5. If Jennifer babysits for 3 hours at $4 per hour, her producer surplus is $1+$1+$1 = $3. If she babysits for 5 hours at $5 per hour it is $2+$2+$2+$1+$0=$7.
6. The gains from trad ein the shoe-store example and the two-student example are the consumer and producer surplus from those trades.
10. The shaded area represents the gains from trade that people would have had at the equilibrium quantity and price. By limiting the output to Q0, the marginal cost of producing additional units would be less than the marginal benefit. So the benefit to consumers of producing one more unit of output (the marginal benefit) is larger than the cost of producing that output (the marginal cost), meaning that it would be economically efficient to produce that an unit of output. If that extra unit is not produced, there is a deadweigt social loss. Deadweight social losses occur whenever marginal benefit and marginal cost are not equal.
11. It is economically inefficient to produce more than the equilibrium quantity because the marginal cost of producing more units exceeds the values that consumers place on those units, as measured by their willingness to pay (the height of the demand curve at those quantities).
12. A law preventing Bill from riding would cause a $1.75 deadweight social loss. A law limiting him to one ride would cause a 75-cent deadweight social loss.
13. See figure 11 on page 221 and the table below it, showing consumer and producer surplus with and without international trade, and the deadweight social loss from a law prohibiting international trade.
14. Draw a graph to show consumer and producer surplus:
a. Without a tax
b. With a tax on production of a good. (Also show the deadweight
social loss.)
Without the tax, consumer surplus is the sum of Areas A, B, and C. Producer
surplus is the sum of Areas D, E, and F.
With the tax, consumer surplus is Area A and producer surplus is Area
F. The sum of Areas B and D shows total tax payments, which the government
collects as tax revenue. The sum of Areas C and E is a deadweight social
loss.
15. Draw a graph to show consumer and producer surplus:
a. Without a subsidy
b. With a subsidy for the production of a good (Also show the
deadweight social loss.)
(a) Without a subsidy, consumer surplus is
area A + B and producer surplus is area F + G.
(b) With a subsidy, consumer surplus is
area A + B + E + F and producer surplus is
area B + C + F + G. The deadweight social loss is
area D.
16. Draw a graph to help explain why a tax does not cause a deadweight social loss if supply is perfectly inelastic.
If the supply of a good is
perfectly inelastic, a tax on that good does not cause a deadweight social
loss. The equilibrium quantity remains unaffected by a tax, and the
total gain from trade to everyone, including the government does not change;
it remains the sum of Areas A, B and C.
19. Use diagrams to show the effect of a tax on consumer and producer
surplus, and to show the deadweight social loss from the tax when:
a. The demand curve is perfectly inelastic.
b. The supply curve is perfectly inelastic.
c. The demand curve is perfectly elastic.
d. The supply curve is perfectly elastic.
(a) Using the notation from the class, draw a graph that
looks like Figure 10 in chapter 8 on page 194. A tax of T dollars
per unit raises the price that buyers pay (including tax) to PB, while
the price that sellers receive (net of tax) remains unchanged at PS.
The equilibrium quantity remains unaffected by the tax. As
a result, producer surplus remains unchanged, and consumer surplus falls
by the same shaded area that shows the gain to government.
There is no deadweight social loss from the tax in this case.
(b) See the figure in the answer to problem 16 (above), which is like
Figure 14 on page 223 of the text (you may also want to look back at panel
(b) of Figure 10 on page 194). A tax of T dollars per unit lowers
the price that sellers receive (net of tax) to PS, while the price that
buyers pay (including tax) remains unchanged at PB. The equilibrium
quantity remains unaffected by the tax. Consumer surplus remains
unchanged at area A, producer surplus falls by area B, and the government
gains area B. There is no deadweight social loss from the tax in
this case.
(c)
Draw a graph that looks like
panel (c) of Figure 10 from chapter 8, on page 194. Except for the
fact that demand is horizontal, the graph is the same as Figure 12 on page
222. A tax of T dollars per unit lowers the price that sellers receive
(net of tax) to PS. Because demand is horizontal, the price that
buyers pay (including tax) remains unchanged at PB and consumer surplus
remains unchanged at zero. Producer surplus falls by the sum of areas
D and E, and the government gains only area D, so area E shows the
deadweight social loss from the tax. (Areas A, B, and C are all zero
since the demand curve is a horizontal line at the price P1 ).
