Problem Set 1 Solutions Spring 2010

Problem Set 1 Solutions Spring 2010 - Econ 3377 Spring,...

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Econ 3377 – Spring, 2010 Prof. Scott Imberman Problem Set 1 Due Tuesday, Feb 9 at the beginning of class. Late problem sets will not be accepted and will receive a grade of 0. Each problem set is graded out of 10 points – 5 points on the one graded problem and 5 points based on overall effort on the other problems. To receive full credit you must show all of your math work and provide explanations for essay-type questions. (1) Alex just got a $1000 tax refund from the government. He decides that he will spend the money on CDs and video games. Let C = # of CDs Jonathan buys & G = # of video games he buys. John’s marginal utility from CD’s is 1000 – 20C while his marginal utility from video games is 2000 – 50G. The price of CDs is P C = 20 and the price of video games, P G = 60. Note: you can always assume that a person can buy a fraction of a good unless I specifically state otherwise. (a) Write down and draw Alex’s budget constraint. Make sure you label your axes, write down the slope, and write the values of the points where the BC intercepts the horizontal and vertical axes. Budget Constraint (BC) 20C + 60G = 1000 To make it easier to graph, let’s rearrange the constraint C = 50 – 3G.
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slope = P G /P C = -3 50 VG’s CD’s 16 and 2/3 You could also do this with CD’s on the horizontal axis & video games on the vertical axis. In this case, the graph looks like this slope = P C /P G = -1/3 16 and 2/3 CD’s VG’s 50 (b) Calculate the amount of CD’s and video games Jon will buy First we need to calculate the MRS using the ratio of marginal utilities. 1000 20 2000 50 G C MU C MRS M UG ==
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Then we set the MRS = price ratio. Remember that the good for which you put the marginal utility on top in the MRS calculation is the good whose price should be on top in the price ratio.
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Problem Set 1 Solutions Spring 2010 - Econ 3377 Spring,...

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