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# Derivation of the LM and IS schedules

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2. Let us take a look at nominal versus real interest rates . The following equations describe the economy of Hermisia:

Consumption: C=.8 (1-t) Y where t, the tax rate is .25.

Investment: I=900 -2r where r is the real interest rate.

Government: G=700

Money Demand: L=.25Y - 25(r + &#61552;*) where &#61552;* is expected inflation.

Money Supply: M/P = 250

a. Give a name to the expression r + &#61552;*.
b. Provide an economic/financial explanation for having investment demand as a function of r ( and not
r + &#61552;* ) and money demand a function of r + &#61552;*.
c. Assuming that &#61552;* = 0, derive an IS schedule, an LM schedule and find the equilibrium output and interest rate.

Suppose now that the FED increases the money supply form 250 to 265, a 6 % increase.. This also causes &#61552;*, expected inflation, to jump from 0 to 6%.

d. Why might inflationary expectation change with the FED's announcement ?
e. Derive a new LM curve given the above changes.
f. Determine equilibrium output and both the nominal and real interest rates. Give me an accounting as to what happened compared to the nominal and real interest rate.

https://brainmass.com/economics/supply-and-demand/derivation-of-the-lm-and-is-schedules-93015

#### Solution Preview

a. This is the real interest rate. It is defined as the nominal interest rate plus expectation of future price increases.

b. Investment is speculative in nature, because of the time required to realize a return. Therefore people will factor in their expectations of future price increases into their investment decision. However, purchasing is done in the present, and therefore doesn't need to be adjusted for expectations.

c.
The requirement that the demand for money equal the supply of money yields the LM schedule.
L=.25Y - 25(r + pi*)= M/P = 250 can be reduced ...

#### Solution Summary

How interest rates determine the value of investments. Derivation of the LM and IS schedules; using them to determine equilibrium in an economy

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