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 P

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

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

Now, set P

60 - 2Q = 14 + 3Q

46 = 5Q

Q = 9.2 m

To get P

P

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

20 = 10 + 3Q

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

Q

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 |

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

24. 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 $9 and the level of imports will be 16 million.