# equilibrium taxes

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```					APPENDIX TO CHAPTER 2
Market Equilibrium,
Efficiency & Taxes
Main Ideas
 Market  Equilibrium
 Efficiency
 Social Surplus
 Pareto Efficiency

 Market    Interventions
   Price Ceilings & Price Floors
 Taxes   and Tax Incidence
Market Equilibrium

 Equilibrium:  A situation where there is no
incentive for change.

 Market Equilibrium: A market is in equilibrium
when total quantity demanded by buyers equals
total quantity supplied by sellers
 In a market equilibrium, buyers have no incentive to
offer a higher price, and..
 Sellers have no incentive to offer a lower price
Excess Supply
Market         Market
p
demand         supply
q=S(p)
D(p’) < S(p’); an excess
p’                    of quantity supplied over
p*                    quantity demanded.
q=D(p)

D(p’)       S(p’)    D(p), S(p)
Market price must fall towards p*, i.e.
sellers must offer a lower price to buyers
Market Equilibrium
Market          Market
p
demand          supply
q=S(p)
D(p”) > S(p”); an excess
of quantity demanded
p*                    over quantity supplied.
p”                    q=D(p)

S(p”)    D(p”)      D(p), S(p)
Market price must rise towards p*, i.e.
buyers must offer more to sellers
Market Equilibrium
Market        Market
p
demand        supply
S(p) = c+dp
What are the values
p*                 of p* and q*?

D(p) = a-bp

q*         D(p), S(p)
Market Equilibrium
D(p)  a  bp
S(p)  c  dp

At the equilibrium price p*, D(p*) = S(p*).
That is,           *           *
a  bp  c  dp
which gives      * ac
p 
bd
Market Equilibrium
D(p)  a  bp
S(p)  c  dp

At the equilibrium price p*, D(p*) = S(p*).
That is,           *           *
a  bp  c  dp
which gives      * ac
p 
bd
*        *
and q  D(p )  S(p )  ad  bc
*
.
bd
Market Equilibrium
Market        Market
p
demand        supply
S(p) = c+dp
*
p 
ac
bd
D(p) = a-bp
q 
*
bd
Summary: Market Equilibrium
 We have learnt that a Demand Curve reflects a
consumer’s marginal utility from consumption,
as captured by his WTP. He buys QD: P = MU

 Supply  Curve: Later in the course, we will see
that firms (in a competitive market) sell a quantity
such that the price received for the last unit is just
above (or equal to) its cost, i.e.
QS: P = MC (as long as P > min AC)

 AtMarket Equilibrium, P*: QD = QS = Q* =>…
 Market Equilibrium results in an output level Q*,
such that at Q*: MU=MC
Efficiency
   Economists are very concerned with the goal of “efficiency”
 i.e. to minimize waste of resources
   E.g. Gasoline taxes are a more efficient way of collecting
taxes than Income Taxes: Why?
 No govt. resources spent on collection
 Scope for fraud is zero, hence no expenses on audits
   When a competitive market produces an output level Q*:
MU = MC, it is efficient, why?
 The benefit of the marginal unit produced is at least as
high as its cost.
 If Q’: MU > MC? Too little output
   There are two different concepts of efficiency. We will
focus more on one here, but I will mention the second.
Economic Surplus
 Social  Surplus = Consumer surplus + Producer
surplus
 measures the benefits of economic activity in monetary units.
 where Consumer surplus is the benefit obtained by
consumers and producer surplus is the benefit obtained by
producers.

   Pareto efficiency An outcome/situation is termed
pareto efficient if nothing can be done to change it
without making at least one person worse off
   If things can be changed such that no one is worse off, and at
least one person is better off, then the change is a Pareto
improvement over the initial outcome (which is not pareto
efficient).
A double blind-date story…
   Pete has a blind date with Jenny and his friend David has
a blind date with Michelle on a Friday night..

   The dates are both disasters  …

   As the pairs are walking back to their dorms they bump into
each other….
 David and Jenny are thunder-struck by one another,
and…
 Pete and Michelle are totally bedazzled by the other’s
witty remarks.
 Half an hour after they get to their dorms, Jenny and
Michelle have already exchanged the guys’ cell phone
numbers and [censored]…

   Economists say this outcome is a Pareto improvement
over the original outcome (which is not pareto optimal)
Blind Date Story – Take 2
 The    David-Michelle pair did not really hit it off,
and
    Jenny thought Pete was really cool and..
    Michelle thought Pete was really cool too!
    (Pete feels he’d be just happy going out with either
of them)…
 Is   a Pareto-improvement possible?
    Michelle can’t be better off without making Jenny
worse off..
    So a Pareto improvement is not possible..
    (although a cat-fight may be ;)
 Here,  is the initial outcome pareto
efficient?
    Yes 
Example: Market for Apartment Rentals
 The       market:
demand
                                  Market Demand & Supply
 supply

Price
 equilibrium price                                           S
 equilibrium quantity
 Consumer surplus (CS)                 CS
 Producer surplus (PS)
 Social surplus (SS)
P*
PS
SS = CS + PS                                                  D

   The area SS measures the size of the Pareto Q* Quantity
improvement created by the market.

