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Mathematically, the LM curve is defined by the equation / = (,), where the supply of money is represented as the 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.
In monetary economics, the equation of exchange is the relation: = where, for a given period, is the total money supply in circulation on average in an economy. is the velocity of money, that is the average frequency with which a unit of money is spent.
In macroeconomics, money supply (or money stock) refers to the total volume of money held by the public at a particular point in time. There are several ways to define "money", but standard measures usually include currency in circulation (i.e. physical cash ) and demand deposits (depositors' easily accessed assets on the books of financial ...
I is real physical investment, including intended inventory investment; G is real government spending (an exogenous variable) M is the exogenous nominal money supply; P is the exogenous price level; i is the nominal interest rate; L is liquidity preference (real money demand) T is real taxes levied; NX is real net exports
The real values of individual goods or commodities may rise or fall against each other, in relative terms, but a representative commodity bundle as a whole retains its real value as a constant from one period to the next. Real values can for example be expressed in constant 1992 dollars, with the price level fixed 100 at the base date.
The theory is often stated in terms of the equation M V = P Y, where M is the money supply, V is the velocity of money, and P Y is the nominal value of output or nominal GDP (P itself being a price index and Y the amount of real output). This equation is known as the quantity equation or the equation of exchange and is itself uncontroversial ...
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For a given money supply the locus of income-interest rate pairs at which money demand equals money supply is known as the LM curve. The magnitude of the volatility of money demand has crucial implications for the optimal way in which a central bank should carry out monetary policy and its choice of a nominal anchor .