Consumption | Demand and Supply 1
Consumer Surplus
Consumer surplus is a measure of how much money a consumer would need to be given,in order to be just willing
to give up their entire consumption of a particular good.
Consumer surplus is approximately the area behind the demand curve,The change in consumer surplus following a
price change is illustrated in the second graph.
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
....
.......................................................................................................................................,......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
....
.......................................................................................................................................
......
......
......
......
......
......
......
......
......
......
......
......
......
......
.....
......
......
......
......
......
......
......
......
......
......
......
......
......
......
.....
...................................................
...............................................................................
..........................
0 0
p
x
p
x
p?
x?
p?1
x?1 x?2
p?2
R
￠R
.....
......
.
..
.....
......
.
......
.
......
.
....,.....
......
.
.....
.
......
.
......
......
.
The demand curve shows how much the consumer values each consecutive unit of the good,The consumer actually
only pays p? for each unit,Hence consumer surplus is the difierence between what the consumer is willing to pay
and what they actually pay.
Consumption | Demand and Supply 2
Compensating and Equivalent Variation
Two more accurate (but harder to calculate) measures of the loss or gain to a consumer following a price change are
compensating variation and equivalent variation,These are based on the Hicks decomposition.
......
......
......
......
.......
.......
.....
......
......
.......
........
.............
..................
......
.....
.....
......
......
......
......
.......
.......
.....
......
......
.......
........
............
...................
....................
.....
......
......
......
.......
..............
........................
.....
.....
......
......
......
......
.......
.......
.....
......
......
.......
........
............
...................
....................
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
.....
..............................................................................................................................................
......
......
......
......
......
......
......
......
......
..
......
......
......
......
......
......
......
......
......
..
......
......
......
......
......
......
......
...
......
......
......
......
......
......
......
......
......
......
....
......
......
......
......
.....
......
......
......
......
......
.,.......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
...
..............................................................................................................................................
......
......
......
......
......
......
......
......
......
......
......
.
......
......
......
......
......
......
......
...
......
......
......
......
......
......
......
.....
......
......
...
......
......
......
......
.....
......
......
......
......
......
.
......
......
......
......
......
......
......
......
......
......
.............
.......
..
.......
..
......
......
......
......
......
......
......
......
......
......
.............
.......
..
.......
..
0
x2
x1

0
x2
x1


EV
x1x
2
CV
x1x2
Price increases | the budget line gets steeper,Choice alters from x1 to x2.
Equivalent variation (EV ) in the flrst graph is the amount of money income which would have to be taken away
from the consumer in order to put them on their new indifierence curve.
Compensating variation (CV ) in the second graph is the amount of money income required to put the consumer
back on their initial indifierence curve | the money needed to compensate the consumer for the price change.
For quasi-linear preferences,CV = EV = consumer surplus.
Consumption | Demand and Supply 3
Producer Surplus
Producer surplus,PS,is a measure of how much money a producer would need to be given,in order to be just
willing to give up their entire supply of a particular good.
Producer surplus is the area behind the supply curve,The change in producer surplus following a price change is
illustrated in the second graph.
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
....
.......................................................................................................................................,......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
....
.............................................................................................................................................
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
.
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
....................................................
...............................................................................
.........................
0 0
p
x
p
x
p?
x?
p?1
x?1 x?2
p?2PS
￠PS
.....
......
.
......
.
......
.
......
.
......
.
......
......
......
.
......
.
......
.
....
.....
......
.
..
The supply curve shows how much each consecutive unit of the good costs the producer,The producer actually gets
p? for each unit,Producer surplus is the difierence between what it costs to make each unit and the actual price.
Consumption | Demand and Supply 4
Market Demand
To obtain market demand for good 1 from individual demands,simply add them all up:
X1(p1;p2;m1;:::;mn) =
nX
i=1
xi1(p1;p2;mi)
The demand curve is written D(P) and will look something like this:
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
....
.......................................................................................................................................
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
...........................................................
0
P
X
D(P)CS
P?
X?
......
......
.
......
.
......
.
......
.
