Homework_3_solutions

Homework_3_solutions - Type equation here.1. Henry is a...

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. Type equation here 1. Henry is a typical New Yorker. Each month he has $120 to spend on transportation. The price of a subway ride is $2 and the price of an average cab ride is $10. You may assume that the goods are not perfect complements. Given these prices and his income of $120 he purchases 45 subway rides and 3 cab rides per month. a) Putting subway rides on the x-axis and cab rides on the y-axis illustrate Henry’s budget set. Include in your diagram an indifference curve through his best bundle. Answer: Cab Rides Henry’s budget set includes all the consumption bundles encompassed by the budget line (the black line above) and the x-, y- axes (bundles on the lines are included). Due to a budget shortfall the MTA announces that it will raise the price of a subway ride to $2.50. b) Illustrate the effect of the fare increase on Henry’s budget set in your diagram for part (a). Answer: The new budget line moves inward after the price change and is shown with the blue line in the above picture. The budget set shrinks accordingly. The proposed fare increase causes a public uproar. As a concession to the public the MTA announces that each month it will give a typical New Yorker like Henry a certain number ( n) of free rides. The MTA declares that it does not want subway ridership to decline due to the fare increase. So it proposes to choose n so that Henry can still afford to consume his original best bundle of goods, (45,3). 1
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c) Given that the MTA would like to keep the bundle (45,3) affordable for Henry when the fare is $2.50 and the price of a cab ride and his income are constant (at $10 and $120 respectively) then how many free rides must the MTA give Henry? Answer: To be able to maintain the original bundle, (45, 3), Henry has $120 - $10*3 = $90 left to spend on the subway rides after 3 cab rides. With the increased $2.50 fare, he can afford totally $90/$2.50 = 36 rides. The other 45 – 36 = 9 rides will be subsidized by the MTA. d) In a new diagram illustrate Henry’s new budget set which reflects both the higher subway fare and the free rides that he received from the MTA. In your diagram include both of the budget lines from part (b). 2
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e) The MTA is giving free rides in order to prevent a decline in ridership from the rise in the subway fare to $2.50. Was it successful? In other words will Henry still ride the subway 45 or more times per month? Briefly explain your answer. f) The original reason that the MTA wanted to raise the fare was to increase revenues. Is the fare increase supplemented by the provision of free rides successful at raising revenues? Briefly explain your answer. Answer: No, the MTA will not make as much revenue as before. From the figure in part f), we can see the optimal bundle after the increased fare and the free rides will lead to more consumption on the cab rides, that is, Henry spends more money on cabs and thus less money on the subway. The MTA made $90 from Henry when they charged him $2 per ride; this is
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This note was uploaded on 02/10/2010 for the course IEOR 3600 taught by Professor Chudnovsky during the Winter '09 term at Columbia.

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Homework_3_solutions - Type equation here.1. Henry is a...

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