Question

Suppose Liam’s utility function for ice cream (q1) and pumpkin pie (q2) is ?? = 10??1^0.5??2^0.5. His income is

$1000. The price of a pumpkin pie is $5 and the price of ice cream is $10. Suppose the price of ice cream deceased from $10 to $5, measure the change in Liam’s consumer welfare using CV, EV, and ?CS.

Answer 1

Budget constraint:

For utility maximisation at given prices, the quantites are given by

For cobb-douglas utility function,

the demand function are

Now, the price of icecream decreased from 10 to 5, thus we need to give Liam a compensating variation(CV) in order for him to enjoy same level of utility at new prices.

The expenditure at new prices and old level of utility will be

Now, equivalent variation is the change in wealth, at current prices, that will have same effect in welfare as with price change without effeting the income.

The utility maximisation at new prices and same income gives us,

So,

Change in consumer surplus,