The inverse demand function P(X) is often used,and is simply calculated by flnding price in terms of quantities
from D(P),It measures the marginal rate of substitution of every consumer purchasing the good.
Note aggregate demand is a function of all other prices and incomes,It will shift given a change in these variables.
For example,if the good is normal and there is an increase in income levels it will shift to the right.
Adding each individual’s consumer surplus gives the market consumer surplus,The area behind the demand curve.
Consumption | Demand and Supply 5
Elasticities
The slope of the demand curve is ￠X=￠P,This is a measure of the responsiveness of demand to prices,However,
it depends upon the units demand and price are measured in.
The price elasticity of demand does not,It is written · and given by:
· = PX ￠X￠P … PX dXdP = %Change in quantity demanded%Change in price
This is negative,so absolute values are often taken,If the result is 1,there is unit elasticity,If it is less than 1
demand is inelastic,otherwise it is elastic.
Consider the linear demand curve P = 1?X,Elasticity is given by · =?P=(1?P),This is not constant along the
curve | it ranges from?1 at the vertical axis,through?1 at P = 0:5 to 0 at the X axis.
Elasticities can be found for other variables,for example the income elasticity of demand is:
·m = mx ￠x￠m … mx dxdm = %Change in quantity demanded%Change in income
If ·m? 0 the good is normal,if not it is inferior,If ·m > 1 the good is a luxury.
Consumption | Demand and Supply 6
Revenue
Revenue is the quantity of the good sold times its price,R = PX.
If a small amount more,X + ￠X,is sold at a slightly difierent price P + ￠P,the new revenue becomes
R0 = (X + ￠X)(P + ￠P),Multiplying this out gives,R0 = PX + P￠X + X￠P + ￠P￠X.
Subtracting one from the other gives ￠R = R0?R = P￠X + X￠P + ￠P￠X,The last term is tiny,So:
Marginal revenue | the additional revenue from a small increase in quantity is:
MR = ￠R￠X = P + X ￠P￠X … P + X dPdX = P
1? 1j·j
For the linear case then MR = P(1?(1?P)=P) = P?(1?P) = 2P?1 = 1?2X.
Consumption | Demand and Supply 7
Marginal Revenue Curves
The flrst graph shows linear demand P = 1?X,The marginal revenue curve falls at twice the rate MR = 1?2X.
.......
.......
.......
.....
.....
......
......
.......
.......
.........
..............
..................
..........................
.......
.......
.......
.....
.....
......
......
.......
.......
.........
..............
..................
..........................
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
....
.......................................................................................................................................
......
......
......
......
......
......
......
......
......
......
......
......
......
......
.....
.......
.......
.......
.......
.......
.......
.......
.......
.......
.......
.......
.......
.......
.......
.......
.......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
....
.......................................................................................................................................0
P
X 0
P
X
P(X)
MR
P(X)
MR
The second graph shows the case of constant elasticity,The demand curve which has constant elasticity · is given
by X = aP· where a is a constant,So marginal revenue is MR = P(1?1=j·j).
Consumption | Demand and Supply 8
Market Equilibrium
Putting supply and demand together yields the familiar equilibrium diagram.
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
....
.......................................................................................................................................,......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
....
.......................................................................................................................................,......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
....
.......................................................................................................................................
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
.
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
.
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
.......
......
......
......
......
......
......
......
.....
......
......
......
......
......
......
......
......
.
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
........................................................................................................................
0
P
X 0
P
X 0
P
X
D
S
D
S
D
SP? P? P?
X? X? X?
......
......
.
......
.
......
.
......
.
...........,......,......,......,......,....
......
......
.
......
.
......
.
......
.
...........,......,......,......,......,....
The second graph shows a \perfectly inelastic" supply curve,the third graph shows a \perfectly elastic" one.
Price is solely determined by demand in the flrst case and solely by supply in the second.
Consumption | Demand and Supply 9
Comparative Statics
A reduction in supply causes the supply curve to shift to the left,A reduction in demand causes the demand curve
to shift to the left,This is illustrated in the below diagram.
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
....
