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HW_8_solutions_Problem_Set

HW_8_solutions_Problem_Set - AEM 250 Fall 2008 HW 8...

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AEM 250 Fall 2008: HW 8 Solutions 1. To find the competitive market equilibrium, set MB = MC: MB = P = 60 – (1/2) Q D MC = P = (5/14) Q S P* = 25 and Q* = 70 Recall that the Consumer Surplus is defined as the area below the demand curve and above the price line. Note that the Y-intercept of the MB equation is 60. Then we can calculate: CS = ½ * 70 * 35 = 1225 Producer Surplus is the area above the supply curve and below the price line. The Y intercept of the MC equation is 0, so we calculate: PS = ½ * 70 * 25 = 875 Total surplus = PS + CS = 2100 Competitive Equilibrium We are given that the Marginal External Social Cost is 15, so to get the total external cost, calculate: 70 * 15 = 1050 This external cost must be subtracted from the total surplus. Then the Net Economic Surplus is PS + CS – total external cost: 1225 + 875 – 1050 = 1050 External Costs in Competitive Equilibrium MB PS CS P Q 25 60 70 MC
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Next we need to find the social equilibrium. To find the Social Marginal Cost equation, we just add 15 to the MC equation. Notice that this just shifts the MC curve upward, and does not change the slope. This is because the MESC is constant. Then we set SMC = MB: 60 – (1/2) Q = (5/14) Q + 15 Qsocial = 52.5 and Psocial = 33.75 We calculate CS as we did above: CS = 689.06 To find PS, we have to calculate the area of a triangle and a rectangle. First we need to find the MC associated with the social equilibrium quantity of 52.2. (5/14)*52.5 = 18.75 Now we can calculate the area of the rectangle as: (33.75 – 18.75) * 52.5 = 78.5 And the area of the triangle is: (1/2) * 18.75 * 52.5 = 492.19 So PS is: 787.5 + 492.19 = 1279.69 The total surplus is: 1279.69 + 689.06 = 1968.75 70 MB PS CS P Q 25 60 MC External costs 15
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Social Equilibrum We still have external costs of 15 per unit: 15* 52.5 = 787.5 This must be subtracted from the total surplus to obtain the Net Economic Surplus 1968.75 – 787.5 = 1181.25 External Costs in Social Equilibrium Finally we evaluate the situation with monopoly. The monopolist will set quantity by setting MR = MC: 18.75 15 33.75 MB PS CS P Q 60 52.5 MC 18.75 15 33.75 MB PS CS P Q 60 52.5 MC External costs
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60 – Q = (5/14) Q Q monopoly = 44.21 Price is found by plugging Q monopoly into the MB equation: MB = P = 60 – (1/2) * 44.21 P monopoly = 37.90 Monopolist Equilibrium Note that we need to find the P that corresponds with the intersection of MR and MC so that we can find the Producer Surplus.
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