$If\lambda =0,$what does this imply about the relationship between the nominal interest rate and the inflation rate?

Nominal rate of interest refers thereto level of interest rates which don't include the speed of inflation in an exceedingly given period of your time. It may be represented by the formula given below:

$\text{Nominal interestrate}=\text{Realinterest rate}+\text{Inflation rate}$

Real interest rates are the rates which takes into consideration rate of inflation and changes with due change within the rate of inflation over the amount of your time.

Inflation rates seek advice from the speed of increase in price of products and services in an economy over the amount of time.

$\lambda$is equal to zero.

Where,

$\lambda$measures the responsiveness of change in real interest rate to the rate of inflation.

The value of $\lambda$being zero depicts that there no relation exists between real interest changes to alter in inflation rates. This also means real rate of interest will remain same with due change in inflation rates.

But, the nominal interest rates will change with the equal amount of change within the interest rates and real rate of interest remains constant.