Chapter 11
APPLIED COMPETITIVE
ANALYSIS
Total consumer (CS) and producer surplus (PS) is maximized at the long-run competitive equilibrium.
CS + PS is the additional value obtained by market participants by being able to make market
Price
transactions in a good.
Graphical Proof
A
Distance AB is total surplus for the first unit produced. For each additional
unit produced, total surplus increases by less than AB until the last unit
provides no additional surplus at Q*. This happens at the equilibrium price P*.

F
P1
P*
Total surplus is not maximized at Q1. Demanders would value an additional
unit of output at P1, whereas marginal costs would be given by P2. As long as
P1 > P2, total welfare would increase by producing and trading one more unit
of output. Both parties would gain surplus at any non-equilibrium price
between P1 and P2.
LS
E
G
P2

D
B
0
Q1
Q*
Q/period
At Q1, the total welfare loss is given by area FEG regardless of the price.
However, the distribution of the surplus depends on the non-equilibrium price.
For example, at a price of P1, CS reduces to area AFP1, but producers could
gain because PS is now P1FGB. At a price of P2, the opposite is true.
Mathematical Proof
In long-run equilibria along the long-run supply curve, P(Q) = AC = MC. Maximization of CS with respect to Q
yields U΄(Q) = P(Q) = AC = MC, or marginal value of an additional unit of production equals its MC, where U(Q)
is the utility function for the representative consumer and P(Q) is the long-run supply function. So maximization
of U(Q) – P(Q), over quantities from 0 to Q, occurs where the marginal value of Q to the representative consumer
is equal to market price. But this is precisely the competitive long-run supply-demand equilibrium, because the
demand curve represents consumers’ marginal valuations, whereas the supply curve reflects firms’ marginal costs.
Applied Welfare Analysis
We are interested in showing how the competitive model is used to examine the
consequences of changing economic conditions on the welfare of market participants.
Usually such welfare changes are measured by looking at changes in CS and PS.
Welfare Loss Computations
Losses in surplus can be used to calculate losses in welfare from restrictions on voluntary
transactions. Losses are triangular for linear supply and demand curves. E.g.: if Demand is QD =
10 – P and Supply is QS = P - 2, market equilibrium occurs at P* = 6, Q* = 4. Restriction of
output to Q1 = 2 would create a gap between what demanders are willing to pay (PD = 10 – Q1 = 8)
and what suppliers require (PSS = 2 + Q1 = 4).
P
10


