Step by Step Solutions

(Step-by-Step) [IS - LM Model] 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

Question: [IS - LM Model]

Let the IS equation be given as

\[Y=\frac{A}{1-b}-\frac{g}{1-b}i\]

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

\[Y=\frac{{{M}_{0}}}{k}+\frac{l}{k}i\]

where k and l are income and interest sensitivity of money demand, respectively and M0 is the real money balances.

If

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

then

  1. Write the IS-LM system in matrix form.
  2. Solve for Y and i by matrix inversion. Recall the formula for matrix inversion in the 2×2 case discussed in class.
  3. Solve for Y and i by Cramer’s rule.

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