Answer to Question 1:

True or False?

The answer is false. The answer would have been true had the question specified that the interest rate in question is the real rate. The government can bring about a change in both the domestic real and nominal interest rates if it can induce a change in the expected rate of appreciation of the domestic real exchange rate. And, under the assumptions stated, this is the only way it can change the domestic real interest rate. It is not the only way the government can affect the nominal interest rate, however. It can change the nominal interest rate by inducing a change in the expected rate of depreciation of the nominal exchange rate, even if the real exchange rate is expected to remain constant. To do this it has to engineer a change in the expected rate of domestic inflation.

The change in the domestic nominal interest rate, given fixed real and nominal interest rates and a constant expected inflation rate abroad, will equal the change in the domestic real interest rate plus the change in the expected rate of domestic inflation. This can be seen from the equation

    [ i_d - i_f ] = [ r_d - r_f ] + ρ + [ E_pd - E_pf ]

The domestic authorities can thus change the nominal interest rate if they can change the expected rate of domestic inflation. And, as can be seen from the above equation and the equation

    r_d = r_f + ρ - E_q

they can change the domestic real interest rate and, assuming unchanged domestic inflation, nominal domestic interest rates as well, if they can change the expected rate of change in the domestic real exchange rate.

Apart from reducing as much as possible the risk of investing in the domestic economy, it makes no sense for the authorities to attempt to change interest rates by changing  ρ .