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Fall 2007
73150 Microeconomics
Problem Set #4 Solution Key
1)
BC
original
:
p
x
x + p
y
y= Income
BC
subsidy
:
(p
x
s)x+ p
y
y= Income
BC
income grant
:
p
x
x + p
y
y = Income+sx
subsidy
From figure 1, above, we see that the optimal bundle C under the income grant program is
at a higher indifference curve than the optimal bundle B under the subsidy program, so it
shows that income grant to a person provides more utility than does a subsidy on good x
that costs the same amount to the government.
.
Graphing BC
original
and BC
subsidy
The government wants to spend the same amount of money on income grant or subsidy.
Before any changes, we will see the BC
original
is our normal budget constraint given by
Indiff.
income grant
Indiff.
subsidy
B
BC
income grant
BC
subsidy
x
y
C
A
Indiff.
original
BC
original
x
subsidy
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View Full Document p
x
x+p
y
y= Income. The goal of subsidy is to reduce price of x for a consumer, and the
government is paying s dollar per unit of x for the consumer. Looking at the equation for
BC
subsidy
: (p
x
s)x + p
y
y= Income, s is the amount of subsidy paid by the government for
each good x, and because s>0, the new price, p
x
s, of x is lower than the old price (p
x
). The
slope of budget constraint is
y
x
p
p
, so if p
x
↓
,
y
x
p
p
would also
↓
, which tells us that BC
subsidy
is less steep than BC
original
.
After you graph the two budget constraints, you will find A to be the optimal bundle given
BC
original
, and B to be the optimal bundle given BC
subsidy
. If bundle B is
(x
subsidy
,
y
subsidy
), because the government will pay s dollar for any amount that is being consumed
(the bundle chosen tells us that the costumer chooses to consume x
subsidy)
, the total
expenditure of the government on the subsidy program would be
s*
x
subsidy
.
Graphing BC
income grant
From the previous section we know the total expenditure on the subsidy program is
s*
x
subsidy
, and because the government wants to spend the same amount of money on
income grant or subsidy, we know:
the cost of subsidy program= the cost of income grant program
the cost of income grant program
= s*
x
subsidy
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This note was uploaded on 07/14/2011 for the course ECON 73150 taught by Professor Keston during the Spring '08 term at Carnegie Mellon.
 Spring '08
 KESTON
 Microeconomics

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