Egwald Economics: Macroeconomics

by

Elmer G. Wiens

How to Derive the LM Curve Graphically

 close the window to return to the IS-LM model The LM Curve. The demand for money, md, is an increasing function of national income, y. Therefore, the demand for money curve, as a function of the rate of interest, shifts upward with an increase in national income. Consequently, a higher level of national income requires a higher rate of interest for equilibrium in the money market. The LM curve is the locus of interest rates and national incomes implicit for equilibrium in the money market, a direct relation between the rate of interest and national income. In the diagram below, the left panel shows the LM curve; the right panel shows the money supply, ms, and three demand for money curves, md, as a function of the rate of interest, r, for three levels of national income, y. The intersections of the money demand curves, md, with the vertical money supply line, ms, yields the rates of interest, r, that will equilibrate the money market, i.e. the demand for money = the supply of money: md = ms.

 The money demand function, md = md(r,y) is: md = 75 + 0.23*y - 35*r + 1.5*r2 For y = 1221.74, money demand as a function of the rate of interest r is: md = md(r) = 356 - 35*r + 1.5*r2     This red money demand curve, md, intersects the green money supply line, ms, at r = 6. The pair (r, y) = (6, 1221.74) lies on the LM curve in the left panel. For y = 980.08, money demand as a function of the rate of interest r is: md = md(r) = 300.42 - 35*r + 1.5*r2     This blue money demand curve, md, intersects the green money supply line, ms, at r = 3.35. The pair (r, y) = (3.35, 980.08) lies on the LM curve in the left panel. For y = 821.74, money demand as a function of the rate of interest r is: md = md(r) = 264 - 35*r + 1.5*r2     This yellow money demand curve, md, intersects the green money supply line, ms, at r = 2. The pair (r, y) = (2, 821.74) lies on the LM curve in the left panel.