(d)
(d) 
Draw a graph that
looks like panel (d) of Figure 10 in chapter 8, on page 194. Except
for the fact that supply is a horizontal line at the price P1, the graph
is the same as Figure 12 on page 222. A tax of T dollars per unit
raises the price that buyers pay (including tax) to PB. Because supply
is horizontal, the price that selles receive (net of tax) remains
unchanged at PS and producer surplus remains unchanged at zero. Consumer
surplus falls by the sum of areas B and C, and the government gains only
area B, so area C shows the deadweight social loss from the tax.
(Areas D, E, and F are all zero.)
20. Draw a diagram to illustrate the effects of a subsidy for the production of candy. Show the effects on (a) output of candy, (b) the prices paid by buyers and received by sellers, (c) consumer surplus, and (d) producer surplus. Also show (e) the cost of the subsidy to the government and (f) the social gain or loss from the subsidy.
21. Comment on these statements:
a. "Economists say that taxes cause a deadweight social loss,
but this is misleading. Obviously, when one person pays money in taxes,
another person collects money in taxes, so there is no loss to society
as a whole."
b. "A tax causes a deadweight social loss to the extent that
people change their behavior so they don't have to pay it."
a. This statement shows a misunderstanding of deadweight social losses
caused by taxes. Taxes cause a deadweight social loss when people
change their behavior to avoid paying the tax. The deadweight social
loss occurs because some people stop making mutually advantageous trades.
(See the discussion of taxes in the two-student example near the end of
Chapter 3, on page 63.) That is why a tax does not cause a deadweight
social loss in cases where the demand curve or supply curve is perfectly
inelastic (as in parts (a) and (b) of question 19 above); in those special
cases the tax does not reduce the number of voluntary trades that people
make, and the equilibrium quantity is unaffected by the tax, so there is
no deadweight social loss (aside from any administrative costs of the tax).
More generally, taxes cause deadweight social losses even though the amount
that one person pays in taxes equals the amount that someone else (the
government) receives.
b. A tax causes deadweight social loss because it prevents some mutually
advantageous trades. So while people may not consciously avoid paying the
tax by changing their behavior, they may change their behavior nonetheless
simply because the price for the good or service is too high once a tax
is imposed on it. The deadweight social loss from the tax represents
the consumer and producer surplus that people would have obtained from
the trades prevented by the tax.
22. Draw a diagram like Figure 11 that shows equilibrium with
international trade. Suppose that foreign demand rises. How much do U.S.
consumers gain or lose? What about U.S. producers, foreign consumers, and
foreign producers?
(This graph is similar to Figure 2 from chapter 7, on page 158, except
this graph shows consumer and producer surplus.)
Consider an initial situation in which the U.S. exports the good, as in the graph. (A similar analysis applies if the U.S. initially imports the good.)
Initially, the price is P1 and
24. Suppose a change occurs in the economy, and you gain something
that you value at $1,000, while I lose something that I value at $200 (and
no one else gains or loses). This change in economically efficient
because you gain more than I lose, but it is not a Pareto improvement because
I lose.
25. (a) With international trade, the equilibrium price is $7.
The U.S. consumes 12 and produces 8; foriegn countries produce 14 and consume
10.
(b) Without international trade, the equilibrium price in the U.S.
is $9. The U.S. consumes and produces 10 units. Foreign countries
have an equilibrium price of $5, and they consume and produce 12 units.
(c) Draw a graph like Figure 11 on page 221. The only difference
is that the U.S. exports the good in Figure 11; they import the good in
this problem -- in other words, for this problem, panel (a) of Figure
11 shows foreign countries and panel (b) shows the United States.
Now consider a law prohibiting international trade.
GAINS/LOSSES IN THE U.S. -- The law reduces U.S. consumer surplus by an area that looks like FG in Figure 11. That area consists of a rectangle with area $20 (since its base is 10 and its height is $2) PLUS a triangle with base 2 and height $2, which has area $2. So U.S. consumers lose $22 from the law. The law raises U.S. producer surplus by an area that looks like F in Figure 11. That area consists of a rectangle with area $16 (since its base is 8 and its height is $2) PLUS a triangle with base 2 and height $2, which has area $2. So U.S. producers gain $18 from the law.