.......................................................................................................................................
.....
.....
.....
.....
.....
.....
.....
.....
.....
.....
.....
.....
.....
.....
.....
.....
.....
.....
.
.....
.....
.....
.....
.....
.....
.....
.....
.....
.....
.....
.....
.....
.....
.....
.....
.....
.....
.......
.....
.....
.....
.....
.....
.....
.....
....
.....
.....
....
.....
.....
.....
.....
.....
.....
.....
.....
.....
.....
.....
.....
.....
.....
.....
.....
....
.....
.....
.....
.....
.....
.....
.....
.
0
P
XD1
S1
D2
S2
P1
P2
X1X2

......
......
.
......
......
.
......
.
..........,......,......,......,...
......
......
.
......
.
....
......
.......,......,......,......,......,......
The equilibrium price and quantity change from P 1 to P2 and X1 to X2 respectively.
Consumption | Demand and Supply 10
Taxation
When a tax is introduced the price the demander pays is not equal to the price the supplier gets.
A quantity tax t means PD = PS + t,The demander must pay the price the supplier sets plus the tax | which is
collected by the state,Alternatively,PS = PD?t,the supplier gets the price the demander pays less the tax.
An ad valorem tax t means PD = PS(1 + t),In both cases it is possible to shift either D or S to the left.
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
....
..................................................................................................................................................................
.....
.....
.....
.....
.....
.....
.....
.....
.....
.....
.....
.....
.....
.....
.....
.....
.....
.....
.......
.....
.....
.....
.....
.....
.....
.....
....
.....
.....
.....
.....
.....
.....
.....
.....
.....
......
......
......
......
......
..
0
P
XD1
S1
D2
S2
P1
PS
PD
X1X2
......
......
.
......
.
......
.
......
.
..........,......,......,......,......,....,.....
......,......,......,......,......,.....
......,......,......,......,......,.........
......
.
......
.
......
.
.,
.,
.,
.,
.,
.
.,
.,
.,
.,
.,
.,
.,
.,
.,
.,
.
.,
.,
.,
.,
.,
The diagram shows a quantity tax,The vertical thick line is of length t,the tax paid.
The total tax revenue is tX2 which is the area of the box between the thick vertical line and the axis.
Consumption | Demand and Supply 11
Passing Along a Tax
How much tax does the supplier pass along to the consumer? (Sometimes called the tax pass-through).
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
....
..................................................................................................................................................................,......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
....
..................................................................................................................................................................
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
....
......
......
......
......
......
......
.
........................................................................................................................
.,
.,
.,
.,
.,
.,
.,
.,
.,
.,
.,
.,
.,
.,
.,
.,
.,
.,
.,
.,
.,
.,
0
P
X 0
P
X
D2 D1
S
D2 D1
S
P?
Pt P?
P? + t
X? X?1

X?2
......,......,......,....,......,....
......,......,......,......,......,....
......
......
.
......
.
......
.
....
......,......,......,....,......,....
......
......
.
......
.
......
.
.....
......
.
.....
A perfectly inelastic supply curve results in the supplier paying all the tax,None of the tax is passed along.
A perfectly elastic supply curve results in the consumer paying all the tax,All the tax is passed along.
In intermediate cases the tax burden is split with the consumer paying more the more elastic the supply curve.
Consumption | Demand and Supply 12
Deadweight Loss
The deadweight loss of a tax is the amount of surplus lost when the tax is imposed,It is a measure of its social cost.
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
....
.......................................................................................................................................
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
......
.......
......
......
......
......
......
......
......
.....
......
......
......
......
......
......
......
......
.
.......................................
.......................................
...................................................................
......
......
......
......
.....
......
......
......
...
......
......
......
......
......
......
......
......
......
......
.............
.......
..
.......
..
0
t
P
X
D
S
X?
PD
PS
a
c
b
d
......
......
.
......
.
..
The area a + b is the consumer surplus lost,The area c + d is the producer surplus lost,The area a + c is the
government revenue raised,Hence,area b + d is simply being thrown away,This area is the deadweight loss.