Chapter Sixteen Equilibrium. Market Equilibrium A market clears or is in equilibrium when the total...
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Transcript of Chapter Sixteen Equilibrium. Market Equilibrium A market clears or is in equilibrium when the total...
Chapter Sixteen
Equilibrium
Market Equilibrium
A market clears or is in equilibrium when the total quantity demanded by buyers exactly equals the total quantity supplied by sellers.
Market Equilibrium
p
D(p), S(p)
q=D(p)
Marketdemand
Marketsupply
q=S(p)
p*
q*
D(p*) = S(p*); the marketis in equilibrium.
Market Equilibrium
p
D(p), S(p)
q=D(p)
Marketdemand
Marketsupply
q=S(p)
p*
S(p’)
D(p’) < S(p’); an excessof quantity supplied overquantity demanded.
p’
D(p’)
Market price must fall towards p*.
Market Equilibrium
p
D(p), S(p)
q=D(p)
Marketdemand
Marketsupply
q=S(p)
p*
D(p”)
D(p”) > S(p”); an excessof quantity demandedover quantity supplied.
p”
S(p”)
Market price must rise towards p*.
Market Equilibrium
An example of calculating a market equilibrium when the market demand and supply curves are linear.
D p a bp( ) S p c dp( )
Market Equilibrium
p
D(p), S(p)
D(p) = a-bp
Marketdemand
Marketsupply
S(p) = c+dp
p*
q*
What are the valuesof p* and q*?
Market EquilibriumD p a bp( ) S p c dp( )
At the equilibrium price p*, D(p*) = S(p*).That is, a bp c dp * *
which gives pa cb d
*
and q D p S pad bcb d
* * *( ) ( ) .
Market Equilibrium
p
D(p), S(p)
D(p) = a-bp
Marketdemand
Marketsupply
S(p) = c+dpp
a cb d
*
dbbcad
q*
Market Equilibrium
Two special cases arewhen quantity supplied is fixed,
independent of the market price, and
when quantity supplied is extremely sensitive to the market price.
Market Equilibrium
S(p) = c+dp, so d=0and S(p) c.
p
q
p*
D-1(q) = (a-q)/b
Marketdemand
q* = c
Market quantity supplied isfixed, independent of price.
Market Equilibrium
S(p) = c+dp, so d=0and S(p) c.
p
q
p* =(a-c)/b
D-1(q) = (a-q)/b
Marketdemand
q* = c
p* = D-1(q*); that is,p* = (a-c)/b.
Market quantity supplied isfixed, independent of price.
Market Equilibrium
Two special cases arewhen quantity supplied is fixed,
independent of the market price, and
when quantity supplied is extremely sensitive to the market price.
Market EquilibriumMarket quantity supplied isextremely sensitive to price.
p
q
Market EquilibriumMarket quantity supplied isextremely sensitive to price.
S-1(q) = p*.
p
q
p*
D-1(q) = (a-q)/b
Marketdemand
q* =a-bp*
p* = D-1(q*) = (a-q*)/b soq* = a-bp*
Quantity Taxes
A quantity tax levied at a rate of $t is a tax of $t paid on each unit traded.
If the tax is levied on sellers then it is called an excise tax.
If the tax is levied on buyers then it is called a sales tax.
Quantity Taxes
What is the effect of a quantity tax on a market’s equilibrium?
How are prices affected?How is the quantity traded affected?Who actually pays the tax?How is the market’s ability to
generate gains-to-trade altered?
Quantity Taxes
A tax makes the price paid by buyers, pb, different from the price received by sellers, ps.
In fact, the buyer and seller prices must differ by exactly the amount of the tax.
p p tb s
Quantity Taxes
Even with a tax present the market must still clear, so the quantity demanded by buyers facing the price pb and the quantity supplied by sellers facing the price ps must be equal.
D p S pb s( ) ( )
Quantity Taxes
p p tb s D p S pb s( ) ( )and
describe the market’s equilibrium.Notice that these two conditions apply nomatter if the tax is levied on sellers or onbuyers.
Quantity Taxes
p p tb s D p S pb s( ) ( )and
describe the market’s equilibrium.Notice that these two conditions apply nomatter if the tax is levied on sellers or onbuyers.Hence, a sales tax levied at a rate of $thas exactly the same effect on acompetitive market’s equilibrium as anexcise tax levied at a rate of $t.
Quantity Taxes & Market Equilibrium
p
D(p), S(p)
Marketdemand
Marketsupply
p*
q*
No tax
Quantity Taxes & Market Equilibrium
p
D(p), S(p)
Marketdemand
Marketsupply
p*
q*
An excise taxraises the marketsupply curve by $t,raises the buyers’price and lowers thequantity traded.
