Answers to selected problem set questions

1.  Think carefully about the role of opportunity costs in determining land prices in the island nation of Japan.

2.  The opportunity costs must be adjusted downward due to the ability to still conduct business while stuck in traffic.

3.

4.  An increase in prison sentences acts as an increase in the price of committing crime. Therefore, the amount of "crime demanded" should fall according to the law of demand.

5.  Price depends not only on supply, but also demand!

6. Beer Market
a) P falls, Q falls
b) P rises, Q falls
c) P rises, Q rises
d) P falls, Q rises
e) P rises, Q rises
f) P falls, Q rises
g) P ?, Q rises
h) P ?, Q falls
i) P rises, Q ?

7. True or False.
a) False. Supply could have risen leading to an increase in sales (in this case, though, price would be lower).
b) True. Only an increase in demand can account for the increase in price and sales. (Now, supply could have changed over time, but the shift in demand must have been greater to explain the data.)
c) True. The inelastic demand for garden weasels indicates that consumers will not reduce their purchases by very much for any given price increase.
d) True.

8. The official is assuming a perfectly inelastic demand curve.  However, you could have normal looking S and D curves and still account for the observed data: leftward shift in S and rightward shift in D will give you a higher price and same quantity.

9.  We did this one in class.

10.

11.  a)  Arc elasticity is another name for the midpoint elasticity formula.  To calculate the arc price elasticity for American economy seats, you must assume that all other factors affecting AA's load factor are constant.  Thus, find a pair of months in which the US price and Income are the same and then compare the change in AA load factor with the change in AA price.  Doing this leads to a comparison of Month 2 and Month 5.  The % change in AA's load factor is (68-62)/65 = 9.2% and the % change in AA's price is (108-109)/108.5 = 0.92%.  This generates an arc elasticity of -10.0  (very elastic).  Notice that in calculating the % changes in each value that we divided by the midpoint of each range.  The arc income elasticity is found by looking for two months in which AA price and US price are constant, this leads to a comparison of Month 1 and Month 3, and generates an income elasticity of 1.52 (normal good).  The arc cross price elasticity is 13.47 (since it's positive, it indicates that US is a substitute).

12.  We did this one in class.

13.  Elasticities.
a) The East German taxicab drivers must have believed demand was price elastic. That is, they were expecting revenues to increase if fares were lowered
b) Ed = (.33)(75%/400%) = .06 -- very inelastic; perhaps due to addiction.
c) Cigarettes!
%change in Qd = - 14%
%change in P = + 10%
==> Ed = (14)/(10) = 1.4 elastic
would expect elasticity to be lower for older folks because cigarettes are a smaller portion of their budget (and maybe because of addiction).
d) False. Consumer expenditures will increase after the price ceiling is removed no matter what the price elasticity of demand is. This happens because the quantity that consumers are able to buy under the price ceiling is artificially restricted below the free market level. Once the price ceiling is removed both price and quantity will relocate to the free market levels; that is, they will both increase so that total expenditures (= P*Q) must increase.

14.  We did this one in class.

15.  Rent Control
a)    P = 500; Q = 75 (or 750,000).  If P = 100, the Qs = 55 (or 550,000) and there will be a decrease of 200,000 apartments from the free market level. Assuming 3 people per apartment, this would imply a loss of 600,000 people.  At P = 100, Qd = 95 (or 950,000) and there is a shortage of 400,000 units.
b)  At P = 900, Qs = 95 (or 950,000) there would be an increase of 200,000 units over the free market level, thus 100,000 units would be constructed.  Note also that Qd = 55 (or 550,000) and a surplus of 400,000 units would exist.

16. Labor market calculations
a) Free market: set Ld = Ls and solve for w: 80 - 10w = 10w
80 = 20w
w = 4
To get L, plug w = 4 into either the demand or supply equation:
Ld = 80 - 10(4) = 40 m employed persons.
Minimum wage: plug w = 5 into each equation:
Ld = 80 - 10(5) = 30 m
Ls = 10(5) = 50 m
A surplus of 20 million workers exists; only 30 million have jobs.
b) Subsidy of \$1/hr/worker: demand curve becomes Ld = 80 - 10(w - 1) = 90 - 10w
Set this equal to demand: 90 - 10w = 10w
90 = 20w
w = 4.50
The new quantity is found by plugging w = 4.5 into the supply or new demand equation:
Ls = 10(4.5) = 45 m
Noe that the net wage to employers is only \$3.50 (4.50 - 1.00).

