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# Homework 1 - Consumer Theory.pdf

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University of Toronto Mississauga

Economics

ECO204Y5

Kathleen Wong

Fall

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ECO204: Homework Assignment 1
1. For each of the questions below, decide whether the statement is true, false or uncertain.
Explain your answer thoroughly to justify the answer you gave.
a. In the graph below, assume that I 2> I1. True, False or Uncertain: This individual views
both goods as normal goods.
I2/PY
Y
F
I1PY
E
I 1/PXI 2/PX X
b. Suppose that Karen’s favorite fruits are apples and strawberries and purchases both fruit
throughout the year. The price for apples remains constant throughout the year, but
strawberries fluctuate depending on the season. Assume: her convex-shaped indifference
curves remain constant throughout the year. True, False or Uncertain: Karen’s
willingness to trade apples for strawberries is constant throughout the year.
c. In general, if a good is inelastic, the consumer’s total expenditures for the good increase
when the price of that good increases.
d. Mike is currently receiving a marginal utility of 4 from consuming pizza and a marginal
utility of 6 from consuming burgers. Pizza costs $3 a slice and burgers cost $5 each.
True, False or Uncertain: To maximize his utility, Mike should consume more burgers.
e. With the utility function U(X,Y), Henrik will choose a bundle of goods that is both
affordable and contain positive values of both good X and good Y to maximize his utility.
2. Charlie only consumes donuts and coffee and has the utility function U(C, D) = CD and an
income of $24. Initially, the price of coffee (C) is $1 and the price of donuts (D ) is $2. Then
the price of donuts rose to $3 and the price of coffee remained at $1.
a. Using you knowledge of utility maximization and the Lagrange multiplier, derive
Charlie’s demand for coffee as a function of I and P C, and his demand for donuts as a
function of I and PD.
b. What is Charlie’s initial consumption bundle when P C= $1 and P D $2? What is his
utility, U(C, D) at this bundle?
c. What is Charlie’s final consumption bundle when P = $C and P = $3?D
d. Calculate the decomposition bundle (referred to as point B in lecture notes).
e. Calculate the substitution effect by comparing the demand for donuts in the original
bundle in part (b) and the demand for donuts in part (d).
f. Calc

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