ps1_sol2 - EEP 101/Econ 125 Spring 2002 GSIs: Alix, McKim,...

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EEP 101/Econ 125 Spring 2002 GSIs: Alix, McKim, Schoengold Solutions to Problem Set #1 Numerical Questions: For the numerical questions, there are graphs at the end of the solution key that show how to calculate the answers using graphical methods. The following are the solutions calculated algebraically. If you have any questions on the connection between the two, please ask one of the GSIs for the course. Question #1 a) The socially optimal level of output is calculated at the point where MB = MSC. MSC is the sum of MPC and MEC. In this example, MB = 90 – 3Q, MPC = 10 + Q, and MEC = 2Q. Setting MB = MSC gives the following: 3 1 13 * * 3 10 * 3 90 = + = Q Q Q At this quantity, the price that clears the market is P* = 50. The welfare measures in all of these questions can be calculated either by using integration or by calculating the area of geometric figures. The numbers that result using either method will be the same. The consumer surplus (CS*) is equal to the area below the demand curve and above the price. Using the formula for the area of a triangle, the following is the level of consumer surplus at the socially optimal outcome. 3 2 266 ) 3 1 13 ( * 40 * 2 1 * = = CS The producer surplus (PS*) is equal to the area below the price and above the MPC curve. This area is composed of a parallelogram here. 5 . 444 ) 3 2 26 40 ( * ) 3 1 13 ( * 2 1 * = + = PS The total externality cost (TEC*) is the total area below the MEC curve. In this example it is: 8 . 177 ) 3 1 13 ( * 2 * ) 3 1 13 ( * 2 1 * = = TEC Here, with no intervention, total social welfare (SW*) is the sum of producer surplus and consumer surplus, less the total externality cost. 4 . 533 8 . 177 5 . 444 3 2 266 * = + = SW
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b) If the market is perfectly competitive, then the externality costs (MEC) will not be accounted for in production and consumption decisions. The result will be that production will occur at the point where MPC intersects the demand curve. In this example, setting MB = MPC gives the following: 20 10 3 90 = + = c c c Q Q Q At Q c = 20, the price that clears the market is P c = 30. The consumer surplus (CS c ) is equal to the area below the demand curve and above the price. Using the formula for the area of a triangle, 600 20 * 60 * 2 1 = = c CS The producer surplus (PS c ) is equal to the area below the price and above the MPC curve. This area is composed of a triangle here. 200 20 * 20 * 2 1 = = c PS The total externality cost (TEC c ) is the total area below the MEC curve. In this example it is: 400 20 * 2 * 20 * 2 1 = = c TEC
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Here, with no intervention, total social welfare (SW c ) is the sum of producer surplus and consumer surplus, less the total externality cost. 400 400 200 600 = + = c SW The dead-weight loss that is incurred because society fails to take the externality into account is the difference between the maximum level of social welfare (SW*) and the level of social welfare under competition (SW c ). This is: 4 . 133 400 4 . 533 * = = = c c SW SW DWL c) If a monopoly is the only producer in an industry, we know that the equilibrium quantity will be lower than under competition, and the price to consumers will be higher.
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This note was uploaded on 08/01/2008 for the course ECON 101 taught by Professor Wood during the Spring '07 term at Berkeley.

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ps1_sol2 - EEP 101/Econ 125 Spring 2002 GSIs: Alix, McKim,...

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