We put together the behaviors of the IS and LM curves laid out in Chap. 14 to see what predictions the IS-LM model makes about different policy actions and external shocks and how they affect output and interest rates. The goal of policy is defined as keeping actual output close to potential output. Depending on the relative slopes of the two curves, we may be able to say that fiscal policy is particularly effective or, with other slopes, that monetary policy is particularly effective.
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Chapters 16 and 18 discuss limits on the efficacy of such efforts, but they are still sometimes effective.
Chapter 14 introduced the algebraic representation of the LM curve in terms of GDP and the nominal interest rate:
$$\displaystyle < Y = \frac<1>>M^ -\frac> > + \frac> >i. >$$1>When you lend or borrow money, the actual real interest rate that you will receive or pay is unknown, because you don’t know what inflation will turn out to be over the duration of the loan. All that you know is the expected real interest rate, which is the (known) nominal rate i and the expected inflation rate π e :
$$\displaystyle.>$$We can use this relationship to take the nominal interest rate out of Eq. 15.1 above describing the LM curve:
$$\displaystyleNow if we regroup the inflation expectation, we get an equation for the LM curve in Y and r, showing the position of the curve as a function of both the money supply and the expected level of inflation:
$$\displaystyle < Y = \left ( \frac<1>>M^ -\frac> > + \frac> >\pi ^\right ) + \frac> >r >$$1>We now have equations for the IS and LM curves, both of them expressing Y as a function of the real interest rate, and other stuff.
The LM curve is above, at the end of Appendix I, and the IS curve (derived in Chap. 14) is:
Equilibrium for the economy as a whole is where there is equilibrium in both the money market and the goods market—the pair of values of Y and r that are on both the IS and the LM curve simultaneously. In other words, equilibrium for the economy as a whole is when IS = LM:
This is now a single linear equation in one unknown (that is, r). If you bring the r terms over to one side, then divide by the items that are multiplied by r, you can solve for the equilibrium level of r.
Once you know the equilibrium value of r, you can plug it back into either the IS or the LM curve to find the corresponding equilibrium level of Y.
Consider an economy with the following parameters:
Table 1Assume potential output is 1,117.
Except where specified, use the same parameters as in Problem 15.1.
Go back to the parameters provided in Problem 15.1, with G = $200.
Once again, go back to the parameters of Problem 15.1. This time, consider expected inflation π e falling from 3% to 2.9%.
Revisit Problem 14.6.