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Consumer welfare from a good is the benefit a consumer gets from consuming that good in excess of the cost of the good.
If you buy a good for exactly what it’s worth to you, you are indifferent between making that transaction and not making it.
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If we can measure how much more you’d be willing to pay than you actually paid, we’d know how much you gained from this transaction.
The demand curve contains the information we need to make this measurement.
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The inverse demand curve reflects a consumer’s marginal willingness to pay: the maximum amount a consumer will spend for an extra unit.
The inverse demand curve plots price as a function of the quantity demanded, p = p(Q).
The consumer’s marginal willingness to pay is the marginal value the consumer places on the last unit of output.
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The monetary difference between what a consumer is willing to pay for the quantity of the good purchased and what the good actually costs is called consumer surplus (CS).
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CS2 = 1CS1 = 2
E3 = 3E2 = 3E1 = 3
21q
p
3
1
2
5
4
0 3 4 5
price = 3
demand
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q
p
0
demand
p1
q1
Consumer Surplus,(CS)
Expenditure (E)
Marginal willingness to pay for the last unit of output
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Illustration:For a Cobb-Douglas utility function below
given as1
1 2a aU q q
with a = 0.6 and Y = 300, then
11 1 1
300 1800.6
Yq a
p p p
Thus, if p1 = 15, q1 = 12, and if p1 = 20, q1 = 9.
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This can be computed by integrating the demand curve between 15 to 20.
The loss of the consumer surplus as p1 increases from 15 to 20 is seen in the graph below as area A + B.
q1
p1
0
demand
e2
e115
20
9 12
BA
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The loss in consumer surplus is
20 20
115151
180180lnCS d p
p
To determine the size of B.
180 ln20 ln15 180 2.9957 2.7081CS
180 0.2876 51.77CS
51.77CS A B A B
20 15 9 45A
51.77B A
51.77 45 6.77B
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The desired measure of consumer welfare is the income that we would have to give a consumer to offset the harm of an increase in price.
It is the extra income we would have to provide so that the consumer’s utility did not change.
We can use the expenditure function to calculate the relevant income compensation.
The expenditure function is given as
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Thus we can evaluate the loss in consumer welfare when price increases from
1 2, ,E E p p U
*1 1 to .p p
*1 2 1 2welfare change , , , ,E p p U E p p U
However, we have to decide which level of utility to use. We could use the original level of utility or the new level of utility. We call the first measure as the compensating variation and the second one as the equivalent variation.
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The amount of money one would have to give a consumer to offset completely the harm from a price increase – to keep the consumer on the original indifference curve.
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0q1
q2
b
ac
assume p2 = 1
Y
Y + CV
CV
II* LaLc Lb
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The amount of money one would have to take from a consumer to harm the consumer by as much as the price increase.
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0q1
q2
b
ac
Y
II* LaLc
Lb
assume p2 = 1
Y - EV
EV
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For a Cobb-Douglas utility function below given as 1
1 2a aU q q
with a = 0.6. and Y = 300 then, if p2 = 20,
q2 = 6.
1 21 2
and 1Y Y
q a q ap p
Also, if p1 = 15, q1 = 12, and if p1 = 20, q1 = 9.
Then
Thus, given p1 = 15 and p2 = 20
0.6 0.412 6 9.09U
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Since the expenditure function of this Cobb-Douglas utility function is
with p2 = 20, and U = 9.09, then we have,
At p1 = 20, q1 = 9. Thus
0.6 0.49 6 7.65U
0.6 0.40.6 0.41 2
1 21.960.6 0.4p p
E U Up p
0.40.6 0.61 11.96 9.09 20 59.08E p p
and the new expenditure function is
0.4* 0.6 0.61 11.96 7.65 20 49.72E p p
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0.6 0.615 20 59.08 15 20CV E E
* * 0.6 0.615 20 49.72 15 20EV E E
59.08 0.96 56.52CV
49.72 0.96 47.56EV
Recall that the loss in consumer surplus is 51.77CS
Thus, EV is a smaller loss than the consumer surplus loss, which is a smaller loss than CV.