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IS LM model

Silly question but I was wondering about the derivation of the IS and LM curves, so far I have for the LM curve:
Money demand function: L=kY-hi
hi=kY-hi
i=kY-M/h

For the IS curve I'm a bit lost, I understand the theory but my textbook isn't explaining it in the best way:
C=cY
I=Ibar-bi
IM=m1Y-m2R
EX=x1Yworld+x2R
and these are supposed to be plugged into the goods market equilibrium condition of Y=C+I+G+EX-IM which leads to an IS curve of:

i= - 1-c+m1 x2+m2 Ibar+G+x1Yworld
------------Y + -------------R + ----------------------------
b b b

However, I'm completely lost on how this comes about :/ Would that order be the correct way to derive an LM curve and can anyone explain the IS curve formula to me?:colondollar:
(edited 8 years ago)
The LM curve looks fine to me.

For the IS curve, we know from the Keynesian cross that it equals Y = C + I + G + NX (assuming an open economy).
You have given us a consumption function of C=cY where c is the marginal propensity to consume (a number between 0 and 1), and basically says that the consumer will only consume a proportion of his income (so this model ignores autonomous consumption and taxes).
You have given the investment function as I = Ibar - bi which means that investment is a function of long run investment and a proportion of nominal interest rates. This means that the higher the nominal interest rate the lower will be investment: as expected.

I dont understand what your export and import functions are though, shouldnt there be an equal sign somewhere?

Once you've done this if you substitute your functions into Y=C+I+G+NX and re-arrange to get an equation in terms of i then you have derived the IS curve.
Technically both curves should be derived in r because the ISLM model is normally given in r,Y space but assuming sticky prices we can equate i to r.

Rhys

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