Assume that a series of inflation rates is 1 percent, 2 percent, and 4 percent, while nominal interest rates in the same three periods are 5 percent, 5 percent, and 6 percent, respectively.

a. What are the ex post real interest rates in the same three periods?
b. If the expected inflation rate in each period is the realized inflation rate in the previous period, what are the ex ante real interest rates in periods two and three?
c. If someone makes a loan in period two based on the ex ante inflation expectation in part b, will he or she be pleasantly or unpleasantly surprised?

a. The ex post real interest rate can be calculated by subtracting the inflation rate from the nominal interest rate.

For period 1: Ex post real interest rate = 5% - 1% = 4%
For period 2: Ex post real interest rate = 5% - 2% = 3%
For period 3: Ex post real interest rate = 6% - 4% = 2%

b. Since the expected inflation rate in each period is the realized inflation rate in the previous period, we can calculate the ex ante real interest rates using the same formula as above.

For period 2: Ex ante real interest rate = 5% - 1% = 4%
For period 3: Ex ante real interest rate = 5% - 2% = 3%

c. If someone makes a loan in period two based on the ex ante inflation expectation calculated in part b, they will be unpleasantly surprised. The actual inflation rate turned out to be 4%, higher than their expectation of 1%. This means that the purchasing power of the money they lent will be eroded to a greater extent than they anticipated.

a. The ex post real interest rate can be calculated by subtracting the inflation rate from the nominal interest rate.

For the first period:
Ex post real interest rate = Nominal interest rate - Inflation rate
Ex post real interest rate = 5% - 1% = 4%

For the second period:
Ex post real interest rate = 5% - 2% = 3%

For the third period:
Ex post real interest rate = 6% - 4% = 2%

b. The ex ante real interest rate can be calculated by subtracting the expected inflation rate from the nominal interest rate.

For the second period, assuming the expected inflation rate is the realized inflation rate in the previous period (2%):
Ex ante real interest rate = 5% - 2% = 3%

For the third period, assuming the expected inflation rate is the realized inflation rate in the previous period (4%):
Ex ante real interest rate = 6% - 4% = 2%

c. If someone makes a loan in period two based on the ex ante inflation expectation from part b (expected inflation rate of 2%), they will be pleasantly surprised because the actual inflation rate turned out to be 4%. This means that the ex post real interest rate will be higher than what they anticipated, resulting in a higher return on their loan.

To calculate the ex post real interest rates, we need to subtract the inflation rate from the nominal interest rate:

a. Ex post real interest rate in period one:
Nominal interest rate - Inflation rate = 5% - 1% = 4%

Ex post real interest rate in period two:
Nominal interest rate - Inflation rate = 5% - 2% = 3%

Ex post real interest rate in period three:
Nominal interest rate - Inflation rate = 6% - 4% = 2%

b. To calculate the ex ante real interest rates in periods two and three, we need to use the expected inflation rate from the previous period:

Ex ante real interest rate in period two:
Nominal interest rate - Expected inflation rate = 5% - 1% = 4%

Ex ante real interest rate in period three:
Nominal interest rate - Expected inflation rate = 5% - 2% = 3%

c. Based on the ex ante inflation expectation in part b, if someone makes a loan in period two, they expected the inflation rate to be 2%. However, the realized inflation rate in period three turned out to be 4%. Therefore, they will be unpleasantly surprised because the actual inflation rate was higher than their expectation. This means that the purchasing power of the money they receive from the loan will be eroded more than they anticipated.