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 1 year ago

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