PD = 8
P* = 6
PSS = 4
QS = P - 2
QD = 10 - P
2
0
0
Q1 Q*
=2 =4
Q/period
The welfare loss from restricting transactions is given by
a triangle with a base of 4 = PD – PSS = 8 – 4 and a
height of 2 (the difference between Q* and Q1). Hence
the welfare loss is $4 = 0.5(8 – 4)(4 – 2) if P is measured
in dollars per unit and Q is measured in units. More
generally, the loss will be measured in the units in which
P · Q is measured.
Welfare Loss Computations with Constant Elasticity Curves. More realistic results can usually be
obtained by using constant elasticity demand and supply curves based on econometric studies.
Assuming P is measured in thousands of dollars and Q in millions of automobiles, and that demand is
given by QD = 200P-1.2 , so eD = -1.2, and supply by QS = 1.3P, so eS = 1 (because S is linear going
through origin).
Equilibrium in the market is given by P* = 9.87, Q* = 12.8. Suppose now that government policy
restricts automobile sales to 11 (million) to control emissions of pollutants. An approximation to the
direct welfare loss from such a policy can be found by the triangular method used earlier.
With Q1 = 11, PD = (11/200)-.83 = 11.1 (set QD = 11 and solve for PD), PSS = 11/1.3 = 8.46.
Hence, the welfare loss “triangle” is .5(PD – PSS)(Q* - Q1) = .5(11.1 – 8.46)(12.8 – 11) = $2.38
billion.
This welfare loss might be weighed against the expected gain from emissions control.
Distribution of Loss. The welfare loss is shared about equally by consumers and producers. An
approximation for consumers’ losses is given by .5(PD – P*)(Q* – Q1) = .5(11.1 – 9.87)(12.8 – 11)
= 1.11, and for producers it is .5(P* - PSS)(Q* - Q1) = .5(9.87 – 8.46)(12.8 – 11) = 1.27. Because
the price elasticity of demand (-1.2) is somewhat greater (in absolute value) than the price elasticity
of supply (1), consumers incur somewhat less than half the loss and producers somewhat more than
half. With an even more price elastic demand curve, consumers would incur an even smaller share
of the loss.
Price Controls and Shortages
Price controls deter long-run supply responses and create welfare losses for both consumers and
producers. Long-run equilibrium is at P1, Q1 (point E). Demand increases from D to D1 causing price to
rise to P2 in the short run and encourage entry by new firms. Assuming increasing costs (slope of LS > 0),
price falls because of entry to P3. Government could impose a ceiling price of P1. Firms would supply
previous output (Q1), but demanders would want Q4, creating a shortage of Q4 – Q1.
Welfare Evaluation
Compare CS and PS under the price-control policy with surplus that would have prevailed in the absence
of controls. First, buyers of Q1 gain CS of P3CEP1 because pay lower price (P1) than would exist in
uncontrolled market (P3). This gain is a pure transfer from producers to consumers. No welfare loss, but
this transfer affects the relative well-being of consumers and producers. Second, the area AE1C is
additional CS that would have been attained without controls. Similarly, the area CE1E is additional PS in
the uncontrolled market. Together, these two areas (area AE1E) are the total value of mutually beneficial
transactions prevented by price-control policy. Area AE1E measures the pure welfare costs of the policy.
Is the transfer from producers to consumers of P3CEP1 worth the cost to society of AE1E?
Disequilibrium Behavior
Assuming that observed market outcomes are generated by Q(P1) Price
= minQD(P1), QS(P1)], then suppliers are content, but not
P2
demanders who are forced to accept an excess demand situation.
They signal dissatisfaction to suppliers by increasing price offers.
P3
Such offers tempt existing suppliers to make illegal transactions
P1
at higher than allowed prices and encourage new entrants to
make such transactions. It is this kind of activity that leads to
black markets in most instances of price control.
E.g., faculty football tickets at half price but can’t sell them.
Tempted to sell when hot game.
SS=∑SMC
A
LS
E1
C
E
D1
D
Q1
Q3 Q4
Q/period
Tax Incidence Analysis
A Welfare Analysis of a Per Unit Tax
A unit tax, t = PD - PSS, creates a vertical wedge
between S and D curves.
Quantity traded declines from Q* to Q1.
Price
F
PD
P*
Demanders incur CS loss of PDFEP*, of which
PDFHP* is a portion of total tax revenues.
LS
t
H
PSS
G
E
D
Balance of total tax revenues (P*HGPSS) is paid by
producers, who lose PS of P*EGPSS.
Reduction in CS + PS exceeds total tax revenues by
FEG = “deadweight” loss because some mutually
beneficial transactions are discouraged by the tax.
Sizes of areas in the figure are affected by the price
elasticities of S and D.
Q1
Q* Q/period
Determining final incidence of the producers’ share of
the tax would require an explicit analysis of input
markets because the burden of the tax would be
reflected in reduced rents for the inputs characterized
by relatively inelastic supply.
A Mathematical Model
Price paid by demanders (PD) is different from price received by suppliers (PSS) because a per-unit tax (t)
introduces a “wedge” between them: PD – PSS = t or in terms of the small price changes we wish to
examine, dPD – dPSS = dt.
Maintenance of equilibrium in the market requires dQD = dQS, or DPdPD = SPdPSS, where DP, SP are
the price derivatives of the demand and supply functions. Solve for the effect of the tax on PD: DPdPD =
SPdPSS = SP(dPD – dt). Hence we have
1)
dPD
SP
eS
,


dt
S P  D P eS  e D
where eS and eD are price elasticities of supply and demand, and the final equation is derived
by multiplying the numerator and denominator by P/Q. Similarly for a change in supply
price we have
2)
dPSS
eD

.
dt
eS  e D
Because e D  0, eS  0, these calculations provide the obvious results: dPD  0, dPSS  0.
dt
dt
If eD = 0 (demand is perfectly inelastic), dPD dt  1 and the per-unit tax is completely paid by
demanders.
If e D  , dPSS/dt  1 and the tax is wholly paid by producers.
dPSS
dt   e D , which shows that the actor with the less
Dividing Equation 2 by Equation 1 yields 
dPD
eS
dt
elastic response (in absolute value) will experience most of the price change occasioned by the tax.
Deadweight Loss and Elasticity
Nonlump-sum taxes create deadweight losses because behavior of economic actors is altered.
The size of losses depends on the elasticities of D and S.
A linear approximation of deadweight loss from a small tax, dt, is
3) DW = .5(dt)(dQ).
But from the definition of elasticity, we know that
4) dQ = eDdPD(Q0/P0) because eD = dQ times the inverse of dPD(Q0/P0)
where Q0 and P0 are the pretax values for quantity and price. Combining equations 4 and 1 yields
e
 dt( Q0
),
dQ  e D  S
P0
 e S  e D 
and substitution into Equation 3 provides a final expression for the loss
2
5)
 dt  e e
 P0Q0.
DW  .5   D S



