Eco 405
Assignment 4 (Due Feb. 27, Wednesday)
1.
Connie has a monthly income of $200, which she allocates between two goods: meat
and potatoes.
a.
Suppose meat costs $4 per pound and potatoes cost $2 per pound.
Draw her budget
constraint.
Let
M
= meat and
P
= potatoes.
Connie’s budget constraint is
$200 = 4
M
+ 2
P
, or
M
= 50  0.5
P
.
As shown in the figure below, with
M
on the vertical axis, the vertical intercept is 50.
The horizontal intercept may be found by setting
M
= 0 and solving for
P
.
Meat
Potatoes
U
= 100
50
25
75
100
25
50
75
100
125
Budget Constraint
and Utility Function
b.
Suppose also that her utility function is given by the equation u(M, P) = 2M + P.
What combination of meat and potatoes should she buy to maximize her utility?
(Hint: Meat and potatoes are perfect substitutes.)
When the two goods are perfect substitutes, the indifference curves are linear.
To find
the slope of the indifference curve, choose a level of utility and find the equation for a
representative indifference curve.
Suppose u=50, then 2M+P=50, or M=250.5P.
Therefore, Connie’s budget line and her indifference curves have the same slope.
Connie’s utility is equal to 100 when she buys 50 pounds of meat and no potatoes or no
meat and 100 pounds of potatoes.
The indifference curve for
U
= 100 coincides with
her budget constraint. Any combination of meat and potatoes along this line will
provide her with maximum utility.
c.
Connie’s supermarket has a special promotion.
If she buys 20 pounds of potatoes (at
$2 per pound), she gets the next 10 pounds for free.
This offer applies only to the
first 20 pounds she buys.
All potatoes in excess of the first 20 pounds (excluding
bonus potatoes) are still $2 per pound.
Draw her budget constraint.
Assume that potatoes are on the horizontal axis.
Connie’s budget constraint has a
slope of –1/2 until Connie has purchased twenty pounds of potatoes, is then flat from 20
to 30 pounds of potatoes, since the ten next pounds of potatoes are free, and then has a
slope of –1/2 until it intercepts the potato axis at 110.
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An outbreak of potato rot raises the price of potatoes to $4 per pound. The
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 Spring '08
 Mingaling
 Utility, Meredith, Connie

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