The following equations describe a Keynesian Cross model. This version of the Ke

Question

The following equations describe a Keynesian Cross model. This version of the Keynesian Cross model is just a little bit more complicated than the one discussed in class. The third equation describes desired investment spending to be a positive function of income (Y). The fourth equation indicates that government spending (G) is an exogenous variable.

AE=C^d +I^d +G

C ^d =a+bY

I ^d =c+dY

G=G

AE=Y

All symbols have their usual interpretation. All parameters have positive values. In addition, we assume O < b < 1.

a) Solve these equations for the reduced form of endogenous variable Y. Show and explain each step in your derivation.

b) Derive the comparative static multiplier showing the effect on the equilibrium value of output (Y) of a change in the amount of government spending (G). Show and explain each step in your derivation.

c) Referring to your answer to (b ), when government spending ( G) increases, what happens to the equilibrium value of output (Y)? That is, does Y increase or decrease when G increases? How do you know? Explain. You may find it useful to prove your answer with a diagram.

Explanation / Answer

The following equations describe a Keynesian Cross model. This version of the Ke

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