Suppose that investment I in the goods market is not responsive to the interest rate that is I does ...........

Economics- Phase (I & II) Investment Function

Suppose that investment (I) in the goods market is not responsive to the interest rate (that is, I does not depend on the interest rate at all). Then

The IS curve is a vertical line and monetary policy is very effective in raising output.

The IS curve is a horizontal line and monetary policy is very effective in raising output.

The IS curve is a vertical line and monetary policy does not affect output in the IS-LM model.

The IS curve is a horizontal line and monetary policy does not affect output in the IS-LM model.

The IS curve still has a negative slope, but monetary policy monetary policy does not affect output in the IS-LM model.

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Explanation:

If we assume that C = c₀ + c₁ (Y-T) and I = b₀+ b₁Y – b₂i, then aggregate demand is given by Z = c₀ + c₁(Y-T) + b₀ + b₁Y – b₂i + G. In equilibrium Z = Y. Solving for Y in equilibrium, we get

Solving this for i so that we can see the equation for the IS curve in the (i,Y) space, we get

Now, the assumption that investment is not responsive to the interest rate is equivalent to saying that b₂ = 0. You can see that this implies that the slope of the IS curve is infinite and that the intercept is also infinite. Thus, the IS curve is a vertical line. Monetary policy leads to shifts in the LM curve, however, these shifts do not change output at all since the equilibrium point always remains on the vertical IS curve.