Download ECO 100Y INTRODUCTION TO ECONOMICS

Prof. Gustavo Indart
Department of Economics
University of Toronto
ECO 100Y
INTRODUCTION TO ECONOMICS
Problem Set 4
1. Jane’s marginal rate of substitution of apples for oranges is equal to 5. Both apples and
oranges are measured in pounds. [Note: substituting apples for oranges means that the
quantity of apples increases while the quantity of oranges decreases.]
a. Draw an indifference diagram (with apples on the horizontal axis) showing an indifference
curve with a point (point A) that has a marginal rate of substitution of 5.
b. Draw a budget line tangent to your indifference curve (at point B) for the case where the
price of apples is $1 per pound and the price of oranges is $0.50 per pound.
c. Given a marginal rate of substitution of 5 and the prices in part b., does Jane substitute
apples for oranges (i.e., more apple and less oranges) or substitute oranges for apples
(i.e., more oranges and less apples) to improve satisfaction?
d. What is the marginal rate of substitution at the point on the indifference curve which
maximizes Jane’s satisfaction at the above prices?
e. For consumer satisfaction to occur when the marginal rate of substitution is 5, what must
the price of apples be if the price of oranges is $1?
2. Draw a consumer’s indifference curve diagram, showing an original budget line and a new
budget line, and the original equilibrium and the new equilibrium for each of the following
cases (considered separately). In each case, indicate how your diagram fits the specification
of the case it illustrates.
a. The consumer’s income falls, and his response indicates that X is an inferior good for him.
b. The price of X and the price of Y both increase by 25%.
c. The price of X falls by 20%. Although the consumer buys more X at the lower price, his
demand for X is inelastic.
3. Syema spends all her disposable income on pizza and steak. Her demand curve for pizza is
downward sloping. If Syema’s disposable income falls 25% because of a recession, does
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she necessarily consume fewer units of pizza? Explain your answer with an indifference
curve diagram with pizza on the X-axis.
4. Suppose that John consumes only two commodities: commodity X and commodity Y.
a. Draw John's budget line when the price of Y is $20/ton, the price of X is $50/ton, and the
John's income is $10,000. Label this budget line B0.
b. Assume that John's preferences for X and Y are known. Draw the highest attainable
indifference curve to indicate the equilibrium quantity of X (X0) for the given income,
prices, and preferences.
c. Now draw John's budget line (B1) if income and the price of Y do not change, but the price
of X decreases to $25/ton.
d. Using the slope of this new budget line to represent the new price ratio (relative prices),
indicate the quantity of X (XS) chosen by John if we assume that his level of utility (a proxy
for real income) remains unchanged when relative prices change. Use an arrow to show
the direction and amount of this substitution effect between X0 and XS.
e. Assume that X is a normal good. Since movement from XS to a point on the new budget
line B1 represents a change in real income only and not a change in relative prices, pick a
point (X1) on the new budget line that satisfies the criteria of consumer equilibrium and X
is a normal good. Use an arrow to show the direction and amount of this income effect
between XS and X1.
f. Use an arrow to show both the direction and the amount of the total effect of the change in
the price of X.
g. Given the information on your diagram, draw a diagram to identify two points on the
demand curve for good X.
5. A student claims that the negative slope of the typical demand curve occurs because the
substitution effect and the income effect both cause quantity demanded to move in the
opposite direction of the price change. Is this claim true of false? Justify your answer by
drawing an appropriate diagram for the case of an increase in price. If your answer is true,
your diagram should demonstrate that the income and substitution effect move in the
opposite direction to price in all downward sloping demand curves. If your answer is false,
your diagram must demonstrate an example disproving the student's claim. Be sure to label
all axes, intercepts, and curves correctly.
a. Indicate the initial equilibrium quantity of X and label it X0.
b. Find the quantity of X consumed solely due to the change in the relative prices of X and Y
and label it XS.
c. Label an arrow SE to indicate the amount and direction of the substitution effect due to the
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price increase.
d. Indicate the equilibrium quantity of X after the full effect (including both substitution and
income effects) of the price increase and label it X1.
e. Label an arrow IE to indicate the amount and direction of the income effect due to the
price increase.
f. Draw and label a demand diagram showing that your substitution and income effects
produce a downward sloping demand curve.
g. Explain your answer and diagram in a few sentences
6. Each of the following statements requires an answer with a position (true/false), a clearly
labelled diagram, or set of diagrams, and a brief paragraph of analysis which justifies your
position. Note: Your explanation is more important than whether your position is correct or
not.
a. Sean, a commissioned salesman, consumes only meat pies and tuna fish steak. In tough
economic times, Sean's commissions have fallen. Statement: “As a result of the decrease
in Sean's level of disposable income under the consumer satisfaction maximization model,
Sean must buy fewer units of meat pies and fewer units of tuna fish steak.”
b. Murphy and Kerry spend all their disposable income on scampi and cod cakes. Murphy's
level of disposable income falls by 20% and Kerry's level of disposable income increases
by 20%. Assuming no other changes, at the new levels of equilibrium, both Murphy and
Kerry consume more cod cakes. Statement: "Under the assumption that each individual is
maximizing his level of consumer satisfaction after the disposable income adjustment, the
increased consumption of cod cakes by both Murphy and Kerry is not consistent with
consumer behaviour analysis."
c. Colleen spends all her disposable income on Product C (the X-axis product) and Product
D. For Colleen, the income and the substitution effects for Product C work in the opposite
direction. Suppose that the price of Product C falls. Statement: "As a result of this price
decrease, if the substitution effect were greater than the income effect, then Colleen's
demand curve for Product C must have a negative price elasticity of demand.”
d. Melanie spends all her disposable income on Product S (the X-axis good) and Product T.
For Melanie, the income and the substitution effects for Product S work in opposite
directions. Suppose that the price of Product S decreases. Statement: "As a result of this
price decrease, if the substitution effect were greater than the income effect, the Product S
must be a Giffen inferior good and the demand curve for Product S must be positively
sloped."