e
e

S
D 

 P0  
Deadweight losses are zero when either eD or eS is zero because the tax does not alter the quantity of the
good traded.
Deadweight losses are smaller when eD or eS is smaller.
Equation 5 can be used to evaluate the deadweight losses accompanying any complex tax system.
The Deadweight Loss from Taxes (Automobile Example)
In the automobile sales example we examined the loss of consumer and producer surplus that would occur
if automobile sales were cut from their equilibrium level of 12.8 million to 11 million. An auto tax of
$2,640 (i.e., 2.64 thousand dollars) would accomplish this reduction because it would introduce exactly the
wedge between demand and supply price that was calculated previously. If we have assume eD = -1.2 and
eS = 1.0, and initial spending on automobiles is approximately $126 (billion), equation 5 predicts the
deadweight loss from the auto tax at
9.84 x 12.8 = P*Q*
2


 2.64  - 1.2
126   2.46
DW   0 .5 

2.2
 9.87 
2
 dt  e e
 P0Q0.
DW  .5   D S
eS  e D 
 P0  
This loss of 2.46 billion dollars is about the same as the deadweight loss from emissions control (reducing
Q to 11.0) calculated in the example ($2.38 billion). It might be contrasted to total tax collections, which
in this case amount to $29 billion ($2,640 per automobile times 11 million automobiles in the post-tax
equilibrium). Here the deadweight loss equals approximately 8 percent of total tax revenues collected
(2.46/29=0.08).
Marginal Burden
An incremental increase in the auto tax would be relatively more costly in terms of deadweight losses.
Suppose the government decided to round the auto tax upward to a flat $3,000 per car. In this case, car
sales would drop to approximately 10.7 (million). Tax collections would amount to $32.1 billion, an
increase of $3.1 billion over what was computed previously. Equation 5 can be used to show that
deadweight losses now amount to $3.17 billion; an increase of $0.71 billion above the losses experienced
with the lower tax. At the margin then, additional deadweight losses amount to about 23% (=0.72/3.1) of
additional revenues collected. Hence marginal and average excess burden computations may differ
significantly.
The model above can be used for other economic applications with a wedge between buyers’ and
sellers’ prices.
Transaction Costs (costs associated with making market transactions)
Explicit fees: fees charged by third parties who facilitate transactions in real estate, stocks and bonds,
boat and airplane tickets, and most things solid at auction.
Implicit fees: when purchasing a used car, time and effort spent reading classified advertisements and
examining vehicles.
The tax model applies when transaction costs are on a per-unit basis (e.g., auctions). As determined in
the tax model, the fee will be shared between buyers and sellers, depending on elasticities of S and D.
The analysis does not consider possible benefits obtained from brokers. To the extent that these
services are valuable to the parties in the transaction, demand and supply curves will shift outward to
reflect this value. Hence trading volume may actually expand with the availability of services that
facilitate transactions, although the costs of such services will continue to create a wedge between
sellers’ and buyers’ prices.
If transaction costs were a lump-sum amount per transaction, individuals would seek to reduce the
number of transactions, but the existence of the charge would not affect the supply-demand equilibrium
itself. For example, the cost of driving to the supermarket is mainly a lump-sum transaction cost on
shopping for groceries. The existence of such a charge may not significantly affect the price of food
items or the amount of food consumed, but the charge will cause individuals to shop less frequently, to
buy larger quantities on each trip, and to hold larger inventories of food in their homes than would be
the case in the absence of such a cost.
Trade Restrictions
Restrictions on the flow of goods in international commerce have effects similar to those we
just examined for taxes. Impediments to free trade may reduce mutually beneficial
transactions and cause a variety of transfers among the various parties involved.
Gains from International Trade
With no trade, the domestic equilibrium price is P* and quantity is Q*.
If world price, PW, is less than P*, opening trade causes the domestic price to fall to PW (assumes the
importing country is a price taker).
Quantity demanded increases to Q1.
Quantity supplied by domestic producers falls to Q2.
Imports equal Q1 - Q2. The quantity demanded by domestic consumers that is not supplied by domestic
producers is supplied by foreign producers at the world price.
Price
LS
E0
P*
PW
A
E1
D
Q2
Q*
Q1
Q/period
The shift in market equilibrium from E0 to E1 causes
an increase in CS of P*E0E1Pw. Part of this gain
reflects a transfer from domestic producers
(P*E0APW) to domestic consumers, and part
represents an unambiguous welfare gain (E0E2A);
buyers get more of the good at a lower price than
without trade.
Losses of PS accrue to inputs that give LS its upward
slope. If, for example, the domestic industry
experiences increasing costs because wages are driven
up as industry output expends, the decline in output
from Q* to Q2 causes wages to fall.
Tariff Protection and the Politics of Trade
Producers are few with large losses, while consumers are many
with small gains, so producers are more likely to organize
opposition to imports than consumers are to organize to keep
trade open.
Price
PR
Producers will likely press government to restrict imports to
prevent loss of PS.
PW
LS
B
E2
DW2
DW1
E1
A
C
D
D
A tariff is a tax on the imported good.
A per-unit tariff for domestic buyers of t raises the effective price
to PW + t = PR.
Quantity demanded falls from Q1 to Q3.
Domestic production expands from Q2 to Q4.
Quantity imported falls from Q1 – Q2 to Q3 – Q4.
Total tariff revenue is BE2DC, measured by t(Q3 – Q4).
Q2
Q4
Q3 Q1
Q/period
Part of CS reduction goes to tariff
revenues and part goes increased
domestic PS (PRBAPW).
BCA and E2E1D are losses of CS not
transferred to tariff revenues or
producers; deadweight loss or excess
burden of the tax.
CS is reduced by area PRE2E1PW.
What if t is such that PR = P*?
Can measure these areas if estimates
of domestic demand and supply
elasticities are available.
Quantitative Estimates of Deadweight Losses from a Tariff
Nicholson redefines t = (PR – Pw)/Pw to represent the proportional increase in price caused by the tariff
(not t = PR – PW). The proportional change in quantity demanded brought about by this proportional
change in price is given by Q  Q
P P
3
Q1
1

