### (Solved) Let the IS equation be given as Y = A 1−b − g 1−b i, where 1−b is the marginal propensity to save

Let the IS equation be given as Y = A 1−b − g 1−b i, where 1−b is the marginal propensity to save, g is the investment sensitivity to the interest rate i, and A is an aggregate of exogenous variables.

Let the LM equation be Y = M0 k + l k i, where k and l are income and interest sensitivity of money demand, respectively and M0 is is the real money balances.

If b = 0.7,g = 100,A = 252, k = 0.25,l = 200, and M0 = 176, then

(a) Write the IS-LM system in matrix form.

(b) Solve for Y and i by matrix inversion. Recall the formula for matrix inversion in the 2×2 case discussed in class.

(c) Solve for Y and i by Cramer’s rule.