 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).

CS 2 = 1CS 1 = 2 E 3 = 3E 2 = 3E 1 = 3 21 q p price = 3 demand

q p 0 p1p1 q1q1 Consumer Surplus,(CS) Expenditure (E) Marginal willingness to pay for the last unit of output

Illustration: For a Cobb-Douglas utility function below given as with a = 0.6 and Y = 300, then Thus, if p 1 = 15, q 1 = 12, and if p 1 = 20, q 1 = 9.

This can be computed by integrating the demand curve between 15 to 20. The loss of the consumer surplus as p 1 increases from 15 to 20 is seen in the graph below as area A + B. q1q1 p1p1 0 demand e2e2 e1e BA

The loss in consumer surplus is To determine the size of B.

 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  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.

0 q1q1 q2q2 b a c assume p 2 = 1 Y Y + CV CV I I*I* LaLa LcLc LbLb

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

0 q1q1 q2q2 b a c Y I I*I* LaLa LcLc LbLb assume p 2 = 1 Y - EV EV

For a Cobb-Douglas utility function below given as with a = 0.6. and Y = 300 then, if p 2 = 20, q 2 = 6. Also, if p 1 = 15, q 1 = 12, and if p 1 = 20, q 1 = 9. Then Thus, given p 1 = 15 and p 2 = 20

Since the expenditure function of this Cobb- Douglas utility function is with p 2 = 20, and U = 9.09, then we have, At p 1 = 20, q 1 = 9. Thus and the new expenditure function is

Recall that the loss in consumer surplus is Thus, EV is a smaller loss than the consumer surplus loss, which is a smaller loss than CV.