Ec5p052007

Ec5p052007 - Economics 5 Principles of economics Fifth Problem Set D Richards Fall 2007 1 Two adolescent boys who share living quarters with my

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Economics 5 D. Richards Principles of economics Fall, 2007 Fifth Problem Set 1. Two adolescent boys who share living quarters with my wife and I are given a weekly payment in return for leaving us alone and not bothering us for most of each day, as well as for joining us at meal times but keeping quiet unless asked to speak. For lack of a better term, we will call this payment an allowance. As we are about to enter a new year, these two young people have been asking for an increase in their allowance. They claim that the cost of entertainment goods, X-Box and PS3 games, CD’s, DVD’s, sports equipment as well as the cost of necessities—transportation, lunches and so forth—have both increased over the last year so that the allowance payment to which we all agreed earlier is no long sufficient. The question is, how should we measure the extent to which the “cost of adolescence” has risen. We are considering two basic alternatives. The first of these is to use a means similar to that long used in constructing the Consumer Price Index, i.e., a Laspeyres Index. This Index measures the increase as the rise in expenditure necessary to buy the same quantities of entertainment-related items and necessities in the second year as were bought in the first. That is: Laspeyres Index = S NECESSITIE NECESSITIE ENT ENTERTAINM ENT ENTERTAINM S NECESSITIE S NECESSITIE ENT ENTERTAINM ENT ENTERTAINM Q P Q P Q P Q P 2007 2007 2007 2007 2007 2008 2007 2008 + + The alternative is to use a Paasche Index. This index is measured as what it cost to buy the combination of video items and sports equipment actually purchased in 2007, relative to what it would have cost to buy that same 2008 bundle if prices had remained at their 2007 level. Hence, the Paasche Index is calculated as: Paasche Index = S NECESSITIE S NECESSITIE ENT ENTERTAINM ENT ENTERTAINM SS NECESSITIE S NECESSITIE ENT ENTERTAINM ENT ENTERTAINM Q P Q P Q P Q P 2008 2007 2008 2007 2008 2008 2008 2008 + + The boys had studied sampling theory and gone out and gathered data for the individual prices of toys and sports equipment for 2007 and 2008, as well as the amount of each product purchased by a typical adolescent American male. These data are shown below. Based on this data, which index will the boys prefer to be used for determining the increase in their allowance? Equipment Necessities Quantity Price Quantity Price 2007 100 units $5 10 units $30 2008 150 units $5.25 10 units $40 Laspeyres index: [(5.25)(100) + (40)(10)] / [(5)(100) + (30)(10)]= 1.156 Paasche index: [(5.25)(150) + (10)(40)] / [(5)(150) + (30)(10)]= 1.131 The boys will prefer the Laspeyres index if they want to maximize the increase in their allowance As you can see, different ways of calculating the price index give rise to different measures of changes in the cost of living (or the cost of adolescence). The search for a perfect price index has lately led to the use of so- called chain indices. The simplest chain index is one proposed by the great Yale economist, Irving Fisher in
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This note was uploaded on 04/01/2008 for the course EC 0005 taught by Professor Richards during the Spring '08 term at Tufts.

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Ec5p052007 - Economics 5 Principles of economics Fifth Problem Set D Richards Fall 2007 1 Two adolescent boys who share living quarters with my

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