Econ 302 - Suppose a consumer has preferences represented

Econ 302
Homework 2

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Carefully answer each of the questions below.
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1. (24 points) Suppose a consumer has preferences represented by the utility function U(X,Y) =
MIN[X,3Y]. Suppose PX = 1 and PY = 2. Draw the Income Consumption Curve for this
consumer for income values M = 100, M = 200, and M = 300. Your graph should accurately
draw the budget constraints for each income level and specifically label the bundles that the
consumer chooses for each income level. Also, for each bundle that the consumer chooses, draw
the indifference curve that goes through that bundle. Make sure to label your graph carefully and
accurately.

2. (24 points) Suppose a consumer has preferences represented by the utility function U(X,Y) =
X2Y Suppose PY = 1, and the consumer has $180 to spend. Draw the Price-Consumption Curve
for this consumer for income values PX = 1, PX = 2, and PX = 5. Your graph should accurately
draw the budget constraints for each income level and specifically label the bundles that the
consumer chooses for each income level. Also, for each bundle that the consumer chooses, draw
the indifference curve that goes through that bundle. Make sure to label your graph carefully and
accurately.

3. (24 total points) Suppose a consumer’s utility function is given by U(X,Y) = X*Y. Also, the
consumer has $720 to spend, and the price of X, PX = 9, and the price of Y, PY = 9.
a) (4 points) How much X and Y should the consumer purchase in order to maximize her utility?

b) (4 points) How much total utility does the consumer receive?

c) (4 points) Now suppose PX decreases to 4. What is the new bundle of X and Y that the
consumer will demand?

d) (6 points) How much money would the consumer need in order to have the same utility level
after the price change as before the price change?

e) (6 points) Of the total change in the quantity demanded of X, how much is due to the
substitution effect and how much is due to the income effect?

4. (16 points) Suppose a consumer has preferences represented by the utility function U(X,Y) =
MIN[2X,Y]. Suppose PX = 1 and PY = 2. Sketch the graph of the consumer’s Engel Curve for
good X.

5. (12 points) Refer to the following graph:

Assuming that this consumer has $100 to spend on Juice and Snacks, identify three price
quantity combinations that lie on the consumer’s demand curve for snacks.

Price of Snacks

QD of Snacks