Question

Homework Blanchard Chapter 6-1, 6-2 1) Calculate the real interest rate using first the mathematically precise formula and second the approximation formula in both of the following cases a) 1-4%, p.-2% b) 1-54%, pe 46% 2) Can the nominal interest rate ever be negative? Explain your answer 3) Can the real interest rate ever be negative? If so, under what circumstances? And if so, why not just hold cash instead of interest-bearing securities? 4) In class, we showed both the supply of and demand for bonds (assumed to be of a given maturity) as a function of their nominal yield (i.e., interest rate). If we wanted to show both the supply of and demand for bonds as a function of the ex-ante (expected) yield (interest rate r) what conceptual problem would that present? What assumption would you have to make to resolve the problem so that you could express supply and demand together on the same graph as functions of r? What would change on that graph if there were a given change in the expectations of inflation over the life of the bonds, a change shared identically by all participants in the market?

Answer 1

1) It is computed using the following fisher equation :

i = r + p^e

where i is nominal interest rate, r is the real interest rate, and p^e is expected inflation.

a) It is given that i= 4% = 0.04, and p^e= 2% = 0.02.

r= 0.04 - 0.02 = 0.02, that is r = 2%.

b) It is given that i=0.54, and p^e= 0.46

r= 0.54 - 0.46 = 0.08, that is r = 8%.

2) As according, to fisher equation it is established that nominal interest is the sum of expected inflation and real interest rate. Thus, if is expected that prices to be increasing and positive real interest rate then in that case nominal interest is positive. But if the inflation is negative, that is, deflation and the absolute value of inflation is more than the real interest rate, in such case, the nominal interest rate will be negative.

Thus, the nominal interest is negative when expected inflation is negative and its absolute value is more than the real interest rate.

3) According to Fisher equation real interest rate is computed as -

r = i - p^e

If the expected inflation (p^e) is more than the nominal interest rate (i), then, in this case, the difference of i and p^e is negative, which is equal to the real interest rate (r).

Thus, the real interest is negative when expected inflation is more than the nominal interest rate.

And the cash that pays zero interest is better than the securities which yield negative real interest rate.

4) The real interest rate is defined as the difference of nominal interest rate and expected inflation. So, the real expected interest rate can also be defined as the difference of nominal interest rate and expected inflation. The expected real interest rate also depends on the expected inflation.

So, the actual problem is that expected inflation possibly different from actual inflation.

To solve this problem it should be assumed that actual inflation is in accordance with expected inflation. If the expected inflation changes then it will also impact the equilibrium interest rate.