EC2065: If Money Demand is Perfectly Interest inelastic Then fiscal Policy has no Effect on Real GDP According to the IS-LM model: Macroeconomics Assignment, UOL, Singapore

SECTION A
Answer ALL EIGHT questions in this section (5 marks each).

Briefly explain whether each of the following statements is true or false.

1. If money demand is perfectly interest inelastic then fiscal policy has no effect on real GDP according to the IS-LM model.

2. There are costs of positive rates of inflation, but no costs of deflation.

3. The Fisher model of consumption predicts the current consumption of savers is unambiguously lower after a fall in interest rates.

4. Firms’ incentives to pay efficient wages can be a cause of classical unemployment.

5. An increase in the ratio of cash holdings to deposits raises the money multiplier.

6. If real interest rates become negative, the neoclassical model of investment predicts there is now no limit to how many capital firms want to purchase.

7. Monetary policy set with discretion is said to feature an inflation bias because commitment to a rule could achieve lower inflation at no cost in terms of higher unemployment.

8. In the AK model of economic growth, a country that raises its saving rate has a permanently higher growth rate of income per person.

SECTION B

Answer THREE questions from this section (20 marks each).

9. In the Solow growth model, output Y is produced using capital K and labour L. Assume the production function is Y = √ K √ L, which has total factor productivity constant over time. The change over time in the capital stock is ∆K = I−δK, where I is investment and δ is the depreciation rate. The population and labor force L are constant over time. Investment I is equal to saving S, which is a fraction s of income.

Let k = K/L and y = Y/L denote capital per worker and output per worker.

(a) [5 marks] Show that y = √ k and ∆k = s √ k−δk, and solve for the steady-state values of k and y where ∆k = 0.

(b) [2 marks] Using a diagram, explain intuitively why there is a steady state where growth of output per worker is zero, and why the economy converges to this steady state in the long run.

Suppose that around the world, some countries choose to save a higher fraction s of income. In all other respects, assume countries are identical.

(c) [3 marks] Explain what is meant by the terms absolute convergence and conditional convergence. Explain which one is predicted by the Solow model.

(d) [1 mark] Comparing two countries where one has double the saving rate of the other, what is the Solow model’s prediction for their relative levels of income per worker in the long run?

Now suppose that the saving rate s is not constant in a country. When income is low, households must spend most of their incomes on essential goods and services, while if income were higher, households would be able to save a greater fraction of income. Specifically, assume that the saving rate is s = 0.05 if y < 1, and s = 0.35 − (0.3/y) if y ≥ 1. This behaviour of the saving rate s is common to all countries. The depreciation rate in all countries is δ = 0.1.

(e) [1 mark] Assuming y < 1, find the steady-state level of y.

(f) [3 marks] Show that there are two steady-state values of y greater than 1, and find these values of y. [Hint: One steady state is y = 1.5.]

(g) [3 marks] Illustrate the new ‘saving line’ sy in your diagram from part (b) and use it to explain which steady state the economy will converge to if it starts from a level of k where y < 1.5. Which steady state will the economy converge to if y > 1.5 initially?

(h) [2 marks] Empirically, saving rates and levels of income per worker are positively correlated across countries. In light of your findings above, can this be taken as evidence that exogenous differences in saving behaviour across countries are the cause of some of the income differences? Explain.

10. The demand for money is Md/P = L(Y, i), where L(Y, i) is an increasing function of real income Y. For i > 0, money demand is decreasing in the nominal interest rate i. Money demand becomes perfectly interest elastic at i = 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 (Md = Ms ). Assume the central bank targets a constant money supply Ms 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 I and expected future inflation π e is i = r + π e.

(e) [3 marks] Analyse the effects of higher inflation expectations π e 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 undershoots 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 expectations π e adjust so that (π + π e)/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?

11. In November 2016, the Reserve Bank of India announced that all 500 and 1,000 rupee bills would no longer be legally valid. By removing this currency from circulation, there was an immediate fall in the money supply Ms To begin with, assume that prices and wages are fixed in terms of money, and that output and interest rates are determined by the IS-LM model (suppose no future price changes are expected for now).

(a) [2 marks] Analyse the demonetization policy using the IS-LM model and predict its effects on interest rates and output. Now consider a model of aggregate supply where prices and wages are fully flexible even in the short run.

(b) [4 marks] Explain why the equilibrium levels of employment and output should not be affected by the demonetization once the policy has become known to everyone and no money illusion remains.

(c) [2 marks] In light of your answer to part (b), should the real interest rate be affected by the demonetization if prices and wages are fully flexible and the policy quickly becomes known by everyone in the economy? Explain.
Assume that the demand for money is represented by the equation Md/P = L(Y, I), where P is the price level and L(Y, i) is an increasing function of real income Y and a decreasing function of the nominal interest rate i.

(d) [4 marks] Briefly outline why the Baumol-Tobin model provides a theoretical foundation for a money demand equation with the properties above. The nominal interest rate i satisfies the Fisher equation i = r+π e , where r is the real interest rate and π e is expected future inflation. As in parts (b) and (c), assume prices and wages are fully flexible in what follows.

Demonetized bills could be replaced by newly issued 500 or 2,000 rupee bills, so suppose Ms is expected to return to its previous level Ms 0 after a period of time.

(e) [3 marks] Assuming no further changes to monetary policy are anticipated, what relationship is expected between the price level P in the long run and the price level P0 before the demonetization?

Explain. Suppose that Ms falls by 50% when the demonetization occurs, but is expected to recover in the future to its previous level. If P denotes the new price level after the demonetization has occurred and Pe the expected price level in the future then expected inflation is π e = (P e − P)/P. Assume P e is equal to P ∗ from part (e).

(f) [5 marks] Considering money-market equilibrium at the time of the demonetization, that is, Ms/P = L(Y, i), is the price level P predicted to drop by more than 50%, less than 50%, or exactly 50%? Carefully explain your reasoning.