HW1sol

HW1sol - EEP101/ECON125 Spring 99 Prof D. Zilberman TA's:...

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EEP101/ECON125 Spring 99 Prof D. Zilberman TA's: Malick/Marceau Suggested Solutions to Problem Set 1 * Part A 1. l 0 20 30 80 100 120 140 180 200 0 10 20 30 40 50 60 70 80 90 100 MC - s* MSC MB MR a b c d e f g h i j k 97.5 Q*s Qm Quantity $ Pm P*c P*p s* 40 MC m a) Social Optimum MSC = MC + MEC = (20 + 2Q) + (10 + 0.25Q) = 30 + 2.25Q Social Equilibrium => MSC = MB => Point g => 30 + 2.25Q = 200 - 2Q => 40 => Q * S = 40 Total External Cost , TEC, at Q * S => Area ekgl => 40 (10 + 20)(1/2) = 600 => TEC = 600 b) Monopolist 's Equilibrium Total Revenues TR = PQ = (200 - 2Q)Q = 200Q - 2Q 2 . Marginal Revenue MR = TR Q = 200 - 4Q Equilibrium Quantity => MR = MC => Point d => 200 - 4Q = 20 + 2Q => 30 => Qm = 30. Equilibrium Price => 200 - 2(Qm) => 200 - 60 => 140 => Pm = 140 Deadweight Loss => Area cgf => (140 - 97.5)(40-30)(1/2) = 212.5 => DWL = 212.5 Total external Cost => Area elfd => (30)(10 +17.5)(1/2) = 412.5 =>TEC = 412.5 * Part A was prepared by G. Malick, while part B was prepared by S. Marceau.
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EEP101/ECON125 Spring 99 Prof D. Zilberman TA's: Malick/Marceau c) Welfare under the monopolist Consumer's Surplus => Area abc => (200 - 140)(30)(1/2) = 900 => CS = 900 Producer's Surplus => Area bcde => (30)(120 + 60)(1/2) = 2,700 => PS = 2,700 Correction of the externality The government wants to shift the MC curve so that it intersects the MR at the desired optimal level of output Q * S . Let's call "x" the amount by which the MC curve should change. MC(Q * S ) + x = MR(Q * S ) (20 + 2 Q * S ) + x = (200 - 4 Q * S ) But we know that Q * S = 40. Therefore, 20 + 2(40) + x = 200 - 4 (40) 100 + x = 40 x = - 60 The MC must shift down by 60. That is, the government should impose the monopolist a unit subsidy of 60 per unit produced. Hence, s* = 60. This seems to be strange, how come we end up subsidizing a polluter ? The intuition for this is simple. The monopolist restricts output and increases the price of the good. In this particular example, the monopolist's equilibrium output (Qm = 30) is less than the social optimum (Q * S = 40), so imposing a tax on the polluter is not a solution because it would move the monopolist's output further away from the social optimum. Thus, in order to move towards the social optimum, we actually need to increase the monopolist's output. We achieve this by subsidizing the monopolist. The new monopolist equilibrium occurs at point m, where the monopolist will produce the desired optimal level of output. The new market price faced by consumers is determined by the demand P * C = 200 - 2(40) = 120. The effective price received by producers is the market price plus the subsidy P * P = P * C + s* = 120 + 60 = 180 . Welfare implications of the government's policy Government Expenses => s* Q * S => Area hijg => (60)(40) = 2,400 Old Consumer Surplus => Area abc => (200 - 140)(30)(1/2) = 900 New Consumer Surplus => Area ahg => (200 - 120)(40)(1/2) = 1,600 Change in Consumer Surplus => Area hbcg => 1,600 - 900 = 700
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HW1sol - EEP101/ECON125 Spring 99 Prof D. Zilberman TA's:...

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