AECO 300. Spring 2021 Assignment 3
Professor Zhao
Max = 33 points. Explain your answers for Q2 – 5.

1. True or False questions (2points each)

(1) If a consumer does not have convex preferences, then a point of tangency between her
indifference curve and her budget line must be an optimal consumption point.

(2) Millie’s utility function is U(x, y) = min{x, y}. She maximizes her utility subject to a budget
constraint. The price of x is the same as the price of y. If the price of x rises and the price of y
and her income remain constant, then her consumption of y will certainly decrease.

(3) Clara’s utility function is U(x, y) = (x + 2)(y + 1). If her consumption of both x and y are
doubled, then her marginal rate of substitution between x and y remains constant.

(4) Charlie’s utility function is U(x, y) = xy2. His marginal rate of substitution between x and y
does not change if the amount of both goods doubles.

2. Max has the utility function U(x, y) = xy. The price of x is $2 and the price of y is $1. Income is $10.
(Apply the budget equation and the tangent condition: Px/Py = MUx/MUy)

a. (4 points) How much x does Max demand? How much y?
b. (2 points) If his income doubles and prices stay unchanged, find Max’s new demands. Is the
demand for each good doubled?

3. Max has utility function U(x, y) = x(y + 1). The price of x is $2 and the price of y is $1. Income is $10.

a. (4 points) How much x does Max demand? How much y?
b. (2 points) If his income doubles and prices stay unchanged, check to see if Max’s demand for
both goods will double.

4. Casper consumes Goods x and y. Good x is sold at a price of $2 per unit. Good y is sold at a price of 3
dollars per unit. Casper’s income is 20 dollars and his utility function is U(x, y) = x + 2y.

a. (1 points) Sketch Casper’s budget line.
b. (1 points) Sketch some of his indifference curves and label the point that he chooses
as the optimal bundle.
c. (2 points) Calculate the amount of each good Casper demands at these prices and this income.
d. (2 points) Given the price of Good x at $2 per unit, for what prices of y will Casper changes his
demand?

5. Max has a utility function U(x, y) = 2xy + 1. The prices of x and y are both $1
and Max has an income of $20.

a. (3 points) How much of each good will he demand?
b. (2 points) A tax is placed on x so that x now costs Max $2 while his income and the price of y stay
the same. How much of good x does he now demand?
c. (2 points) Would Max be as well off as he was before the tax if after the tax was imposed, his
income rose by an amount equal to $1 times the answer to part (b)?

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