Download Econ 301 Name___________________________ Problem Set 5

Econ 301
Problem Set 5 Key
Name___________________________
10 October 2007
Perloff, chapter 5
1. George the Gourmet consumes only two goods, pizzas and hamburgers. His utility is
determined solely by his consumption of these two goods.
The table below gives some of the combinations of goods along some of his indifference curves.
His indifference curves have all the properties that well-behaved indifference curves should
have.
0
1
U
Pizzas
10
4
2
1
2
U
Burgers
1
2
5
10
Pizzas
11
7
4
2
3
U
Burgers
2
3
5
12
Pizzas
12
7
5
3
U
Burgers
3
5
7
12
Pizzas
14
10
6
4
Burgers
5
6
10
17
George’s allowance is 32 dollars a week, and he spends all this money each week on
consumption of these two goods. A pizza costs 4 dollars, and a burger costs $3.20.
a) How many pizzas and burgers, respectively, will George consume per week? Solve the
problem graphically.
Given George’s budget, his utility is maximized when he consumes 4 Pizzas and 5 Burgers.
b) Work out at least two points along George’s demand curve for burgers, and use these points to
sketch his demand curve.
Recall that the demand curve
describes the relationship
between price and quantity
demanded. To construct the
demand curve, we can
“experiment” with various
burger price levels, holding all
else equal (i.e. holding
preferences, income and the
price of other goods
constant). As we experiment
with new burger prices, the
budget constraint in our
preference space will change.
From the budget constraint
corresponding to the “new”
price, we can determine the
“new” quantity demanded. If
we repeat the exercise for
many price levels, we can
construct George’s demand
curve for burgers.
c) Suppose that the government feels that George should be able to afford to buy 10 pizzas per
week, and wants to decide how to bring this about. One option being considered is to give a
subsidy to pizza producers that will lower the price of pizzas sufficiently that George can buy 10
pizzas per week using his current income. How much would the government need to subsidize
each pizza in order to achieve this? How much would it cost to subsidize 10 pizzas in this
fashion?
For George to be able to afford 10 pizzas, the price of pizzas must be at most $3.20 – his
$32 income is exhausted in this case. Since the current price of pizza is $4.00, then
government must subsidize the $0.80 difference between the prices. It would cost the
government a total of $8.00 to subsidize these 10 pizzas. (Alternatively, you could
calculate what the price of pizza would need to be to induce George to actually buy 10
pizzas.)
d) An economist suggests that if the government simply gave that money (i.e., the money needed
to subsidize 10 pizzas) directly to George, rather than to the pizza producers, he would probably
be better off. Is the economist right? Solve the problem graphically.
An $8.00 payment
increases George’s income
to $40. Graphically, we
can see how the income
subsidy allows George to
achieve a higher utility
than the price change
offered by the
government in part (c).
2. The federal government provides poor households with food stamps. These are vouchers that can be exchanged
for food; if a food stamp has a nominal value of, e.g., 100 dollars, it can be used to buy 100 dollars’ worth of food.
Using a standard utility theory framework, with a consumer choosing between two goods – “Food” and “Other
stuff” – try to draw indifference maps for
a) a consumer who is worse off with a food stamp with a nominal value of 100 dollars than she/he would be if the
government gave her/him 100 dollars in cash,
b) a consumer who is just as well off with a food stamp with a nominal value of 100 dollars as she/he would be if
the government gave her/him 100 dollars in cash,
a) This is one example of preferences that result in a strict preference for cash over food
stamps. Any indifference mapping that results in choices of positive “other good” consumption will
lead to a similar conclusion.
(Alternatively, you could draw a single budget constraint with preferences that suggest that the
individuals would prefer to spend less than $100 on food. Then, the individual is worse off with the
food stamps than with the cash – being forced to spend at least $100 on food limits his/her options
and leaves him/her on a worse indifference curve than the one he/she could reach with $100 in
cash.)
b) If the consumer spends all his money on food, then he is indifferent between food stamps and
cash—he can use both with equal ease at the grocery store.
(Alternatively, you could draw a single budget constraint with preferences that suggest that the
individual wants to spend at least $100 on food anyway. Then, the individual may use the food
stamps for food and the “leftover” cash for other goods.)
3.
4. Suppose the demand curve for bus travel is downward sloping, and the income elasticity of demand
for bus travel is negative.
(i)
(ii)
(i)
Design an indifference curve-budget line diagram showing the substitution and income
effects created when the price of bus travel falls. In your diagram, place bus travel on the
horizontal axis and all other goods on the vertical axis.
How you can tell from your diagram that the income elasticity of demand for bus travel
is negative? Explain.
Bus travel is an inferior good, so the substitution and income effects must be in
opposite directions. Since the demand curve for bus travel is downward sloping, the
substitution effect must be larger than the income effect. This situation is shown
in the accompanying diagram, where point A is the initial optimum and point B is the
final optimum.
(ii)
Consider points C and B in the diagram. The parallel shift in the budget line shows a
rise in income, but quantity demanded is falling from C to B. Therefore, income and
quantity demanded are moving in opposite directions, so bus travel is an inferior
good. The income elasticity of demand for inferior goods is negative.