R
W
PW
(e D )  te D .
and the CS loss of E2E1D is given by DW1  .5(PR  PW )(Q1  Q 3 )  .5t 2 e D Pw Q1.
The CS loss of BCA is given by DW2  .5(PR  PW )(Q 4  Q 2 )  .5t eS Pw Q 2 .
2
The values of DW1 and DW2 are both convex functions of t and each depends on the initial value of total
revenue, PWQ1 or PWQ2.
When imports initially are a large share of the domestic market and eD and eS are similar sizes (in absolute
value), DW1 will generally be larger than DW2 because Q1 > Q2.
DW1 + DW2 may be larger than total transfers to producers (PRBAPW), thereby leading to rather large
estimates for the “costs” of some tariffs relative to the value of production benefits.
Other types of Trade Protection
A quota limiting imports to Q3 – Q4 would have effects similar to a tariff of t, except no revenues are
collected by the government.
Loss of CS of BE2DC must go elsewhere other than tariff revenue; for example, to owners of import
licenses or to foreign producers, depending on how quota rights are assigned.
Nonquantitative restrictions such as inspection or testing requirements also impose cost and time delays
that can be treated as an “implicit” tariff on imports.
Trade and Tariff Example
Assume S and D are: QS = 1.3P and QD = 200P-1.2, then the domestic market has a long-run
equilibrium of P* = 9.87, Q* = 12.8.
Assume PW = 9, demand would expand to QD =14.3 and domestic supply would shrink to QS =
11.7.
Imports would amount to 2.6 (million) cars.
CS would expand by 11.8 billion dollars, with 10.7 billion being transferred from domestic
producers to consumers.
Now government adopts a $0.5 thousand tariff, the world price rises to 9.5 (thousand dollars),
quantity demanded will contract to 13.4, and domestic supply will expand to 12.4.
Imports would contract to 1.0 (million) cars.
0.0566 = 0.5/9 = (PR – PW)/PW
Welfare effects of the tariff are estimated as
DW1  .5(.5)(14.3  13.4)  0.225  .5(.0566) 2 (1.2)(9)(14.3)  0.238,
DW2  .5(.5)(12.4  11.7)  0.175  .5(.0566) 2 (1)(9)(11.7)  0.165.
Total deadweight loss from the tariff (0.4 billion) is about equal to total tariff revenue (0.5
billion = $0.5 times 1.0 million).
Effects of a Quota will be the same as a tariff, except there is no tariff revenues. The $0.5
billion loss in CS will is transferred to whomever can appropriate the rights to import cars.
This right is worth $500, so it seems likely there will be active interest in acquiring such
rights.