EMC = q Socially optimal output occurs were P = PMC + EMC: 100-q = 10 + q + q 90 = 3q 30 = q P = 100 – 30 = 70 = P b) Competitive equilibrium P =100 – q PMC = 10 +q EMC = q Competitive equilibrium occurs where P = PMC 100 - q = 10 + q 90 = 2q 45 = q P = 100 – 45 = 55 = P DWL = 45 30 ∫ (10 + 2q) – (100- q) = ∫ (3q – 90) q^3 – 90q |45 30 [45^3 – 90(45)] – [30^3 – 90(30)] = 62,775 = DWL

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c) Graph d) Unit tax on competitive firms to produce socially optimal output. Qs = 30 P =100 – q PMC = 10 +q Tax to produce socially optimal output occurs where:

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Unformatted text preview: P - T = PMC 100 – q* - T= 10 + q* 100 – 30 – T = 10 + 30 70 – T = 40 30 = T e) f) Monopoly equilibrium P =100 – q MR = 100 – 2q PMC = 10 +q Monopoly equilibrium occurs were MR = MC 100 – 2Q = 10 + Q 90 = 3Q Q = 30 P = 100 – 2(30) = 40 = P DWL = 30 30 ∫ SMC – P ∫ [10 + 2q] – [100 – Q] ∫ 3Q – 90 Q^3 – 90Q | 30 30 = 0 DWL = 0 g) h) In the absence of a tax, society is better off with a monopoly given the externality. The output by the monopoly is less than competitive and since the good has a negative externality, the lower output is better for society....
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## This note was uploaded on 04/11/2009 for the course ARE 100B taught by Professor Whitney during the Fall '08 term at UC Davis.

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Hw 5 #2 - P T = PMC 100 – q T= 10 q 100 – 30 – T = 10...

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