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Unformatted text preview: PADP 8670 F erti g Fall 2011
UGA Homework 4 Solutions 1. The diagram shows the demand and supply for passenger rail service between two cities. Initially the price per ticket is $4 and 1000 trips are made per week. An
excise tax of $2 is placed on each ticket, which raises supply to S' and reduces the number ofrail trips to 800. a. Identify the area on the diagram that represents the tax revenue collected. b. What does consumer surplus mean? Identify the area on the diagram that
represents the consumer surplus received by rail passengers after the tax has
been imposed. c. identify the area on the diagram that represents the deadweight loss (or
equivalently the “efficiency cost") of the tax. Explain the meaning ofthis concept.
pm a M aim aware/We %
aw Wk‘vm Law/m. ca WW4,
acme/L5 bin/r! ﬁ/m 409C 4%“ C5 6%
a??ng
ﬂ) M
WM. " TECKSlS per
week 2. There are forty consumers in an economy who purchase a drug to relieve the pain of
arthritis. They think that the only effective drug is Namebrand. However, the same
drug can be bought by its chemical name acethistestamine, or ace for short. The
drug costs $2 to produce no matter what it is called; any quantity demanded can be
supplied at that price. The company producing Namebrand exploits consumer
ignorance by charging $6 for each unit; that is, the consumers buy Namebrand at $6
per unit, not realizing that ace is a perfect substitute available for only $2. The
aggregate demand curve ofthe 40 uninformed consumers is (1:400 — 40?. a. What would be the value to consumers of knowing that ace and Namebrand are identical? B: {bowl 1‘ (9+0
a: (320~ito)*4/1:52,© Baa @SIOWdBQ Lalo/fog;
erbb (9:520 b. How much is deadweight loss due to the consumers‘ lack of perfect
information? 3. Suppose that you have $5000 in income to spend on two goods, durable goods [D]
and all other goods [0). The price of both D and 0 is $1. Your utility function is
U=D03007. Your demand for D is D : (0.3*M]/P9 and your demand for O is O =
[0.7*M)/P0. Calculate the compensating variation needed to maintain your initial
utility level ifa tax of$1 is imposed on D. ri‘he following are the steps necessary to do this calculation. Show all ofyour work.
a. Find the initial utility. To do this, plug the prices into the demand equations to figure out the quantity ofD and 0 currently chosen. Then plug these
quantities into the utility function and calculate the utility at this bundle. l) t: Ot%i=ii;oooo/i 2 1600
O :: Oi7‘iéilsooaO/l 2 $5500 .7 u ‘1 DD'JOO'? =2: i600” b. Derive the expenditure function. To do this, plug the demand functions for D
and 0 into the utility function. Rearrange the equation using the property of
exponents that xaxbzxaw to collect M by itself. Then, solve the equation for M
as a function of U, PD, and Po. This is the expenditure function. u :ioBM/Pplé‘g [OH M/fﬂ M V07 a». ~05 0.1% #055 U7 "(9.7"?
#0.?) M PD 0.7 M lo u ‘3(On/nUEiCQI’?0110'? M ‘ ﬁrm774  _..__....a............_a..._...f———4 M S 0.56%?)037 . [,3
Owe.._mm._r....._..ww.__.___.m_,_/IJ “me. c. Calculate the compensating variation. To figure out how much money you
would need to get back to your initial utility ifthe price of D increased from
$1 to $2, plug in the initial U, Po, and the new PD into your expenditure
function. The difference between the new value of M and the original M
($5000) is the compensating variation. i I7 ...
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