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Evans School of Public Affairs, Mark Long
PBAF 516: Microeconomic Policy Analysis
Problem Set 1 -- Answers
Supply and Demand, Elasticity
1) Using a supply and demand graph for apples, explain how the following would affect the supply and
demand for apples, the quantity of apples sold, and the price of apples:
a. Apple pickers go on strike reducing the number of apples which are harvested.
Supply curve shifts in, demand curve does not shift, the quantity of apples sold declines, and the
price of apples rises.
b. Health researchers announce evidence that consuming apples leads to lower risk of cancer.
Supply curve does not shift, demand curve shifts out, the quantity of apples sold increases, and
the price of apples rises.
c. The price of gasoline falls, affecting the cost of shipping apples to grocery stores.
Supply curve shifts out, demand curve does not shift, the quantity of apples sold increases, and
the price of apples falls.
d. A world-wide recession hits lowering consumers' incomes (assume apples are a normal good).
Supply curve does not shift, demand curve shifts in, the quantity of apples sold declines, and the
price of apples falls.
2) The city of Seattle has estimated the following demand and supply functions for taxicab rides from
the U-District to the airport (per day):
Demand:
Supply:
P = 100 - 2Qd
P = 10 + Qs
a. Graph the supply and demand curve.
P
100
S
40
10
D
20 30 35
50
Q
Evans School of Public Affairs, Mark Long
PBAF 516: Microeconomic Policy Analysis
b. Solve for the equilibrium price and quantity.
100 – 2Q = 10 + Q
90 = 3Q
Q = 30
P = 40
c. Suppose that city leaders believe that the equilibrium price is too high and decide to impose a $30
price ceiling on taxicab rides. Under this price ceiling, solve for the quantities supplied and
demanded. Show this on your graph. Would there be a shortage or surplus of taxicab rides?
What is the amount of this shortage/surplus?
P = 100 - 2Qd
30 = 100 - 2Qd
-70 = - 2Qd
Qd = 35
P = 10 + Qs
30 = 10 + Qs
Qs = 20
There will be a shortage of 15 cab rides since demand exceeds supply by 15.
3) Suppose that Mercer Island, Washington has only two pastimes, golf and tennis. Mercer Island is also
home to an economist who estimated the demand for golf as a function of its own price ( PG ) and the
price of tennis ( PT ).
QGd = 1000 − .1PG + .9PT
(Golf demand)
a. Does this look like a legitimate demand curve? How do you know?
Yes, this looks like a legitimate demand curve because it expresses the quantity demanded as a
decreasing function of its own price and it is a function of the price of a related good.
b. The price of a reservation at the tennis courts is $100 and the price of a round of golf just
increased from $100 to $110. What is the (own) price elasticity of demand for golf?
Price Elasticity= [(1079 – 1080)/(.5*(1079 + 1080))] / [(110 – 100)/(.5*(110 + 100))]
Price Elasticity = - 0.0097
c. Suppose the demand for Tennis is given by the following demand curve:
QTd = 1000 − .1PT + .9PG
(Tennis Demand)
Find the cross price elasticity of demand of Tennis with respect to Golf using the increase in the price
of a round of golf in part b.
Cross-Price Elast. = [(1089 – 1080)/(.5*(1089 + 1080))] / [(110 – 100)/(.5*(110 + 100))]
Cross-Price Elast. = 0.087
Evans School of Public Affairs, Mark Long
PBAF 516: Microeconomic Policy Analysis
d. Are golf and tennis complements or substitutes? How do you know?
We know that these goods are substitutes because the price of tennis, for example, is positively
related to the demand for golf. Also, substitute goods have positive cross-price elasticities, as
shown in part c.
4) Define the “marginal rate of substitution.” When a consumer chooses amounts of two goods to
purchase, why will her marginal rate of substitutions equal the ratio of the price of the two goods?
Marginal Rate of Substitution = the amount of good y that I am willing to give up to get one more
unit of good x, with no change in utility – that is, it is the slope of the indifference curve.
Note that the price ratio is the amount of good y that I have to give up to buy one more unit of
good x. For example, if apples cost $4 and bananas cost $2, then I must give up 2 bananas to buy
one more apple (Price Ratio = Price Apples / Price Bananas = Px / Py). If the MRS > Price
Ratio, then the value to her of buying more x is more than cost she must pay – thus, she should buy
more x. If the MRS < Price Ratio, then the value to her of buying more x is less than cost she must
pay – thus, she should buy less x and buy more y. At the utility-maximizing point, her MRS will
equal the Price Ratio since she will not want to buy more or less x or y.
Browning and Zupan Problems:
1.9
False. The $5 billion expenditure is a sunk cost. It has already been spent and should not affect
Motorola's current decision. If it is currently costing more to continue operations than the
revenue it can generate, then it should quit immediately and ignore the sunk cost.
1.12
The availability of cell phones lowers the opportunity cost of sitting in traffic, since the time can
be used productively. As a result, we would expect this to lower the opportunity cost of living
great distances from work, thereby increasing demand for houses in the suburbs, thereby
increasing the price of houses in the suburbs.
2.12
a) When the government buys corn, the market price rises from $5 to $10 -- this is a 100% increase
in price. Now, given that consumer demand has a price elasticity of 0.5, then we can expect
demand to fall by 50% (0.5 = % change in Qd / 100%). Thus, consumers will demand ½Q* and
the government will have to buy the other ½Q*. Since both the government and consumers pay
$10 per bushel, both will spend the same amount = $10 × ½Q*.
b) Since farmers’ supply is perfectly price inelastic, they will not change the quantity they supply
when they receive the subsidy – they will still supply Q*. Since neither the demand curve nor the
supply curve shift, the market price will be $5 and consumers will buy Q*. The government will
have to spend $5 × Q*. This is the same amount spent in part a.
Evans School of Public Affairs, Mark Long
PBAF 516: Microeconomic Policy Analysis
3.24
To solve this problem, each hour should be chosen sequentially by choosing the subject with the
highest marginal increase in score.
Hour
1
2
3
4
5
6
7
8
9
Subject
Micro
Micro
Micro or Acct.
Subject not chosen in 3
Micro
Micro
Marketing, Micro, or Acct.
One of the 2 subjects
not chosen in 7
Subject not chosen in 7 & 8
Marginal Increase in Total Score
40
20
10
10
9
8
7
7
7
Your grades would then be: Marketing = 97, Accounting = 97, Micro = 94.
You would spend the following hours: Marketing = 1, Accounting = 2, Micro = 6.