This is the IS-Lm model. Suppose the marginal propensity to consume is a, the multiplier of government purchase expenditure is1(1-a), and the tax multiplier is -a/( 1-a). If the government procurement increases by X, the tax revenue will also increase by X, and the national income will increase by1(1-a) * x+[-a/(1-a)] * x = x, that is, the national income will increase by the same amount. Income increases by x, and corresponding consumption increases by a * X.

Is-lm model, Hicks-Hansen model, is a macroeconomic tool, which shows the relationship between interest rate and asset market (also known as the actual output of goods and services market, plus money market, such as abscissa).

The intersection of the curves of "investment savings" (IS) and "liquidity preference-money supply" (LM) is the "general equilibrium" model, that is, it is assumed that interest rates and asset markets are in equilibrium at the same time.

But there are two equivalent explanations: first, the is-lm model explains the short-term changes in national income when the price level is fixed; Secondly, the IS-LM model explains why aggregate demand curve can translate.

Therefore, this tool is sometimes used not only to analyze economic fluctuations, but also to suggest the potential level of appropriate stabilization policies.

This model was put forward by John Hicks in 1937, and later extended by alvin hansen as the mathematical representative of Keynes's macroeconomic theory. From the 1940s to the mid-1970s, it was the main framework of macroeconomic analysis. Although it has not appeared in macroeconomics research since then, it is still an introductory tool for major concepts in many macroeconomics textbooks.