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HW1,Sp2001sol

# HW1,Sp2001sol - EEP101/ECON125 Spring 01 Prof D Zilberman...

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EEP101/ECON125 Spring 01 Prof. D. Zilberman GSIs: Just/Marceau/St.Pierre Solutions to Problem Set 1 Part A: Numerical Problems 1. The numerical results for question 1 are given in Table 1. Their derivation is explained below. Table 1 Social optimum (question 1a) Monopoly (question 1b) Monopoly with tax (questions 1c and d) Competitive pricing (question 1e) P 380/3 = 126.67 110 380/3 = 126.67 70 Q 65/3 = 21.67 30 65/3 = 21.67 50 CS 4225/9 = 469.44* 900 4225/9 = 469.44 2500 PS 37375/18 = 2076.39* 2250 21125/18 = 1173.61 1250 TEC 6825/6 = 1137.5 1950 6825/6 = 1137.5 4750 GS 0* 0 8125/9 = 902.78 0 W 4225/3 = 1408.33 1200 4225/3 = 1408.33 -1000 DWL 0 625/3 = 208.33 0 7225/3 = 2408.33 tax/unit 0 0 125/3 = 41.67 0 *The answers for CS*, PS* and GS* are consistent with Q* being achieved through a quota or a standard on output. If the economy gets to Q* using another policy instrument, the distribution of the surplus between consumers, producers and government could be different. The total surplus will remain unchanged. a) The socially optimal level of output is the one where marginal social cost is equal to marginal social benefit. The marginal social cost is the sum of marginal private cost and marginal external cost: Q MEC MPC MSC 4 40 + = + = . Marginal social benefits are given by the demand curve: Q P MSB 2 170 - = = . Equating the two and solving for Q gives: MSB Q Q MSC = - = + = * 2 170 * 4 40 * 6 130 Q = 67 . 21 3 / 65 6 / 130 * = = = Q This solution is illustrated in Figure 1. It is possible to find total external cost, consumer surplus and producer surplus geometrically. Recall that consumer surplus is the difference between total benefits from consumption and what consumers pay for the good consumed. If the quantity Q* is consumed, then an equilibrium price will be the one given by the demand curve for that quantity. ( 67 . 126 3 / 380 3 / 65 * 2 170 * 2 170 * = = - = - = Q P ). Consumer surplus is the area below the demand curve and above this price. In Figure 1, it is the shaded triangle labeled CS*. Producer surplus is the difference between total revenues and variable costs. Since variable costs are the sum of the marginal costs for all units produced, producer surplus is the area below the price and

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EEP101/ECON125 Spring 01 Prof. D. Zilberman GSIs: Just/Marceau/St.Pierre above the marginal cost curve. It is the parallelogram with a thick border 1 labeled PS* in Figure 1. The total external cost is the sum of the marginal external costs over all units produced and is given by the area below the marginal external cost curve. It is the shaded parallelogram labeled TEC*. To calculate these areas, we need to know price, marginal private cost and marginal external cost at Q*. To find them, simply plug the value of Q* back into the demand MPC and MEC functions: 85 3 / 65 * 3 20 67 . 41 3 / 125 3 / 65 20 67 . 126 3 / 380 3 / 65 * 2 170 * = + = = = + = = = - = MEC MPC P Calculate TEC* as the area of the parallelogram: 5 . 1137 6 / 6825 3 / 65 * ) 85 20 ( 2 1 * *) 20
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HW1,Sp2001sol - EEP101/ECON125 Spring 01 Prof D Zilberman...

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