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# the multiplier

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Demand: Z=C+I+G
Consumption: C=Co+C1(Y-T)
Investment: I=aY-bi

1) Derive the IS-curve
Now assume that the interest rate is determined by: M/P=d1Y-d2i, where P is the price level, Y is real GDP and M/P is the real money stock.

2) Derive the LM curve

Suppose the value of the parameters of the model are: c1=0.5, a=0.3,b=1,Co=225,T=G=400,d1=1,d2=10.M=5 and P=1

3) solve for the overall equilibrium in the goods and money market. (solve for Y and i)

4) What is the multiplier, and what effect does it have?

Please do step by step and explain along the way.

https://brainmass.com/economics/price-levels/finding-multiplier-derive-iscurve-155922

#### Solution Preview

1) Derive the IS-curve
The aggregate demand is Y=C+I+G
or Y = Co+C1(Y-T) + aY-b i + G
Y = Co+C1Y- C1 T + aY-b i + G
(1-C1-a)Y = Co - C1 T - b i + G

Then, IS curve is:
(1-C1-a)Y + C1 T = Co - b i + G
or
Y = (Co - C1 T -b i + G)/(1-C1-a)

Now assume that the interest rate is determined by: M/P=d1Y-d2i, where P is the ...

#### Solution Summary

The solution finds the multiplier in this case.

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