17.

18. Beer Market (graphs are not provided)
a) Free Market Calculations:
i) To solve for equilibrium, set Pd=Ps and solve for Q:
60 - 2Q = 10 + 3Q
50 = 5Q
Q = 10 m
To get P, plug Q = 10 into either of above equations. For example, using the demand equation we get:
Pd = 60 - 2(10)
P = \$40
ii) Ed = elasticity of demand = (1/2)(40/10) = 2.0
Since Ed > 1, demand is price elastic.
iii) Solving for the relevant welfare triangles:
CS = (1/2)(20)(10) = \$100 m
PS = (1/2)(30)(10) = \$150 m
SW = \$250 m

b) Government Intervention I: Sales Tax
i) Work the tax into the supply equation as follows:
Ps = 10 + 3Q + (4) = 14 + 3Q
Now, set Pd = Ps and solve for Q:
60 - 2Q = 14 + 3Q
46 = 5Q
Q = 9.2 m
To get Pd, plug Q = 9.2 into the demand equation:
Pd = 60 - 2(9.2) = \$41.60
This price represents what buyers must pay and sellers must collect. The net price that sellers keep is \$37.60 (= 41.6 - 4.00).
ii) Government revenue = tax * units sold = (4)(9.2m) = \$36.8 m
iii) Solving for the relevant welfare triangles:
CS = (½)(18.4)(9.2) = \$ 84.64 m
PS = (½)(27.6)(9.2) = \$126.96 m
REV = \$ 36.8 m
SW = \$248.4 m
DWL = \$ 1.60 m

c) Government Intervention II: Price Ceiling
i) The new quantities are:
20 = 60 - 2Qd
20 = 10 + 3Qs
Qd = 20 m and Qs = 3.33 m
A shortage of 16.7 m units exists.
ii) To solve for the "full" price, plug Q = 3.33 into the demand equation and solve for P:
P = 60 - 2(3.33)
P = \$53.34
iii) Solving for the relevant welfare triangles:
CS = (½)(6.66)(3.33) = \$ 11.1 m
PS = (½)(10)(3.33) = \$ 16.7 m
Bribe = (33.34)(3.33) = \$111.0 m
SW = \$138.8 m
DWL = \$ 111.2 m

d) Government Intervention III: Price Floor
i) The new quantities are:
50 = 60 - 2Qd 50 = 10 + 3Qs
Qd = 5 m and Qs = 13.3 m
A surplus of 8.33 m units exists.
ii) The government must purchase the surplus 8.33 m units. This will cost taxpayers
\$416.50 m (= 8.33 * \$50).
iii) Solving for the relevant welfare triangles: CS = (½)(10)(5) = \$ 25.0 m
PS = (½)(40)(13.3) = \$266.0 m
TAX = \$416.5 m
SW = - \$125.5 m
DWL = \$375.5 m

19.  See graph and table below.

 Before Subsidy is Removed After Subsidy is Removed CS a+b+c+e+f+g+h+i+j a+b+c+e PS k k+f Welfare a+b+c+e+f+g+h+i+j+k a+b+c+e+k+f DWL -- g+h+i+j

20. This is for you to ponder.

21.  Check the analysis of your friends to see if you get similar answers.

22. See graph and table below.

 Before Arbitrage After Arbitrage CS in LA a+b+c a+b+c+d+e+f+g CS in SF a+d+h+i a+d PS in LA d+e+f+h+i+j+l+m h+i+j+k+l+m+n PS in SF l+m h+l Welfare 2a+b+c+2d+e+f+2h+2i+j+2l+2m 2a+b+c+2d+e+f+g+2h+i+j+k+2l+m+n Change in Welfare g+k+n-i-m