Derivation of IS LM curves and shifts
10. The demand for money is M/P = L(Y,/), where L(Y, () is an increasing function of real income Y. For / > 0, money demand is decreasing in the nominal interest rate i. Money demand becomes perfectly interest elastic at / = 0. The price level is P. (a) [2 marks] Give a brief justification of each of the properties of the money demand function assumed above. The LM curve represents money market equilibrium (M = MS). Assume the cen- tral bank targets a constant money supply M and that the price level P is fixed. (b) [3 marks] Show how the LM curve is derived from money-market equilibrium. Illustrate the LM curve, taking account of its shape where i = 0. Suppose that owing to tighter lending criteria, firms' investment demand is lower (treat this as affecting the autonomous component of investment demand). (c) [3 marks] Using the IS-LM model, show how this can result in the interest rate i falling to zero. If that happens, explain why the model predicts the economy enters a liquidity trap where conventional monetary policy is ineffective. Now consider the AD-AS model where nominal wages are fixed in the short run at a level where labour demand is less than desired labour supply. (d) [3 marks] Explain how the shape of the AD curve is affected by the liquidity trap. Following the negative shock to investment demand, can lower prices P mitigate the fall in real GDP found in part (c)? The Fisher equation that links the real interest rate r to the nominal interest rate / and expected future inflation ' is i = r+ . (e) [3 marks] Analyse the effects of higher inflation expectations #* using the IS-LM model and deduce the impact on the AD curve. In August 2020, the Federal Reserve Board announced that it would now pursue a policy of average inflation targeting. This means where current inflation under- shoots its target value, the Fed would aim for a higher rate of future inflation to make up for it. Assuming this policy is credible, suppose that inflation expecta- tions * adjust so that (# + #*)/2 remains constant. (f) [4 marks] How would adopting the average inflation targeting policy affect the shape of the AD curve? Would it lead to a better outcome for real GDP following the shock to investment demand compared to part (d)? Explain. (g) [2 marks] According to the AD-AS model, if the economy remains in a liquidity trap in the future, would the Fed be able to ensure the average inflation target is met? What are the implications for the credibility of this policy
