Answer to Question #200330 in Macroeconomics for Showhardo Himel

Question

1.     You deposit $5000 in the bank for one year.

CASE 1: inflation = 0%, nom. interest rate = 20%

CASE 2: inflation = 10%, nom. interest rate = 30%

a.     In which case does the real value of your deposit grow the most? [1]

Assume the tax rate is 15%. 

a.     In which case do you pay the most taxes?[2]

b.     Compute the after-tax nominal interest rate, then subtract off inflation to get the after-tax real interest rate for both cases.[3]

2.     Explain whether the following statements are true, false, or uncertain. [4]

a.     “Inflation hurts borrowers and helps lenders because borrowers must pay a higher rate of interest.”

b.     “Inflation does not reduce the purchasing power of most workers.”

 

Answer 1

1.

a.

Case 1. Real interest rate = Nominal Interest rate - Inflation

        Real interest rate = 20% - 0% = 20%

  Case 2. Real interest rate = 30% - 10% = 20%

Since the real interest rate is the same so the value of the deposit will grow equally in both cases.

      

a.

 The case that has a high nominal interest rate will pay high tax. Therefore, in case 2, more tax will be paid.

b.

Nominal interest rate after the tax= Nominal rate (1- Tax rate)

  Case 1 => After- tax nominal rate = 20% (1- 0.15)

           = 20% (0.85)

           = 17%

Real interest rate after tax = after tax nominal rate - Inflation rate

 = 17% - 0%

 = 17%

 

Case 2 => Nominal interest rate after the tax = 30% (1- 0.15)

           = 30% (0.85)

           = 25.5%

Real interest rate after tax = after tax nominal rate - Inflation rate

 = 25.5% - 10%

 = 15.5%

2.

a.

Where there is a rise in the inflation rate unexpectedly and the lenders did not expect it. This will help the borrowers as they have to pay less money in real terms. This makes lenders worse off.

So, Inflation hurts borrowers and helps lenders, because borrowers must pay a higher rate of interest is false as inflation helps borrowers and hurts lenders.

 

b.

The statement is true because as inflation occurs, prices (wages) of the workers are also increasing. In other words, the nominal wages of the workers keep pace with rising prices as a result people's real income does not fall.