Department of Economics
Intermediate Microeconomic Theory
1. Gore Monde is a food lover who lives on bread and wine. Let his
marginal utility of bread, MUb, be given algebraically by the
expression MUb = 40 - 5b. Similarly, let his marginal
utility of wine be MUw = 30 - w. The current prices of
bread and wine are Pb = 5 and Pw = 1, respectively. Gore's income is
a. What is the greatest quantity of bread that Gore can consume?
b = 40/5
b. What is the greatest quantity of wine that Gore can consume?
w= 40/1 =
c. What is the slope of Gore's budget constraint when you put wine on the
horizontal axis and bread on the vertical axis?
-8/40 = -1/5
d. Given the prices and Gore's income, how much bread and wine should he
consume? Bread = , Wine =
From the hint we know MRSwb = MUw/MUb = Pw/Pb
. Or, (30-w)/(40-5b) = 1/5. This can be
rearranged as w = 22 + b. Whatever w,b choice makes the hint true must
be a choice that also satisfies Gore's budget constraint. Therefore 40
= 5b+(22+b). Solving for b we get b = 3 and w = 25.
e. Suppose that Gore's income falls to 10. How much bread and wine will
he consume now? Bread = , Wine =
use the same reasoning we find 10 = 6b+22, or b = -2. This is not
possible, so it must be the case that Gore consumes no bread at all, and
therefore spends all of his money on wine; w = 10.
2. Al Fabette consumes x's and y's. With y on the vertical and x on
the horizontal, his marginal rate of substitution in consumption is given by
MRS = y/x. At a shop on Sesame Street he can buy his x's and y's at
the prices Px = 5 and Py = 1.
a. Fill in the boxes
below to create Al's income expansion path.
From the hint we know that MRSxy = MUx/MUy = Px/Py
. Making the appropriate substitutions we can write y/x = 5/1. This
must be true regardless of income, therefore y = 5 x + 0 is the income
b. Suppose that the price of a unit of x falls to Px=4.
Then Al's income expansion path will become
3. Put y on the vertical and x on the horizontal. Let Pepe Smith have the
marginal rate of substitution MRS = y. His income is 120 and the price
of y is Py = 1.
a. In the box below write an expression for Pepe's price expansion
Again, the hint is MRSxy = MUx/MUy = Px/Py.
This time, upon substitution y = Px/1; this must always be true
for every tangency between budget constraint and indifference curve.
Whatever choice of x and y makes this true must also be an x,y pair that
lies on Pepe's budget constraint. His budget is 120 = PxX + PyY
= PxX + Y. Now substitute in for Px to get 120 = YX +
Y. The x,y pairs that lie on this line are common to both the MRSxy = Px/Py
rule and the budget constraint. Rearranging gives us the price expansion
path y = 120/(x+1)
b. In the box below write an expression for Pepe's demand curve
associated with the price expansion path you found in part a of the
question. Write your expression in the box below:
The demand curve shows Pepe's reservation price
as a function of quantity. Since we know that y = Px, it must be the
case that Px = 120/(x+1) is Pepe's demand curve.
Hints: MRSxy = MUx/MUy = Px/Py