Download Problem Set 1

Economics 323
Spring 2006
Professor Gronberg
Problem Set 1 - Answer Key
1.
1.4
The only costs that vary with mileage are fuel, maintenance, and tires, which
average $0.25/mile. The cost of driving will thus be $250, and since this is less
than the cost of the bus, you should drive.
1.8
A plane of either type--large or small--should use the state-of-the-art device if the
extra benefits of that device exceed its extra costs. Because the device will save
more lives in large planes than in small planes, its benefits are larger in large
planes than in small ones. Your original recommendation was presumably based
on the calculation that the benefits for the larger planes justified the extra cost, but
did not do so in the case of the smaller planes. Airline passengers are like other
people insofar as their willingness to invest in extra safety is constrained by other
pressing uses for their scarce resources. Where extra safety is relatively cheap, as
in large planes, they will rationally choose to purchase more than when it is
relatively more expensive, as in small planes.
1.10
Assuming that residents are required to recycle cans, they simply cannot put
them with the regular trash. In the first case, the fixed cost of $6/week is a sunk
cost. Therefore, for the residents, the cost of disposing an extra can is $0. In the
tag system, the cost of disposing an extra can is $2, regardless of the number of
cans. Therefore, since the costs are higher and the benefit of setting out a can is
assumed to be the same in both cases, you expect less cans to be collected in the
tag system.
1.14
Benefit
Cost (initial)
Cost (final)
Ani DiFranco
Bp
$75
$75
Dave Matthews
Br
$75
$50
In the problem, we are given that
Bp - $75 > Br - $75
or
Bp > Br
(*)
Now, we need to find out whether the following is true or not:
Bp - $75 > Br - $50
which is the same as
Bp > Br + $25
(**)
Notice that (*) does not necessarily imply (**). For example, if Bp=$80 and
Br=$60, then (*) holds while (**) does not. So we can conclude that you should
not go to the Ani DeFranco concert in the above scenario if you are a rational
utility maximizer.
Your decision will depend on the relative values of Bp and Br. The fact that you
would have bought a Ani DeFranco ticket means that the benefit of attending the
Ani DeFranco concert, denoted Bp, must be greater than $75. Let Bs denote the
benefit of going to the Dave Matthews concert. The fact that you would have
chosen the Ani DeFranco concert before receiving your Dave Matthews concert
ticket means that Bp > Bs. But this does not imply that you should go to the Ani
DeFranco concert. Suppose Bp = $80 and Bs = $60. When you now choose
between the two concerts, the opportunity cost of attending the Dave Matthews
concert is $50, so the net benefits of attending each concert are given by Bd - $75
=$5 and Bs - 50 = $10, which means you should go to the Dave Matthews
concert. So FALSE.
2.8
a) Under the original demand curve, quantity demanded was Q = 900 units and
quantity supplied Q = 300 units, so excess demand was 900 - 300 = 600 units.
With the larger demand, quantity demanded becomes Q = 1100 units, so excess
demand becomes
1100 - 300 = 800 units. Excess demand has grown by
800 - 600 = 200 units.
b) Quantity demanded is Q = 1400 - P; quantity supplied is Q = P. Subtracting
quantity supplied form quantity demanded gives excess demand of 1400 - 2P
units. Set excess demand equal to the original level of 600 and solve 600 = 1400 2P for the required price floor of P = $400. If the government accommodates the
increase in demand by raising the rent control form $300 to $400, the degree of
excess demand will be unchanged.
2.9
a) With a price support of P = $500/ton and the original supply of P = Q, quantity
supplied must be Q = P = 500 tons. Meanwhile, quantity demanded is Q = 100
tons, so excess supply is 500 - 100 = 400 tons. With the expanded supply of P =
(½)Q, quantity supplied grows to Q = 2P = 1000 tons. Quantity demanded is still
Q = 100 tons, so excess supply grows to 1000 - 100 = 900 tons.
b) The extra 900 - 400 = 500 tons the government has to buy of excess supply
costs the government $500/ton, so the added expenditure is 500(500) = $250,000.
2.
Notice first that the shift in the demand curve does not affect aggregate quantity supplied
! under either scheme 105 million kilograms are supplied. The government costs under
the buy-and-store program decrease as the demand curve gets steeper since the quantity
bought by consumers at the $3 support price increases. Conversely, its costs under the
price subsidy program increase as the demand curve gets steeper since the market
clearing price for 105 million kilograms decreases, necessitating an increase in the per
kilogram subsidy.
3.
Using the cost-benefit criterion, we conclude that in this situation the price subsidy
scheme is preferred to the buy-and-store scheme. We want to argue, however, that some
people are made worse off when we move from the buy-and-store scheme to the price
subsidy scheme. It is useful to focus on two types of people: a type 1 person does pay
taxes but does not consume butter; a type 2 person does consume butter but does not pay
taxes. There are, of course, other types of people, but we can make our point by focusing
on just these two types. Clearly, individuals of type 1 prefer the buy-and-store scheme,
while individuals of type 2 prefer the price support scheme. A move from the buy-andstore scheme to the price support scheme trades off losses for type 1 people against gains
for type 2 people.
4.
a)
Given total demand, Q = 3244 - 283P, and domestic demand, Qd = 1700 - 107P,
we may subtract and determine export demand, Qe = 1544 - 176P.
The initial market equilibrium price is found by setting total demand equal to
supply:
3244 - 283P = 1944 + 207P, or
P = $2.65.
The best way to handle the 40 percent drop in export demand is to assume that the
export demand curve pivots down and to the left around the vertical intercept so
that at all prices demand decreases by 40 percent, and the reservation price (the
maximum price that the foreign country is willing to pay) does not change. If you
instead shifted the demand curve down to the left in a parallel fashion the effect
on price and quantity will be qualitatively the same, but will differ quantitatively.
The new export demand is 0.6Qe = 0.6(1544 - 176P) = 926.4 - 105.6P.
Graphically, export demand has pivoted inwards as illustrated in the figure below.
Total demand becomes
QD = Qd + 0.6Qe = 1700 - 107P + (0.6)(1544 - 176P) = 2626.4 - 212.6P.
Equating total supply and total demand,
1944 + 207P = 2626.4 - 212.6P, or
P = $1.63,
which is a significant drop from the market-clearing price of $2.65 per bushel. At
this price, the market-clearing quantity is 2280.65 million bushels. Total revenue
has decreased from $6614.6 million to $3709.0 million. Most farmers would
worry.
b)
With a price of $3.50, the market is not in equilibrium. Quantity demanded and
supplied are
QD = 2626.4 - 212.6(3.5) = 1882.3, and
QS = 1944 + 207(3.5) = 2668.5.
Excess supply is therefore 2668.5 - 1882.3 = 786.2 million bushels. The
government must purchase this amount to support a price of $3.5, and will spend
$3.5(786.2 million) = $2751.7 million per year.
5.
a) Since the price is now per cup, expect that the size of the mugs will increase (and thus
lowers price per ounce of coffee).
b) No best answer here. Depends upon how you model the individual decision not to pay
for a cup of coffee. You would want to consider potential differences in monitoring
costs, probability of detection, and in transactions costs under the two pricing regimes.