Editing IS–LM model (section)

==Formation==

The point where the IS and LM schedules intersect represents a short-run [[General equilibrium|equilibrium]] in the real and monetary sectors (though not necessarily in other sectors, such as labor markets): both the product market and the money market are in equilibrium.<ref>{{cite book |author-link=Robert J. Gordon |first=Robert J. |last=Gordon |title=Macroeconomics |edition=Eleventh |year=2009 |location=Boston |publisher=Pearson Addison Wesley |isbn=9780321552075 }}</ref> This equilibrium yields a unique combination of the interest rate and [[real GDP]].

===IS (investment–saving) curve===
[[File:I-S and Y=AD to IS NT Wiki.png|class=skin-invert-image|thumb|IS curve represented by equilibrium in the capital market and Keynesian cross diagram.]]
The IS curve shows the causation from interest rates to planned investment to national income and output.

For the investment–saving curve, the [[independent variable]] is the interest rate and the [[dependent variable]] is the level of income. The IS curve is drawn as downward-[[slope|sloping]] with the interest rate ''r'' on the vertical axis and GDP (gross domestic product: ''Y'') on the horizontal axis. The IS curve represents the [[Locus (mathematics)|locus]] where total spending ([[consumer spending]] + planned private investment + government purchases + net exports) equals total output (real income, ''Y'', or GDP).

The IS curve also represents the equilibria where total private investment equals total saving, with saving equal to consumer saving ''plus'' government saving (the budget surplus) ''plus'' foreign saving (the trade surplus). The level of real GDP (Y) is determined along this line for each [[interest rate]]. Every level of the real interest rate will generate a certain level of investment and spending: lower interest rates encourage higher investment and more spending. The [[multiplier effect]] of an increase in fixed investment resulting from a lower interest rate raises real GDP. This explains the downward slope of the IS curve. In summary, the IS curve shows the causation from interest rates to planned fixed investment to rising national income and output.

The IS curve is defined by the equation
:<math>Y = C \left({Y}-{T(Y)}\right) + I \left({r}\right) + G + NX(Y),</math>
where ''Y'' represents income, <math>C(Y-T(Y))</math> represents consumer spending increasing as a function of disposable income (income, ''Y'', minus taxes, ''T''(''Y''), which themselves depend positively on income), <math>I(r)</math> represents business investment decreasing as a function of the real interest rate, ''G'' represents government spending, and ''NX''(''Y'') represents net exports (exports minus imports) decreasing as a function of income (decreasing because imports are an increasing function of income).

===LM (liquidity-money) curve===

[[File:Money Market diagram.svg|class=skin-invert-image|thumb|270px|The money market equilibrium diagram.]]

The LM curve shows the combinations of interest rates and levels of real income for which the money market is in equilibrium.  It shows where money demand equals money supply.  For the LM curve, the independent variable is income and the dependent variable is the interest rate.

In the money market equilibrium diagram, the liquidity preference function is the willingness to hold cash. The liquidity preference function is downward sloping (i.e. the willingness to hold cash increases as the interest rate decreases). Two basic elements determine the quantity of cash balances demanded:
# [[Transactions demand]] for money: this includes both (a) the willingness to hold cash for everyday transactions and (b) a precautionary measure (money demand in case of emergencies). Transactions demand is positively related to real GDP. As GDP is considered exogenous to the liquidity preference function, changes in GDP shift the curve. 
# [[Speculative demand]] for money: this is the willingness to hold cash instead of securities as an asset for investment purposes. Speculative demand is inversely related to the interest rate. As the interest rate rises, the [[opportunity cost]] of holding money rather than investing in securities increases. So, as interest rates rise, speculative demand for money falls.

Money supply is determined by central bank decisions and willingness of commercial banks to loan money. Money supply in effect is perfectly [[elasticity (economics)|inelastic]] with respect to nominal interest rates. Thus the money supply function is represented as a vertical line – money supply is a constant, independent of the interest rate, GDP, and other factors. Mathematically, the LM curve is defined by the equation <math>M/P=L(i,Y)</math>, where the supply of money is represented as the [[Real versus nominal value (economics)|real]] amount ''M''/''P'' (as opposed to the nominal amount ''M''), with ''P'' representing the [[price level]], and ''L'' being the real demand for money, which is some function of the interest rate and the level of real income.

An increase in GDP shifts the liquidity preference function rightward and hence increases the interest rate. Thus the LM function is positively sloped.