Question

Interest Rate Tax

Consider a two-period economy, where the consumers can lend or borrow and the income of the consumers in both periods is exogenous. Suppose the government introduces a tax on the interest earnings of the lenders. That is, while borrowers face a real interest rate of r before and after the tax is introduced, lenders face a real interest rate of (1 − x)r, where x is the tax rate, after the tax is introduced.

1. Show the effects of the increase in the tax rate on consumer’s lifetime budget constraint.

2. How does the tax affect the optimal choices (consumption in current and future periods and saving)? Show how income and substitution effects matter for your answer, and how it matters whether the consumer is initially a borrower or a lender

Answer 1

1. Solution

• Tax on interest income causes lender's budget constraint to pivot (the central point) down around initial endowment.
• Budget constraint for borrowers doesn't change.

2. Solution

• Consumer is unaffected if initially a borrower
• If initially a lender, and post- policy consumption bundle is at point C.
• Then there will be substitution effect (A -B) and income effect (B - C)
• Decreases as a result, but effect on C (hence S) is ambiguous and depends on shape of utility.

There are 2 possible cases; the consumer can be either borrower or lender before the change in the taxation.

• Assume that the consumer was a borrower before the change in the taxes. Then the set feasible consumptions is smaller (lending is less profitable), however, the allocation which she / he chose before the change in the taxes is still feasible, hence it still must be the best allocation in the smaller feasible set. Hence the consumer chooses the same allocation and she remains a borrower in the first period. Finally, as she/ he chooses the same allocation, her/ his utility is not affected.

• On the other hand, if the consumer was originally a lender, then the original allocation is no longer feasible, hence she must be worse off. The substitution effect will induce the consumer to consume more today, as saving has became less profitable.

Thank you.....