Answers to selected problem set questions

1. #2 page 18:

a) Real price of milk in 1980 prices:

b) Percent change from 1980 to 1998: (1.05 - .81)/1.05 = -22.8%

c) Real price of milk in 1990 prices:

d) Percent change from 1980 to 1998: (1.67 - 1.29)/1.67 = - 22.8%

2. 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 ?

3. Check your notes or book.

4. 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) False. Since demand is greater in the cities than in rural areas, one would expect more services to be provided at a higher price.
d) True. The inelastic demand for garden weasels indicates that consumers will not reduce their purchases by very much for any given price increase.
e) True.

5. This might end up on the exam.

6.  #2, p62:
a)  E = -0.40 when P = 80; E = -0.56 when P = 100.
b) E = 0.50 when P = 80; E = 0.56 when P = 100.
c) P = 100 and Q = 18 million
d) Shortage of 4 million units.

7.    You did this one for homework.

8.  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.

9. 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
Note that the net wage to employers is only $3.50 (4.50 - 1.00).

10. 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) Beer! Ed = 1 note that when demand is unitary elastic, total expenditures don't change, no matter what the change in price. This is not perfectly inelastic! (That would mean that quantity never changes. Here, it is total expenditures that never changes.)
d) Athletic ticket prices!
%change in Qd = - 8%
%change in P = + 25%
==> Ed = (8)/(25) = .32 inelastic
since the college raised ticket prices and revenues increased by 16%, this is consistent with the notion that demand is inelastic.
e) 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).
f) The demand for personalized plates must've been price elastic if revenues fell after a price increase.
g) Quantity demanded would fall by approximately 11%. The price increase from $275 to $325 represents an 18% increase. Since elasticity = %D Q / %D P = 0.60, you can solve for %D Q with a little algebra. Based on this estimate, we can expect approximately 89,000 units to be rented at $325 per month.
h) 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.

11. We did part of this in class.

12. This one could end up on the exam.

13. Beer Market (graphs are not provided)
a) Free Market Calculations:
i) To solve for equilibrium, set P^d=P^s 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:
P^d = 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:
P^s = 10 + 3Q + (4) = 14 + 3Q
Now, set P^d = P^s and solve for Q:
60 - 2Q = 14 + 3Q
46 = 5Q
Q = 9.2 m
To get P^d, plug Q = 9.2 into the demand equation:
P^d = 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 - 2Q^d
20 = 10 + 3Q^s
Q^d = 20 m and Q^s = 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 - 2Q^d 50 = 10 + 3Q^s
Q^d = 5 m and Q^s = 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

14. 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.

15. See graph and table below.

16.  Coffee imports.
a)  Consumers will pay P = 10 (which is the sum of the $8 import cost and $2 distribution cost).  Q = 150 m.
b)  P = 12 and Q = 130 m.
c)  Lost CS = $280m
d)  Tariff revenue = $260m 
e)  DWL = $20m 

17. Liquor tax
a) The "pass through" fraction formula for determining the burden of a tax is: Es/(Es-Ed) = 4/(4-(-0.2)) = 0.95. Therefore, 95 percent of the tax is passed through to the consumer because supply is relatively elastic and demand is relatively inelastic.
b) With an increase in the price of liquor, consumers will substitute away from liquor to beer (shifting the demand for beer outward).  With an infinitely elastic supply for beer, there will be no change in the equilibrium price of beer.

18. We discussed this in class.

19. /This is for you to ponder.

20. See graph and table below.