HW 3a q1 has wrong answer - AEM 250 Spring 2007 Homework...

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AEM 250 Spring 2007 Homework #3: Market Failure – Externalities: SOLUTIONS 1) a. Step 1 : Using the information in the table, find the MB and MC curves: MB = -Qd + 220 MC = 1/2 Qs + 10 Set MB = MC to find Q* (private optimum quantity) -Q + 220 = 1/2 Q + 10 Q* = 140 Plug Q* into either MB or MC to obtain P* P* = MC = (1/2) * (140) + 10 P* = 80 Private equilibrium is at (Q*, P*) = (140, 80) e* on graph Step 2 : Find the Social MC curve and solve for the social optimum: SMC = MC + external costs (this is what we refer to as marginal external social costs in the lectures) SMC = 1/2 Qs + 10 + 60 = 1/2 Qs + 70 Set SMC = MB and follow the same process as above to obtain: Social equilibrium at (Q*, P*) = (100, 120) e’ on graph $ 220 120 80 70 10 100 140 Q (mil. tons) SMC MC e’ MB e* $60 per ton external cost
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b. Net Economic Surplus at e*: You can calculate CS and PS, and sum them, or simply calculate the entire triangle: CS = (1/2) * (220 – 80) * (140) = (1/2) * (140) * (140) = 9800 PS = (1/2) * (80 – 10) * (140) = (1/2) * (70) * (140) = 4900 NES = CS + PS = 14700 (note: times 1 million) or NES = (1/2) * (220 – 10) * (140) = (1/2) * (210) * (140) = 14700 You were not asked to calculate this, but remember that this NES does not account for the loss from external costs, which we can subtract out: External cost = 140 * 60 = 8400 Adjusted NES at market equilibrium= 14700 – 8400 = 6300 Net Economic Surplus at e’: Using the same method as above we can find the NES at the social optimum: CS = (1/2) * (220 – 120) * (100) = (1/2) * (100) * (100) = 5000 PS = (1/2) * (120 – 70) * (100) = (1/2) * (50) * (100) = 2500 NES = CS + PS =7500 or NES = ½(120-70)*100 = 7500 If we calculate the NES at the market optimum (without accounting for the externality) we get an inflated measure because we are not taking into account the external costs associated with pollution. The NES at the social optimum actually represents the maximum amount of benefit society can achieve once all of the costs are taken into account. c. i.) A Pigouvian tax is a tax levied on an agent who is creating a negative externality with the intention of reducing the level of the negative externality. It is a per unit tax set equal to the Marginal External Social Costs at the social optimum. ii) The optimal level of Pigouvian tax is equal to the marginal external social cost at the social optimum. In this case we have constant external cost of $60 per unit (which is like our oil example discussed in lecture) for all levels of output, including the socially optimal level. So the optimal tax is $60 per unit.
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iii) When the Pigouvian tax is implemented, the total tax revenue collected will be equal to the number of units produced times the amount of the tax per unit. So the amount will be: $60 * 140 mil. tons = $8400 mil iv) The NES with the Pigouvian tax is the same as the NES at the social optimum. The difference is that now a tax revenue is collected. Remember, taxes to not impose a true resource cost on society – they are
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HW 3a q1 has wrong answer - AEM 250 Spring 2007 Homework...

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