Question 1
Andy purchases only two goods, apples (a) and kumquats (k). He has an income of $40
and can buy apples at $2 per pound and kumquats at $4 per pound. His utility function
is U(a, k) = 3a + 5k. That is, his constant marginal utility for apples is 3 and his constant
marginal utility for kumquats is 5. What bundle of apples and kumquats should Andy
purchase to maximize his utility? Why?
[Solution]
Andy’s marginal utility of apples divided by its price is 3/2=1.5. The marginal utility for
kumquats is 5/4=1.25. That is, a dollar spent on apples gives him more extra utilities
than a dollar spent on kumquats. Thus, he maximizes his utility by spending all his
money on apples and buying 40/2=20 apples.
Question 2
Yuka consumes mangos and oranges. She is given four mangos and three oranges. She
can buy or sell mangos for $2 each. Similarly, she can buy or sell an orange for $1. If
Yuka has no other source of income, draw her budget line and write the equation.
[Solution]
It is given: C(mango) = 4, O(orange) = 3, PC = $2, PO = $1.
The most he can spend on these goods, Y = 4 × 2+3 × 1 = 8+3 = $11.
The budget constraint: 2C +1O = 11 → 2C +O = 11.
Question 3
Nadia likes spare ribs(R) and fried chicken(C). Her utility function is U = 10R2C. Her
weekly income is $90, which she spends on only ribs and chicken.
a. If she pays $10 for a slab of ribs and $5 for a chicken, what is her optimal
consumption bundle? Show her budget line, indifference curve, and optimal bundle,
e1, in a diagram.
b. Suppose the price of chicken doubles to $10. How does her optimal consumption of
chicken and ribs change? Show her new budget line and optimal bundle, e2, in your
diagram.
[Solution]
a. Setting MUR/pR = MUC/pC yields 20RC/10 = 10R2/5 or 2C = 2R. Therefore R = C. We
then substitute R = C into the budget equation to obtain: 10C + 5C = 90 or C = 6 (and R
= 6). The diagram looks like Figure 4.8 with only the middle indifference curve shown
and with R and C on the axes.
b. Using the same method as in part a), the new solution is R = 6, C = 3. In this case the
budget line from part a) has the same intercept on the R axis, but the intercept on the
This study source was downloaded by 100000804585776 from CourseHero.com on 07-08-2023 17:23:38 GMT -05:00
https://www.coursehero.com/file/65290196/Tutorial-3pdf/
C axis falls by half, so the budget line pivots inward.
Question 4:
Julie consumes two goods, X and Y. Julie has a utility function given by the expression:
U=4X0.5Y0.5
The current prices of X and Y are 25 and 50, respectively. Julie has an income of 750
per time period.
a. Write an expression for Julie’s budget constraint.
b. Calculate the optimal quantities of X and Y that Julie should choose, given her
budget constraint. Graph your answer.
c. Suppose that the government rations purchases of good X such that Julie is limited
to 10 units of X per time period. Assuming that Julie wants to spend her entire income.
How much Y would Julie consume. Calculate the impact of the ration restriction on
Julie’s utility.
[Solution]
This study source was downloaded by 100000804585776 from CourseHero.com on 07-08-2023 17:23:38 GMT -05:00
https://www.coursehero.com/file/65290196/Tutorial-3pdf/
This study source was downloaded by 100000804585776 from CourseHero.com on 07-08-2023 17:23:38 GMT -05:00
https://www.coursehero.com/file/65290196/Tutorial-3pdf/
Powered by TCPDF (www.tcpdf.org)