Suppo that investment in the goods market is not responsive to the interests rate (that is , Investment does not depend on the interest rate at all) then the IS Curve is vertical line and monetary policy does not affect output in the IS-LM model

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If investment in the goods market is not responsive to the interest rate, this means that changes in the interest rate will not have any effect on investment decisions. As a result, the investment component of aggregate demand will remain constant regardless of changes in the interest rate.

In the IS-LM model, the IS curve represents the equilibrium relationship between output and the interest rate in the goods market. Typically, the IS curve is upward sloping, indicating that a decrease in the interest rate leads to an increase in investment and hence an increase in output.

However, if investment is not responsive to the interest rate, the IS curve becomes a vertical line. This means that changes in the interest rate will have no effect on output, as investment remains constant.

In this scenario, monetary policy, which operates through changes in the interest rate, will not have any impact on output. The LM curve, representing the equilibrium relationship between the interest rate and the money market, may still exist and determine the nominal interest rate. But since investment is not influenced by the interest rate, changes in monetary policy will not affect output in the economy.

This implies that the effectiveness of monetary policy in stimulating or dampening economic activity is limited in this specific scenario. Other factors, such as fiscal policy or external shocks, may become more important in driving changes in output.