# the multiplier

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.

© BrainMass Inc. brainmass.com October 9, 2019, 8:35 pm ad1c9bdddfhttps://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.