9780070109100, Chapter 10 7, Problem 10E

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Chapter 10.7, Problem 10E Step-by-step solution Step 1 of 2 It is given that the demand for money Md is a function of national income Y and interest rate i, both of which are functions of time. That is, The following relationship is required to be shown as valid. where, is the rate of growth of Md, ry is the rate of growth of national income, is the rate of growth of interest rate is the elasticity of money demand with respect to national income is the elasticity of money demand with respect to interest rate Step 2 of 2 Differentiate the money demand function with respect to t. dt d Md = d dt d Md = of dY dt + of di dt di (1) Now find the expression of rate of growth of money demand. Using equation (1), the above expression may be written as follows: of dY + of di = dt Md di dt of Y dY + of i di = Y dt = 1 of Y dY + 1 of i di Md Y dt di i dt of This shows that the expression = is valid.