PARSONS GWU ECONOMICS 2101 SP 2014 MAKEUP
PARSONS SP 2014
ECONOMICS 2101
FIRST MIDTERM EXAMINATION
Answer All Questions. The test has one hundred points. You have one hour and 10 minutes to
complete the examination.
(1) (15 points) Demand Curves
Consider a linear demand curve of the following form:
Q 350 7P d = − , (D)
(a) (5 points) Derive the inverse demand curve corresponding to this demand curve. Simplify your
answer to the extent possible.
(b) (5 points) what is the price elasticity of demand at P=40? . Simplify your answer to the extent
possible.
PARSONS GWU ECONOMICS 2101 SP 2014 MAKEUP
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(c) (5 points) How much will the consumer spend on this product in total if P=30. . Simplify your
answer to the extent possible.
PARSONS GWU ECONOMICS 2101 SP 2014 MAKEUP
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(2) (15 points)
The gasoline market can be well approximated by the linear demand and supply model:
Demand: Q 0 1P D = α + α , α 0 > 0; α1 < 0, (1)
Supply: Q 0 1P S = β + β , β 0 , β1 > 0; (2)
where P is the price and QD and QS are the quantity demanded and quantity supplied.
Now consider the imposition of a sales tax of t per gallon of gas that the customer must pay to the
government along with her gas purchase. That is the consumer must pay an amount t in addition
to the price for each gallon of gas.
First explain how you might most reasonably introduce the tax into this model. Justify your
answer.
Then derive algebraically the impact of the tax on equilibrium price in this market. How much will
the equilibrium price be changed by this new tax. Briefly explain what you are doing.
PARSONS GWU ECONOMICS 2101 SP 2014 MAKEUP
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Q2 Continued
(3) (35 points) Consider a consumer in a static twogood world (x, y). The consumer has an
income of I and faces a competitive product market with prices x p and py , and has a utility
function: U = xy + y .
(A) (10 points) Derive the marginal rate of substitution of x for y. Is it decreasing in x,
suggesting the usual convex to the origin indifference curves we normally expect? Show your
work.
(B) (20 points) Derive the individual’s demand curve for x, showing your work.
PARSONS GWU ECONOMICS 2101 SP 2014 MAKEUP
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(C) (5 points) Is x a normal good or an inferior good? Prove your answer.
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(4) (15 points) Vouchers and the Demand for Housing
The government provides a worthy but poor individual a housing voucher worth amount S that
must be spent on housing. The housing voucher cannot be resold, but the individual can
supplement the voucher with resources of his own. The individual has an income I and can buy
housing in the open market at a price per space unit of PH Alternatively he can buy food at a
price per unit of PF. Graphically characterize how the voucher will affect his demand for housing.
Briefly explain what you are doing, being sure to specify precisely how the program will affect his
budget constraint as well as his purchase decision.
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(5) (20 points) The Odd Music Listener
Consumer J is an odd fellow. He likes all sorts of music, including Willie Nelson and Luciano
Pavarotti, but the more he listens to Willie the more he likes Willie relative to Luciano.. The
converse is true as well. (In our jargon, his MRS of Willie for Luciano is increasing in Willie
listenings.)
Assume that he has a fixed amount to spend on songs, say I, and can buy songs by both artists on
itunes at a fixed price per listen, PW and PL respectively. Graphically characterize his demand
for songs by the two artists, briefly explaining what you are doing.
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