$4.$ A central bank is considering two alternative monetary policies:

$-$ Holding the money supply constant and letting interest rates adjust $($Hint: this is the IS$-$LM model as we have analyzed it in class$)$

$-$ Adjusting the money supply to ensure interest rates constant $($Hint: in this case the IS$-$LM curve becomes horizontal as the central bank always adjust M to ensure equilibrium in the money market such that the interest rate does not change$)$

Using the IS$-$LM model, which policy would be better at keeping income stable under the following conditions:

a$.$ All shocks to the economy arise from exogenous changes in the demand for goods and services

b$.$ All shocks to the economy arise from exogenous changes in the demand for money