Department of Economics
University of Maryland
Economics 325
Intermediate Macroeconomic Analysis
Practice Problem Set 2 Suggested Solutions
Professor Sanjay Chugh
Spring 2011
1.
Interaction of Consumption Tax and Wage Tax.
One basic idea of President
Bush’s economic advisers throughout his administration had been to move the U.S.
further away from a system of investment taxes (which we will discuss later in the
course) and more towards a system of consumption taxes
.
Discussion of a federal
consumption tax, which would essentially be a national sales tax, has again emerged
in recent policy discussions.
Here, you will modify the basic consumptionleisure
framework to include both a proportional wage tax (which we will now denote by
n
t
,
where, as before, 0
1
n
t
d±
) as well as a proportional consumption tax (which we will
denote by
c
t
, where 0
1
c
t
).
A proportional consumption tax means that for every
dollar on the price tags of items the consumer buys, the consumer must pay (1
)
c
t
²
dollars.
Throughout the following, suppose that economic policy has no effect on
wages or prices (that is, the nominal wage
W
and the price of consumption
P
are
constant throughout).
a.
Construct the budget constraint in this modified version of the consumption
leisure model.
Briefly explain economically how this budget constraint
differs from that in the standard consumptionleisure model we have studied
in class.
Solution:
The representative agent’s net income from working is now given by
(1
)
n
Yt
W
n
³ ´´
, where
n
t
is the labor tax rate and the other notation is the same as in
Chapter 2.
He spends all of this income on consumption, which now costs
)
c
Pt
´²
dollars per unit (inclusive of the consumption tax).
Using the fact that
168
nl
³
in the
weekly model, equating the representative agent’s labor income with his expenditures on
consumption gives us
)
)
(168
)
cn
c
t
W
l
´² ´ ³ ´ ´
³
.
If we multiply out the righthandside of this expression
and
then
move
the
term
involving the labor tax rate to the lefthandside we obtain
)
)
168 (1
)
n
c
t
W
l
t
W
´² ´²³ ´ ´
´³ ´
.
Then, solving this last expression for
c
, we arrive at
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168 (1
)
(1
)
)
)
nn
cc
tW
cl
tP
±
²±
²
³
±³
±
.
This last expression can now readily be graphed with consumption on the vertical axis
and leisure on the horizontal axis.
As in the standard model, the horizontal intercept is
168
l
.
However, the slope is now
)
)
n
c
²
±
²
³
±
.
Clearly, however, if we set the consumption tax rate to zero, we recover the budget
constraint in our standard consumptionleisure model – indeed, the model we studied in
Chapter 2 is simply a special case of the model here.
The reason the budget constraint
differs here from the standard model is simple:
the consumption tax is yet another tax for
the consumer to take account of when making his choices about consumption and leisure.
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 Spring '08
 chugh
 Economics, Supply And Demand, representative, labor supply curve

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