GAINS/LOSSES IN OTHER COUNTRIES -- The law raises foreign consumer surplus by an area that looks like B in Figure 11. That area consists of a rectangle with area $20 (since its base is 10 and its height is $2) PLUS a triangle with base 2 and height $2, which has area $2. So foreign producers gain $22 from the law. The law lowers foreign consumer surplus by an area that looks like BC in Figure 11. That area consists of a rectangle with area $24 (since its base is 12 and its height is $2) PLUS a triangle with base 2 and height $2, which has area $2. So oreign consumers lose $26 from the law.
DEADWEIGHT SOCIAL LOSS: (Actually, we can tell from the answers
just above that each country loses $4 in deadweight social loss from the
law -- but here is another way to calculate it.) The deadweight social
loss looks like areas C and G in the graph. Now calculate are G for
the U.S. and are C for the foreign country. Since the U.S. imports
4 units in this problem, the base of the triangle G is 4. Since the
price with international trade is $2 below the price that the U.S. would
have without international trade, the height of the triangle is $2.
So the area of the triangle is (1/2)(2)($2) = $2. The same calculation
shows that the area of triangle C is $2. So each country takes a
$2 deadweight social loss from a law outlawing international trade, for
a total world loss of $4.
A1. The price is $10 per unit and the quantity sold is 20 units. Total spending on the good is $200, Producer surplus is the area of a triangle base 20 units and height $10 per unit, or $100. Consumer surplus is the area of a triangle with height $20 (since the price is $10 and the demand curve intercepts the Y axis at a price of $30) and base 20, so consumer surplus is $200.
A2. The price is $10 per unit and the quantity sold is 200 units. Total spending on the good is $2000, Producer surplus is the area of a triangle base 200 units and height $10 per unit, or $1000. Consumer surplus is the area of a triangle with height $20 (since the price is $10 and the demand curve intercepts the Y axis at a price of $30) and base 200, so consumer surplus is $2000.
B1. Without a tax, the price is $50 and the quantity is 400.
With the $8 per unit tax, buyers pay $56 per unit and sellers receive a
net price of $48 per unit. The equilibrium quantity with the tax
is 388. As a result of the tax, producer surplus falls by ($2)(388)+(1/2)($2)(12)
= $788. Consumer surplus falls by ($6)(388)+(1/2)($6)(12) = $2364.
The total loss in producer and consumer surplus is $3152. The government
gains ($8)(388)=$3104. The deadweight social loss from the tax is
$48.
B2. Without a tax, the price is $5 and the quantity is 400. With the $4 per unit tax, buyers pay $6 per unit and sellers receive a net price of $2 per unit. The equilibrium quantity with the tax is 280. As a result of the tax, producer surplus falls by ($3)(280)+(1/2)($3)(120) = $1020. Consumer surplus falls by ($1)(280)+(1/2)($1)(120) = $340. The total loss in producer and consumer surplus is $1360. The government gains ($4)(280)=$1120. The deadweight social loss from the tax is $240. Note that $240 = (1/2)($4)(120).
B3. (Redo problem B2 with a $4 subsidy instad of a $4 tax.) Without a subsidy, the price is $5 and the quantity is 400. With the $4 per unit subidy, buyers pay $4 per unit and sellers receive a net price of $8 per unit. The equilibrium quantity with the subsidy is 520. As a result of the subsidy, producer surplus rises by ($3)(400)+(1/2)($3)(120) = $1380. Consumer surplus rises by ($1)(400)+(1/2)($1)(120) = $460. The total gain in producer and consumer surplus is $1840. The government spends ($4)(520)=$2080 on the subsidy. So the deadweight social loss from the tax is $240. Note that $240 = (1/2)($4)(120).
B4. Without a tax, the price is $100 and the quantity is 400.
With the $30 per unit tax, buyers pay $112 per unit and sellers receive
a net price of $82 per unit. The equilibrium quantity with the tax
is 328. The deadweight social loss from the tax is (1/2)($30)(72)
= $1080.