Equilibrium & Efficiency                             p 15
Surplus with Competitive Equilibrium
 Surplus   is maximized in
competitive equilibrium.
 All units that generate
Market Demand & Supply
positive CS and PS (to
the left of Q*) are

Price
produced and sold.                                               S
 But units that would create
 negative CS …                         CS
 and negative PS
P*
are not produced or sold.               PS
 Policies that interfere with
the competitive equilibrium                                      D
reduce surplus.                                      Q* Quantity

Equilibrium & Efficiency                              p 16
Price Ceilings: Rent Control
   Price Ceiling: Upper bound              Market Demand & Supply
on price (below market price)
   Price Floor: Lower bound
on price (above market
price)

Price
   The market:                                                       S
  controlled rent PC                             CS Lost
 transacted quantity QC               CS            PS Lost
 excess demand QX
   Suppose consumers with
highest WTP get apartments. P*
   Rent controls cause transfer of PC
surplus from producers to           PS                          D
consumers,                                            QX
   but controls also cause both
consumers and producers to                       QC        Quantity
   Total surplus has decreased. Surplus Transferred

Equilibrium & Efficiency                               p 17

            is a retired guy who lives in sunny Florida and
owns an apartment in NYC
 There is a rent ceiling of \$500 on the apartment.
 At any price under \$1000, Mr. Wilson prefers to keep the
apartment locked up and use it for a few weeks a year
when he visits his kids in NYC
 The Jones are a family of four who are willing to pay up
to \$1200 for the apartment.
 Deadweight loss because of \$500 rent ceiling:
 Mr. Wilson is willing to rent out for \$1000, but cannot
 The Jones are willing to rent for \$1000, but cannot

Equilibrium & Efficiency                              p 18
Effects of Abolishing Rent Control
Market Demand & Supply
   If controls are removed…
disappears,…

Price
S
 but so does the surplus transfer.
 Surplus has increased, but           CS
some renters will be worse off.
   Thus, removing price controls is P*                DWL
normally not a Pareto            PC
improvement.                         PS                              D

   The market with price controls may
be Pareto efficient,                             QC          Quantity
even though surplus isn’t
maximized.                       Surplus Transferred

Equilibrium & Efficiency                                    p 19
Rationing with Prices
 Every economic system
has a process for deciding
who gets what.                Market Demand & Supply
 This process is called

Price
rationing.
 In free markets, rationing
S
is done with prices.
 Consumers with                WPT > P*
WTP > P* …
P*
 acquire goods with
MC < P*
MC < P*.                                             D
 Consumers with lower
WTP do not acquire any                     Q* Quantity
goods.

Equilibrium & Efficiency                     p 20
Who gets rent-controlled apartments?
 With controlled prices and excess demand, buyers are
attempting to acquire more goods than are available.
 Therefore, nonprice rationing must be used.
 What nonprice-rationing mechanisms determine who
gets rent-controlled apartments?
 first-come, first-served
 bribery and “under-the-table” payments
 connections

Equilibrium & Efficiency                       p 21
Nonprice rationing is not Efficient
 People  with lower WTP may get more of the rationed
good than those with higher WTP.
   This lowers consumer surplus.

 Non-price                rationing mechanisms are costly to use.
 For example, renters may waste a lot of time trying to
convince landlords to let them have apartments.
 These costs are called transactions costs.
 Transactions costs also lower consumer surplus

 Are  these additional costs captured on the rent-control
diagram we saw earlier?
   No!
   So actual dead-weight loss is bigger than in diagram
Equilibrium & Efficiency                                      p 22
Taxes
 Governments                tax goods and services for a number of
reasons:
 for revenue to finance government activities,
 to discourage the consumption of certain goods and services,
 or to increase equity.

 In most cases, taxes reduce efficiency,…
 though some taxes (e.g. on gasoline) may increase
efficiency.

Equilibrium & Efficiency                                     p 23
The Effect of Taxes on Markets
 An  excise tax is a tax of a fixed size applied to
each unit of a good sold, e.g.
   a tax of £2 on each pack of cigarettes
 Suppose             you buy a £4-pack of cigarettes.
 as you are handing the 4 dollar to the seller,…
 the government reaches out and snatches 2 of the bills
away.
 Result: you pay £2 more than the seller receives.

