EC3102: Consider a Two-period Model of a Closed Economy with Government: Macroeconomics and Public Policy Assignment, DBS,

1. Consider the following IS/LM model for a closed economy:

𝑌 = 𝐶(𝑌 − 𝑇) + 𝐼(𝑟) + (𝐺 − 𝑇)
(𝑀/𝑃)^𝑑= 𝐿(𝑖, 𝑌)

Assume that the real interest rate (𝑟) is given by 𝑟 = 𝑖 − 𝜋^𝑒, where 𝜋^𝑒 represents expected inflation, and 𝑖 denotes the nominal interest rate. Answer the following:

(i) What happens to output and interest rate in this model, when a fall in the price level is expected in the future?

(ii) Suppose that the economy is in recession and the government tries to bring down the deficit by reducing its expenditures. Using this model, explain what kind of monetary policy the Central Bank should pursue to complement the government’s fiscal policy to steer the economy out of recession.

2. Consider a two-period model of a closed economy with government. Assume that the representative agent is endowed with 𝑦1 and 𝑦2 as initial endowments in period 1 and period 2 respectively, and has the utility function 𝑈 = ln 𝑐1 + 𝜌 ln 𝑐2, where 𝑐1 and 𝑐2 denote consumption and 𝜌 is the discount rate. Suppose that the government spends 𝑔1 and 𝑔2 in period 1 and period 2 and finances its expenditure through lump-sum taxes 𝑡1and 𝑡2 in periods 1 and 2 respectively.

(i) Derive the inter-temporal budget constraints of the representative agent and the government.

(ii) Suppose if the government borrows 𝑏 units at the interest rate of 𝑟 to finance its expenditure in period 1, derive the amount of taxes that would satisfy its inter-temporal budget constraint. Explain whether Ricardian Equivalence holds in this situation.

3. Suppose the economy has the Phillips curve 𝜋𝑡 = 𝜋𝑡−1 − 0.5(𝑢𝑡 − 𝑢𝑡^𝑛), where the natural rate of unemployment is given by the average of past two years’ unemployment: 𝑢𝑡^𝑛 = 0.5(𝑢𝑡−1 + 𝑢𝑡−2).

(i) Why might the natural rate of unemployment depend on recent unemployment (as is assumed in the preceding equation)? [5]

(ii) Suppose the Central bank follows a policy to reduce the inflation rate permanently by 1 percentage point. What effect will that policy have on the unemployment over time?

(iii) What is the sacrifice ratio for this economy in practice?

4. Consider that the central bank is attempting to minimize the following loss function subject the inflation-unemployment trade-off as given below:

Minimize 𝐿 = (𝑦1 − 𝑦𝑒)^2 + 𝛽(𝛱1 − 𝛱𝑇)^2                     (Loss function)
subject to 𝛱1 = 𝛱0 + 𝛼(𝑦1 − 𝑦𝑒)                                      (Phillips curve).

(i) Explain what is meant by the Central bank’s loss function and how are the central bank’s preferences reflected in the loss function? Draw the loss ‘circles’ for the cases where 𝛽 = 1; 𝛽 > 1; 𝛽 < 1. In which of the three cases will the central bank reduce inflation back to target quickest after an inflation shock?

(ii) Using the loss function and the Phillips curve, drive the MR-AD curve.

(iii) Using the MR curve in (ii), derive the interest rate rule. Assume the case where 𝛼 =𝛽 = 1 and the slope of the IS curve 𝑎 = 1 in the interest rate rule. Suppose if the inflation target is set to 2 percent and the actual inflation is 4 percent, use the interest rate rule to derive how much interest rate should be raised above the natural rate of interest to bring inflation rate down to its target?

5. Assume a closed economy without Government. However, there exists a financial sector that creates an array of financial assets on which both households and firms invest. Let 𝑥 denote the average earnings from these financial assets. The consumption expenditure of the households is influenced by their wage income and the financial income and is given by 𝐶 = 𝐶(𝑌, 𝑥); 𝐶𝑌 > 0, 𝐶𝑥 > 0, where 𝐶𝑌, 𝐶𝑥 are partial derivatives of consumption with respect to income 𝑌 and financial earnings 𝑥 respectively.

Similarly, the real investment expenditure of firms is given by 𝐼 = 𝐼(𝑌, 𝑥); 𝐼𝑌 > 0, 𝐼𝑥 < 0, where 𝐼𝑌, 𝐼𝑥 are the partial derivatives of the real investment with respect to income and financial earnings.

Using either the Keynesian cross model or the Multiplier analysis, answer the following questions.

(i) Derive the relationship between output 𝑌 and financial earnings 𝑥, and examine the analytical conditions under which the relationship is positive (𝑑𝑌𝑑𝑥 > 0) and negative (𝑑𝑌/𝑑𝑥< 0).

(ii) Describe why the scenario where the expansion in output driven by the rise in financial earnings, i.e. when 𝑑𝑌/𝑑𝑥 > 0, could make the economy unstable and vulnerable to crisis?