Question

3. (20 points) Totally differentiate the following IS-LM model and show what happens to the equilibrium interest rate (*) when the money supply increases, and all other things remain the same. Y = C(Y) + I(i) +G M° = KY +L(i) where total income (Y) and interest rates (i) are endogenous. In this case, I(i) is investment and it decreases when interest rates go up. Let Li) be the demand for 1 cash, which goes down when interest rates go up, and G be government expenditures. C(Y) is consumption as a function of income, and it goes up when income goes up by a factor between 0 and 1 (i.e. 0 <C' < 1).

Answer 1

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In denominator, (1 - c'(4) L'li) <o and i-cxo. since 2'li) co and k. I'(i) Lo since 1'(i) < denominator Lo SO, di lo since numerator 70 but denominator Lo Interest rate goes down increases when money ss