Q2 [40 points]

Suppose that Pt : price of a slice of pizza in year t;

Pet+1 : expected price of the pizza in year t + 1; et+1: expected rate of inflation between period t and t + 1;

it: one-year nominal interest rate.

Suppose you borrow the equivalent of a slice of pizza.

a) Given this information, obtain an expression that represents the amount of pizza slices you must repay in one year? Explain in words the reasoning behind the expression you have obtained. (See Figure 6.1 in the textbook)

b) Derive the one-year real interest rate from information about the one-year nominal interest rate, the price of pizza, and inflation rate. (See pp.113-4 in the textbook)

c) Suppose that

Price of a slice of pizza in 2019: $3.00;

Expected price of a slice of pizza in 2020: $5;

e: expected rate of inflation between 2019 and 2020;

One-year nominal interest rate: 25%.

Suppose that you borrow $3 from a friend at the nominal interest rate to eat one more slice of pizza in 2019.

Calculate the amount of pizza slices you must repay in 2020.

How would the number of pizza slices you must repay change if your friend decides to charge you at an interest rate of 150%? Explain in detail which borrowing-lending case would favor you as a borrower and which one would favor your friend as a lender?

What is the interest rate that implies that the real cost of borrowing and the real benefit of lending would be zero?