consumer welfare from a good is the benefit a consumer gets from consuming that good in excess of...

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.

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.

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.

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).

CS2 = 1CS1 = 2

E3 = 3E2 = 3E1 = 3

21q

p

3

1

2

5

4

0 3 4 5

price = 3

demand

q

p

0

demand

p1

q1

Consumer Surplus,(CS)

Expenditure (E)

Marginal willingness to pay for the last unit of output

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.

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

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

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

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.

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.

0q1

q2

b

ac

assume p2 = 1

Y

Y + CV

CV

II* LaLc Lb

The amount of money one would have to take from a consumer to harm the consumer by as much as the price increase.

0q1

q2

b

ac

Y

II* LaLc

Lb

assume p2 = 1

Y - EV

EV

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

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

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.