$tpb
qt
And sellers receive only ps = pb - t.
ps
Quantity Taxes & Market Equilibrium
p
D(p), S(p)
Marketdemand
Marketsupply
p*
q*
No tax
Quantity Taxes & Market Equilibrium
p
D(p), S(p)
Marketdemand
Marketsupply
p*
q*
An sales tax lowersthe market demandcurve by $t
$t
Quantity Taxes & Market Equilibrium
p
D(p), S(p)
Marketdemand
Marketsupply
p*
q*
An sales tax lowersthe market demandcurve by $t, lowersthe sellers’ price andreduces the quantitytraded.$t
qt
ps
Quantity Taxes & Market Equilibrium
p
D(p), S(p)
Marketdemand
Marketsupply
p*
q*
An sales tax lowersthe market demandcurve by $t, lowersthe sellers’ price andreduces the quantitytraded.$t
pbpb
qt
pb
And buyers pay pb = ps + t.
ps
Quantity Taxes & Market Equilibrium
p
D(p), S(p)
Marketdemand
Marketsupply
p*
q*
A sales tax levied atrate $t has the sameeffects on themarket’s equilibriumas does an excise taxlevied at rate $t.$t
pbpb
qt
pb
ps
$t
Quantity Taxes & Market Equilibrium
Who pays the tax of $t per unit traded?
The division of the $t between buyers and sellers is called the incidence of the tax.
Quantity Taxes & Market Equilibrium
p
D(p), S(p)
Marketdemand
Marketsupply
p*
q*
pbpb
qt
pb
ps
Tax paid by buyers
Tax paid by sellers
Quantity Taxes & Market Equilibrium
An example of computing the effects of a quantity tax on a market equilibrium.
Again suppose the market demand and supply curves are linear.
D p a bpb b( ) S p c dps s( )
Quantity Taxes & Market Equilibrium
D p a bpb b( ) S p c dps s( ) . and
With the tax, the market equilibrium satisfies
p p tb s D p S pb s( ) ( )and so
p p tb s a bp c dpb s .and
Substituting for pb gives
a b p t c dp pa c bt
b ds s s
( ) .
Quantity Taxes & Market Equilibrium
pa c bt
b ds and p p tb s give
The quantity traded at equilibrium is
q D p S p
a bpad bc bdt
b d
tb s
b
( ) ( )
.
pa c dt
b db
Quantity Taxes & Market Equilibrium
pa c bt
b ds
pa c dt
b db
qad bc bdt
b dt
The total tax paid (by buyers and sellerscombined) is
T tq tad bc bdt
b dt
.
Deadweight Loss and Own-Price Elasticities
A quantity tax imposed on a competitive market reduces the quantity traded at equilibrium and so reduces the gains-to-trade; i.e. the sum of Consumers’ Surplus and Producers’ Surplus is reduced.
The loss in total surplus is called the deadweight loss, or excess burden, of the tax.
Deadweight Loss and Own-Price Elasticities
p
D(p), S(p)
Marketdemand
Marketsupply
p*
q*
No tax
Deadweight Loss and Own-Price Elasticities
p
D(p), S(p)
Marketdemand
Marketsupply
p*
q*
No taxCS
PS
Deadweight Loss and Own-Price Elasticities
p
D(p), S(p)
Marketdemand
Marketsupply
p*
q*
$tpb
qt
ps
CS
PS
The tax reducesboth CS and PS
Deadweight Loss and Own-Price Elasticities
p
D(p), S(p)
Marketdemand
Marketsupply
p*
q*
$tpb
qt
ps
CS
PS
The tax reducesboth CS and PS,transfers surplusto government,and lowers total surplus.
Tax
Deadweight Loss and Own-Price Elasticities
p
D(p), S(p)
Marketdemand
Marketsupply
p*
q*
$tpb
qt
ps
CS
PSTax
Deadweight loss
Deadweight Loss and Own-Price Elasticities
p
D(p), S(p)
Marketdemand
Marketsupply
p*
q*
$tpb
qt
ps
Deadweight loss fallsas market demandbecomes less own-price elastic.
Deadweight Loss and Own-Price Elasticities
p
D(p), S(p)
Marketdemand
Marketsupply
p*
q*
$tpb
qt
ps
Deadweight loss fallsas market demandbecomes less own-price elastic.
Deadweight Loss and Own-Price Elasticities
p
D(p), S(p)
Marketdemand
Marketsupply
ps= p*
$tpb
qt = q*
Deadweight loss fallsas market demandbecomes less own-price elastic.
When D = 0, the tax causes no deadweight loss.
Deadweight Loss and Own-Price Elasticities
Deadweight loss due to a quantity tax rises as either market demand or market supply becomes more own-price elastic.
If either D = 0 or S = 0 then the deadweight loss is zero.