8. The Monetary Models

As learned in Chap. 5, demand for money is a function of real income, the interest rate and the price level. More precisely, the velocity of money, defined as the ratio of demand for money and the price level, is an increasing function of the level of real income and a decreasing function of the level of the interest rate. Reserving these qualitative features, the relationship between these variables in the domestic country can be expressed as follows:where \( {M}_t^D \) is demand for money, P_t is the price level, Y_t is real income and r_t is the interest rate, all at time t, for the domestic country; α > 0 and β > 0 are coefficients representing the income elasticity of money demand, and the interest rate semi-elasticity of money demand. Taking logarithms of Eq. (8.1) yields:

where \( {m}_t^d= Ln\left({M}_t^D\right) \), p_t = Ln(P_t), and y_t = Ln(Y_t). The only differences between Eqs. (5.​8) and (8.2) are that demand for money, real income and the price level are in their original forms in the former, while they are in logarithms in the latter. Nevertheless, both Eqs. (5.​8) and (8.2) point out that the velocity of money increases with real income and decreases with the interest rate.