Download Homework 1: Supply/Demand and Consumer Behavior

Homework 1: Consumer Behavior (to be handed in on Thursday 29th January 2004)
1. Drawing a supply and demand diagram in each case, illustrate the effect of the following on
the market for apples. Make clear the direction in both price and quantity sold (1 point):
a)
b)
c)
d)
Scientists find that an apple a day does indeed keep the doctor away.
The price of oranges triples
A drought shrinks the apple crop to half its normal size
Thousands of college students abandon the academic life to become apple pickers
2. Consider a competitive market for which the quantities demanded and supplied (per year) at
various prices are given as follows (1 point):
Price ($)
60
80
100
120
a)
b)
c)
d)
Demand (millions)
22
20
18
16
Supply (millions)
14
16
18
20
What are the equilibrium price and quantity?
Calculate the price elasticity of demand when the price is $80.
Calculate the price elasticity of supply when the price is $100
Suppose the government sets a price ceiling of $80. Will there be a shortage, and if so,
how much?
3. Suppose the market for vegetable fiber is competitive, where the world price is $9 per pound.
Unlimited quantities are available for import into the US at this price. The US domestic
supply and demand for various prices are as follows (2 points):
Price ($)
3
6
9
12
15
18
a)
b)
c)
d)
US demand (million lbs)
34
28
22
16
10
4
US supply (million lbs)
2
4
6
8
10
12
What is the equation for demand? What is the equation for supply?
At p = $9, what is the price elasticity of demand? And at p = 12$
At p= $9, what is the price elasticity of supply? And at p = $12?
In a free market, what will be the US price and level of fiber imports?
4. For each of the following cases, draw a representative indifference curve for red and blue
marbles passing through the point (5, 5). Use the quantity of red marbles as the number on
the horizontal axis, and that for blue on the vertical axis. Assume these marbles are identical
to each other except for color (1 point).
Case 1: Marbles are used to identify hot and cold water faucets, and are therefore valuable only
in pairs.
Case 2: Marbles are used to line the bottom of an aquarium, and the person prefers more even
mixtures of colors to uneven.
5. Suppose Jones and Smith have decided to allocate $1000 per year to liquid refreshment in the
form of alcoholic or nonalcoholic drinks. Jones and Smith differ substantially in their
preferences for these two forms of refreshment. Jones prefers alcoholic to nonalcoholic
drinks, while Smith prefers the nonalcoholic version (1.5 points).
a) Draw a set of indifference curves for Jones, and a second set for Smith, with alcoholic
drinks on the vertical axis and nonalcoholic on the horizontal axis.
b) Using the concept of the marginal rate of substitution, explain why the two sets of curves
are different from each other.
c) If both Smith and Jones pay the same prices for their refreshments, will their marginal
rates of substitution of alcoholic for nonalcoholic drinks be the same or different?
Explain your answer.
6. Consumers in Georgina pay twice as much for avocados as they do for peaches. However,
avocados and peaches are equally priced in California. If consumers in both states maximize
utility, will the marginal rates of substitution of peaches for avocados be the same for
consumers in both states? If not, which will be higher? (1/2 point)
7. Antonio buys 8 new college textbooks during his first year at school, at a cost of $50 each.
Used books only cost $30 each. When the bookstore announces a 20% price increase in new
texts, and a 10% price increase in used texts, Antonio’s father offers him $80 extra. Is
Antonio better or worse off after the price change? (1 point)
8. The utility that Jane receives by consuming food, F, and clothing, C is given by u(F,C) = FC
(2 points).
a) Draw the indifference curve associated with a utility level of 12, and with a utility level
of 24. Are the curves convex? (Hint: solve C=12/F) and C=24/F, starting with F=1)
b) Suppose that food costs $1 a unit, and clothing costs $3 a unit. Jane has $12 to spend.
Graph the budget line she faces.
c) What is the utility maximizing choice of food and clothing? (Hint: solve the problem
graphically)
d) What is the marginal rate of substitution of food for clothing when utility is maximized?