Consider the macro model with standard notation and definitions.

Y=C+I+G C=f(YT,r)

I=h(r)M=L(Y,r)

M, T, Gare exogenous andY, C, I, rare endogenous. Assume 0< f1<1,f2<0,h<0,L1>0,L2<0.

1. (a)Rewrite the equations in differential form.
2. (b)EliminatedCanddIfrom the system, leaving you with two equations
3. and two unknowns,dranddY.
4. (c)Set the differential system up in matrix form.
5. (d)Use Cramer's Rule to solve fordY/dM,dY/dG(Government spending multiplier) anddY/dT(Tax multiplier). Determine the signs of these.
6. (e)How does income change if new government spending is offset by new taxes?

(g) Use Cramer's Rule to solve fordr/dM.