Prof. Bryan Caplan

bcaplan@gmu.edu

http://www.bcaplan.com

Econ 849

Fall, 2001

 

HW #1 Answer Key

 

2.  The Queen holds on auction on the monopoly right to produce and sell tea.  There are two available producers of tea.  The demand curve for tea, and the costs of the two producers (Lancaster and York), are given in this table:

 

Price

per ton

Quantity (tons)

Total Revenue

Total Cost of Lancaster

Total Cost of York

Total Profit of

Lancaster

Total Profit

of York

£1000

1000

£1,000,000

£400,000

£500,000

£600,000

£500,000

£900

1500

£1,350,000

£600,000

£750,000

£750,000

£600,000

£800

3000

£2,400,000

£1,200,000

£1,500,000

£1,200,000

£900,000

£700

3200

£2,240,000

£1,280,000

£1,600,000

£960,000

£640,000

£600

3400

£2,040,000

£1,360,000

£1,700,000

£680,000

£340,000

£500

3600

£1,800,000

£1,440,000

£1,800,000

£360,000

£0

£400

3800

£1,520,000

£1,520,000

£1,900,000

£0

-£380,000

£300

4000

£1,200,000

£1,600,000

£2,000,000

-£400,000

-£800,000

£200

4200

£840,000

£1,680,000

£2,100,000

-£840,000

-£1,260,000

 

A.         If Lancaster received the monopoly privilege, what price and output level would he set?  What would his (gross) monopoly profits be?

 

Price would be £800; quantity 3000; profits £1,200,000.

 

 

B.                  If York received the monopoly privilege, what would his price, output, and (gross) monopoly profits be?

 

Price would be £800; quantity 3000; profits £900,000.

 

C.                  If the Queen auctioned off the monopoly privilege to Lancaster and York, who would win the auction?  How much would the winner pay?  (Assume the Queen starts at a low price and rises it by a penny at a time until one bidder drops out).

 

Lancaster would win and pay £900,001 - just enough to beat York.

 

D.                  Are there any losses to productive efficiency from this grant of privilege?  To allocative efficiency?  Why?

 

There are only losses to allocative efficiency; bidding ensures that the productively efficient firm wins.

 

E.                  Suppose the Queen, sensitive to the charge that she is enriching herself with these auctions, randomly selects the recipient of the grant (by making Lancaster and York publicly play Rock, Paper, Scissors, for example).  How are the deadweight losses of monopoly likely to be affected?

 

The deadweight costs will be greater if York wins, because York is the less productively efficient producer.

 

F.                  Parliament strips the Queen of the right to give monopolies, and declares that henceforth monopolies will be awarded to whichever firm gets the most votes from the members of Parliament.  Lancaster and York compete for votes by paying for political advertising for their supporters, hiring lawyers, and so on.  Who, if anyone, now benefits - on net - from the distribution of monopoly grants?

 

Probably no one benefits.  Politicians now have to pay more to win elections.  Lobbyists just get paid enough to make them switch from their non-lobbying occupation.  With competitive entry, there will be full rent-dissipation.

 

3.  Suppose that you are narrowly self-interested, risk-neutral, require an hour to vote, and value your time at $100/hour.  Bush is $1000 better for you than Gore, and people other than yourself vote for Bush with p=.505.  Using the probability of decisiveness formula from the notes, calculate the critical number of voters (2n+1) that leaves you exactly indifferent between voting and not voting.

 

You will be exactly indifferent if:

 

, or in other words, if the probability of decisiveness equals 10%.  Using the formula from the notes, then, we solve to find the critical value of n such that:

 

 

Simplifying:

 

 

 

 

Solving numerically by trial-and-error (or Excel Goal Seek), n*=31.65, (2n+1)=64.3.  If n£64, it is selfishly worthwhile to vote; if n³65, it is not.

 


4.  Use diagrams to contrast the deadweight loss from laissez-faire supply of (a) a good that is perfectly non-rival but fully excludable, and (b) a good that is fully rival but perfectly non-excludable.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

5. 

 

A.                  What will the PDV of lifetime earnings be for workers with and without college educations be if...?  (To fill in this table, just take the average PDV for workers with and without college degrees in each of the rows).

Worker #'s w/ College Degrees

Without College PDV

With College PDV

College Premium

1-7

--

$1,642,857

--

2-7

$1,000,000

$1,750,000

$750,000

3-7

$1,100,000

$1,860,000

$760,000

4-7

$1,200,000

$1,975,000

$775,000

5-7

$1,300,000

$2,100,000

$800,000

6-7

$1,400,000

$2,250,000

$850,000

7

$1,500,000

$2,500,000

$1,000,000

B.                 Suppose you are worker #4.  Workers #1-3 don't have college degrees; workers #5-7 do.  What is your PDV of earnings without a college degree?  With a college degree?

 

If you don't get a college degree, you get lumped in with workers #1-3, so you get $1,300,000.  (Look at the #5-7 w/college degree row, in bold).  If you do get a college degree, you get lumped in with workers #4-7, so you get $1,975,000. (Look at the #4-7 w/college degree row, in italics).

 

 

C.                What are the total earnings of the other workers if you (still worker #4) get a college degree?  If you don't?

 

If you do get a college degree, then workers #1-3 get $1,200,000, and workers #5-7 get $1,975,000.  Total earnings for them: $9,525,000.

 

If you don't get a college degree, then workers #1-3 get $1,300,000, and workers #5-7 get $2,100,000.  Total earnings for them: $10,200,000.

 

 

D.                Suppose worker #4's college costs $500,000 total.  What is the net gain of college to worker #4?  The net gain to all seven workers?

 

If #4 goes to college, he earns $1,975,000; if he doesn't, he earns $1,300,000.  The net gain of college would be $675,000-$500,000=$175,000: a gaining proposition for worker #4.

 

What about the net gain to all 7 workers?  If worker #4 goes to college, he earns $1,975,000, and the other six workers earn $9,525,000.  If worker #4 doesn't go to college, he earns $1,300,000, and all other workers earn $10,200,000.  So:

 

Total Income If #4 Goes to College: $1,975,000+$9,525,000-$500,000=$11,000,000

Total Income If #4 Does Not Go to College: $1,300,000+$10,200,000=$11,500,000

 

In other words, the net social benefit of #4 going to college is -$500,000, precisely the cost of going to college!

 

E.                 Are there externalities of education in this problem?  Explain.

 

Yes: There are negative externalities.  A worker who pays for school raises his own income, but the income of other workers falls by an equal amount.  Since productivity does not change, the cost of schooling is a pure deadweight cost.

 

6.  In a given market:

 

Supply is given by: Q=aP

Demand is given by: Q=c-dP

Social Benefits are given by: Q=c/2-dP

 

At the outset, note that Supply and Social Benefits intersect when , while Supply and Demand intersect when

 

Let us define the former value of Q as Q1 and the latter value as Q2.

 

What is total surplus at the intersection of Supply and Demand? 

 

Using the geometry of triangles, total surplus at the intersection equals the area of triangles 1 and 2 minus the area of triangles 3 and 4. 

 

This comes out to:

 

 

 

 

 

 

 

 

 

 

 

 

At the intersection of Supply and Social Benefits? 

 

This is simply the sum of the area of triangles 1 and 2, which comes out to:

 

 

 

 

 

 

 

 

 

 

Prove that total surplus is maximized at the intersection of Supply and Social Benefits. 

 

Using the geometry of triangles, total surplus as a function of actual Q is:

 

 

Maximizing this expression with respect to Q gives us:

 

 

which implies that total surplus is maximized when Q=Q1, the intersection of S and SB.  QED.