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In mathematics and computing, the Levenberg–Marquardt algorithm (LMA or just LM), also known as the damped least-squares (DLS) method, is used to solve non-linear least squares problems. These minimization problems arise especially in least squares curve fitting .
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.
The IS curve is downward sloped and the LM curve is upward sloped, as in the closed economy IS-LM analysis; the BoP curve is upward sloped unless there is perfect capital mobility, in which case it is horizontal at the level of the world interest rate.
The IS-LM model modified for endogenous money: The central bank controls interest rates but not the money supply. The LM curve is now flat, since, when the money supply increases, the interest rate r does not move. Income Y increases from ya to yb without any rise in interest rates.
If the LM curve is vertical, then an increase in government spending has no effect on the equilibrium income and only increases the interest rates. If the demand for money is not related to the interest rate, as the vertical LM curve implies, then there is a unique level of income at which the money market is in equilibrium.
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 .
Keynes argued with that a drop in aggregate demand could lower both employment and the price level in unison, an occurrence observed in the deflationary depression.In the IS-LM framework of Keynesian economics as formalised by John Hicks, a negative aggregate demand shock would shift the IS curve left; as a result, a simultaneously falling wage and price level would shift the LM curve downward ...
The LM curve depicts the equilibrium in the money market and uses output as an exogenous variable, while the IS curve portrays equilibrium in the goods market using the interest rate as an exogenous variable. Output and interest rate are determined by the junction of the IS and LM. [13]