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The is-lm model, which examines the equilibrium in the goods market and financial markets. The is curve shows the equilibrium level of output as a function of the interest rate, while the lm curve shows the equilibrium interest rate as a function of income. Changes in production, consumption, taxes, and money supply can shift the is and lm curves. The is-lm model helps understand the impact of fiscal and monetary policies on output and interest rates.
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I = I(Y, i) (+, —) where Y denotes both production and sales.
Recall that Y = ZZ = C(Y-T) + I (Y, i) + G and moving to a graph, also recall that the production function was a 45º line (slope=1) and the demand function has a slope smaller than 1, which we assumed, as before I was given constant, that an increase in output leads to a less than one-for- one increase in demand. But now, that we allow investment to respond to production, this restriction may no longer hold. When output increases, the sum of the increase in consumption and the increase in investment could exceed the initial increase in output. As this theory may not hold in practice, we will assume that the response of demand to output is less than one-for-one and draw ZZ flatter than the 45° line.
An increase in the interest at any given level of output decreases investment, the decrease in investment leads to a decrease in output, which further decreases consumption and investment through the multiplier effect and shifts ZZ down.
Equilibrium in the goods market implies that an increase in the interest rate leads to a decrease in output. The IS curve is therefore downward sloping.
Shifts
Changes in either C, G or T will shift the IS curve.
i changesY moves
M/P : Real money (that is, money in terms of goods), real income MP =YL(i) Y: Nominal income divided by the price level equals real income
An increase in the level of output at any given interest rate leads people to increase their demand for money but the money supply is given. Thus, the interest rate must go up until the two opposite effects on the demand for money cancel each other out. (1. Δ Y that leads people to want to hold more money (instead of bonds) 2. Δ interest rate that leads people to want to hold more bonds instead of money). At that point, the demand for money is equal to the unchanged money supply.
The higher the level of output, the higher the demand for money and, therefore, the higher the equilibrium interest rate. The LM curve is therefore upward sloping
Shifts
Changes in the nominal Ms shift the LM curve (real Ms= M/P). Prices are kept constant as we are in a short run model.
The more to the right the LM curve is, the most expansionary policy we have. We can increase output without increasing the interest rate. Otherwise, decreasing the money supply implies a contractionary monetary policy.
Y changesi moves
The LM curve gives, for a given real money stock, the relation between the interest rate and the level of income. For low levels of output, the LM curve is a flat segment, with an interest rate equal to zero. Low levels of income Y’ mean fewer transactions and, therefore, a lower demand for money at any interest rate. The demand for money for a still lower levels of income Y’’ the interest rate equals zero.
In the presence of a liquidity trap, the LM curve, for values of income greater than Y′′, it is upward sloping and for values of income less than Y′′, it is flat at i = 0. (Intuitively: the interest rate cannot go below zero.)
Suppose the economy is initially at a output rate Y and interest rate i and this levels are far below the natural level of output, Yn. The question is: can monetary policy help the economy return to Y n?
decreases from i to zero, and output increases from Y to Y ′. What happens, however, if starting from point B? Expansionary monetary policy no longer has an effect on output.
When the interest rate is equal to zero, the economy falls in a liquidity trap. The central bank can increase liquidity – that is, increase the money supply. But this liquidity falls into a trap: the additional money is willingly held by financial investors at an unchanged interest rate, namely zero.
The adjustment of output clearly takes time.
So with an increase in taxes, takes some time for consumption to respond to disposable income and for production to decrease, yet more time for investment to decrease. And with a monetary expansion, takes some time for investment to respond to the decrease in the interest rate, some more time for production to increase in response to the increase in demand, yet more time for consumption and investment to increase in response to the induced change in output and so on.
Comparing the euro area and the USA we observe that prices react more rapidly in the USA, although the size of the responses are the same. The IS–LM model seems to be a good starting point for the analysis of economic trends in the short term. In the following chapter we will extend the model, considering the effects of openness on goods and financial markets (Chapter 6). Then we will see what determines output in the medium and long run.