Equilibrium & Efficiency                                  p 24
Quantity Taxes & Market Equilibrium
Market         Market
p
demand         supply
An sales tax (paid
pb                         the market demand
p*                         curve by £t, lowers
ps                         the sellers’ price and
t=2         reduces the quantity
qt q*    D(p), S(p)
And buyers pay pb = ps + 2
Quantity Taxes & Market Equilibrium
Market           Market
p
demand           supply
An excise tax
£t      (paid by seller)
pb                           raises the market
p*                           supply curve by \$t,
price and lowers the
qt q* D(p), S(p)

And sellers receive only ps = pb - t.
Quantity Taxes & Market Equilibrium
Market             Market
p
demand             supply
A sales tax levied at
rate £t has the same
pb               £t            effects on the
p*                             market’s equilibrium
ps                             as does an excise tax
£t            levied at rate £t.

qt q*        D(p), S(p)
Quantity Taxes and Market Equilibrium
 To compute the equilibrium price and quantity
under taxes, we need to remember two things:
 (1) Buyer’s price exceeds Seller’s price by tax

              pb = ps+t
 (2) Quantity bought by buyer at price he pays =
Quantity sold by seller at the price she receives
             Qd(pb) = Qs(ps)
Quantity Taxes & Market Equilibrium
D(pb )  a  bpb and S(ps )  c  dps .
3
With the tax, the market equilibrium satisfies

pb  ps  t and D(pb )  S(ps ) so 2
pb  ps  t and a  bpb  c  dps .
1
Substituting for pb gives
a  c  bt
a  b(ps  t )  c  dps  ps             .
bd
Taxes and Surplus
 After QT, PD and PS
are determined,…                           Market Demand & Supply

Price
weight loss,                                                        S
 the taxes collected,                      CS
 the consumer surplus             PD       PD

 and the producer
\$2
Taxes    DWL
surplus.                         PS       PS
PS                        D

QT       Quantity

Equilibrium & Efficiency                                    p 30
Tax and No-Tax Comparisons
   As compared with the no-tax
price P*,                            Market Demand & Supply
   we have a larger demand
price and smaller supply

Price
price,
   which pushes the quantity                                       S
demanded and supplied                CS
below the surplus-
maximizing level.            PD              PD
   This creates the DWL,                        \$2
P*      Taxes        DWL
   reduces the consumer
surplus                      PS              PS
   and reduces the producer             PS                         D
surplus.
   The left-over surplus takes                   QT        Quantity
the form of taxes collected.

Equilibrium & Efficiency                               p 31
Taxes and the Size of the DWL
 Ifsupply is very inelastic,…
P
 then when a tax is
imposed,…                              S
 the quantity transacted
doesn’t change much.
loss will be small.
D
 The same thing happens if
demand is very inelastic.
 In general, lower elasticity of
demand/supply=> smaller                                 Q
QT Q*
DWL
Equilibrium & Efficiency                p 32
Who bears the tax burden?
 Here we have a very          P
elastic demand curve,…             Taxes from
 and an ordinary supply                                       S
curve.
PD
 After a tax is imposed,…
P*
 the quantity, demand price                                   D
Taxes from
and supply price all change.      the seller
 The taxes from the buyer…
PS
 are small compared with the
taxes from the seller.                                           Q
*
QT   Q

Equilibrium & Efficiency                           p 33
Tax Incidence with Elastic Supply
 Here we have a very
elastic supply curve,…       P
 and an ordinary demand
curve.
 After a tax is imposed,…

 the quantity, demand price
PD
and supply price all change.      Taxes from
 The taxes from the seller…
 are small compared with the  P*
PS

QT       *       Q
Taxes from        Q
the seller

Equilibrium & Efficiency                          p 34
Tax Incidence in General
 The  tax incidence is the relative amount of the tax
burden that is borne by the buyer and the seller.
 Tax incidence is unrelated to which party hands over
the money to the government.
 In general, the larger the elasticity of demand,
 the greater the tax incidence on the eller,
 and the small the share from the buyer.
 The larger the elasticity of supply,
 the greater the share of taxes that comes from the
 and the smaller the share from the seller.
 Here’s why…

Equilibrium & Efficiency                         p 35
Tax Incidence 2

Tax Incidence
Taxes from
 QT PD
Taxes from
the seller
 QT PS
QT PD
Ratio                         PD
QT PS                      Taxes from
S
PD   S                P*
Q
                             Taxes from     PS
PS   D                PS
the seller
D
 Can  you prove this from                                               Q
*
the definition of                              QT       Q
elasticity?

Equilibrium & Efficiency                                      p 36
Elasticity and Tax Incidence

Q * QT     PD     Q PD
.           .
PD
 Q*          P*
 Q P*
PS Q * QT        PS     Q PS
.           .
Q*        P*      Q P*
Q PD
S
 Q . P*        
PS Q         D
P*    Q
• More elastic supply=> greater tax incidence on buyer
• More elastic demand=> greater tax incidence on seller
• It matters little whom the govt. levies the tax on, buyer
or seller
Main Ideas

 Social  Surplus & Pareto Efficiency

 Price vs. Non-price Rationing

 Efficiency vs. Equity

 Taxes and DWL

 Elasticity, the size of DWL & Tax Incidence

```
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