Question
In: Economics
The government impose a 20%tax on the sale of milk. Given that Sam has an income...
The government impose a 20%tax on the sale of milk. Given that Sam has an income of 100 pennies, the price of milk is 5 pennies, the price of bread is 4 pennies, and Sam's utility function is U=(M)2/3(B)1/3. The tax on milk is a burden on Sam, how much of a burden is it? calculate the increase in income require to compensate Sam for the imposition of the tax. How does that compare to the money raised from the tax?
Solutions
Expert Solution
Sam's budget constraint is 
. Sam's utility is 
.
The MRS can be found as 
or 
or 
or 
or 
.
The slope of the budget consrtaint would be 
or 
. The optimal consumption bundle will be where the slope of budget
constraint is equal to the MRS, ie 
or 
. Putting the value in the budget constraint, we have 
or 
and aslo, 
or 
. This is the consumption of milk and bread before the tax.
After the tax, the price of M would increase by 20%, and the
budget constraint would be 
or 
. In that case, the optimal bundle would be where the slope is
equal to the MRS. The slope of the budget line would be 
. Hence, the optimal bundle would be at where 
or 
. Putting it in the budget constraint, we have 
or 
and aslo, 
or
.
The decrease in utility is hence from 
to 
, ie a decrease of 4 utils, which is a burden of tax.
If the income was 120, the 
. Hence, an increase in income of 20 is required to compensate. The
tax revenue collected is $
,
and hence, is less than that compensation.
Rahul Sunny answered 2 years agoRelated Solutions
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