Answers to selected problem set questions

1.  Think carefully about the role of opportunity costs.

2.  The lost $5000 is a sunk cost and should be ignored. 

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

4.  Butter prices.

a) Real price of butter in 1980 prices:

1980 1985 1990 1995 2000 2001
$1.88 $1.62 $1.25 $0.87 $1.21 $1.54

b) Percent change from 1980 to 2001: (1.54 - 1.88)/1.88 = -18.1%

c) Real price of milk in 1990 prices:

1980 1985 1990 1995 2000 2001
$2.98 $2.58 $1.99 $1.38 $1.91 $2.44

d) Percent change from 1980 to 2001: (2.98 - 2.44)/2.98 = - 18.1%

5.  Market definitions
a)  False.  People generally won't travel great differences to arbitrage differences in Whoppers or Big Macs.
b)  False.  Because clothing suppliers can easily move clothing from one part of the country to another.
c)  False.  Different brands of cola are similar enough to constitute one market.

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. Check your book.

8. 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.

9. 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.

10.  We did this one in class.

11.  This one could end up on the exam.

12.  We did this one in class.

13.  This was a question from an old exam.

14.  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.

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.  We did something very similar to this in class.

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 = ()(18.4)(9.2) = $ 84.64 m
PS = ()(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 = ()(6.66)(3.33) = $ 11.1 m
PS = ()(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 = ()(10)(5) = $ 25.0 m
PS = ()(40)(13.3) = $266.0 m
TAX = $416.5 m
SW = - $125.5 m
DWL = $375.5 m

19. 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.

20. 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

21. This is for you to ponder.

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

23. 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

24.  We've done similar problems elsewhere.  Compare your answers to your neighbor's.

25.  Vegetable fiber market.
a)  Qd = 40-2P; Qs = (2/3)P
b)  Ed = -0.82; Ed = -1.50
c)  Es = 1.01; Es = 1.01
d)  US price will be $12 and the level of imports will be 8 million.