Final answer:
a) The rate of growth of the demand for real money balances is 1/(5i) * g. b) The velocity of money in this economy is 5i. c) If nominal interest rates and inflation are stable, the rate of change in velocity of money will be zero. d) An increase in the nominal interest rate has no effect on the velocity of money.
Step-by-step explanation:
a) If the real output is growing at a rate g, the rate of growth of the demand for real money balances can be found by taking the derivative of the money demand function with respect to real GDP. Differentiating the function gives d(M/P)^d/dY = 1/(5i), where d represents the derivative. Multiplying both sides by dY/dt (the rate of growth of real GDP) gives d(M/P)^d/dt = 1/(5i) * dY/dt. Therefore, the rate of growth of the demand for real money balances will be d(M/P)^d/dt = 1/(5i) * g.
b) The velocity of money in this economy can be calculated by rearranging and solving the quantity equation of money: M/P = (M/P)^d * velocity = L(i, Y) * velocity. Rearranging again gives velocity = (M/P) / (M/P)^d = 1 / (1/(5i)) = 5i.
c) If nominal interest rates and inflation are stable, the rate of change in velocity of money will be zero. This is because velocity is constant when nominal interest rates and inflation rates are stable.
d) An increase in the nominal interest rate will have no effect on the velocity of money. This is because velocity is determined by the money demand function, which does not include the nominal interest rate as a variable.