HW2,Sp2001sols

HW2,Sp2001sols - EEP 101/ECON 125 Spring 2001 Solutions to...

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EEP 101/ECON 125 Spring 2001 Solutions to Problem Set 2 1. Equilibrium conditions for a competitive market are MC ( Q;t ) = p: Thus, without any government intervention, at any point in time t; Q = 500 + 500cos ¡ 450 ¡ 20 t 157 ¢ : (a) There are 1000 units that can be sold. Thus percent di¤usion is Q ( t ) 1000 ; or 1 2 + 1 2 cos ¡ 450 ¡ 20 t 157 ¢ 0 0.2 0.4 0.6 0.8 D 5 10 15 20 Time (b) If the government wants 50% di¤usion, it must alter the price so that 1 2 = 1 2 + 1 2 cos ³ p 157 ´ ; (1) or cos ³ p 157 ´ = 0 : (2) From trigonometry (or from our calculator) we know that cos ¡ ¼ 2 ¢ = 0 : This means that p 157 = ¼ 2 ; or p = 157 ¼ 2 ¼ 246 : 62 : In year t = 6 ; the price that would occur without intervention is p (6) = MC (6) = 450 ¡ 20 £ 6 = 330 : Thus the government must subsidize the sale of the product by s = 330 ¡ 246 : 62 = 83 : 38 per unit sold in year 6. This is just the di¤erence between the price the government wants and the price that occurs without government intervention. We must multiply this subsidy by the number of units sold in year 6. We know 500 will adopt at t = 6 (50% of 1000). Thus the number adopting are 500 minus the number who had adopted by year 6, or 500 ¡ 500 ¡ 500cos ¡ 450 ¡ 20 £ 6 157 ¢ = 253 : 25 Hence the total expenditures are 83 : 38 £ 253 : 25 = 21116 : (You could use year 5 as the base year if you were considering discrete time). If the government uses this policy in year 6, then 500 will have adopted by the end of year 6. Since the problem assumes there is no unadoption, the government need not do anything to maintain at least 1
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50% di¤usion. Hence they will employ no policy in year 7 through 15, and the cost will be 0. In other words the government can reach di¤usion goals with short term subsidies. When prices go up people seldom sell durable goods, and hence
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HW2,Sp2001sols - EEP 101/ECON 125 Spring 2001 Solutions to...

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