Aggregate Demand and Aggregate Supply

1. Demonstrate the standard properties of AD curve. AD curve is flatter:

(a) the smaller interest responsiveness of money demand;

(b) the smaller the income responsiveness of money demand;

(c) the larger the expenditure multiplier;

(d) the larger the interest responsiveness of investment.

(e) Show that if nominal money supply increases by x% then AD shifts up by x%.

 

2. For a small open economy with flexible wages and prices[1], a rise in foreign countries’ income will lead to an increase in net exports in equilibrium. True or false? Explain.

 

3. If a component of government expenditures is automatically increased when output falls then the AD curve becomes steeper. True or false? Explain.

 

4. Under what circumstances could the aggregate demand curve be vertical? (Note: do not forget to state all the assumptions).

 

5. (a) Derive the sticky wage model of the labour market, derive the short run aggregate supply curve. Be careful to explain what determines the slope of the SRAS curve.

(b) Assume nominal wages are indeed sticky. Assume further that business cycle fluctuations are due to aggregate demand shocks. Using your answer to part (a), derive the implications for the cyclical behaviour of real wages. In particular, will the real wage be positively or negatively correlated with output?

(c) Now suppose that nominal wages are flexible. Assume that the AD curve is stable and that the business cycle is instead driven by shocks to productivity. Now what is the cyclical behaviour of the real wage? (Hint: what happens to the labour demand curve when productivity goes up or down.)

 

6. Consider workers misperception AS model. Assume the following labour demand and supply curves L_s=2w/p^exp.and L_d=100-6w/p. If workers expect p^exp.=1 but actual price level is p^.=2, find the actual level of employment.

 

7. Suppose that neither output nor input markets are competitive. As a result labour supply curve is replaced by wage-setting relation (WS) of the form and labour demand is replaced by the price-setting equation (PS) . Assuming linear production function, derive the SRAS curve.

 

8. (a) Suppose that households only observe their money wage when making their labour supply decision, but firms are fully informed about the real wage. Derive the implied relationship between inflation and employment.

(b) What is the effect of an increase in inflation expectations on the relationship derived in part (a)? Use your answer to explain the Policy Ineffectiveness Proposition.

(c) Suppose households know that changes in wages have become highly correlated with changes in inflation. Under rational expectations, how is the relationship in part (a) affected?

9. (a) Assume production function of the form , where and derive the theoretical version of the Okun’s law: .

(b) Show, how Okun’s law can be used to translate downward sloping Phillips curve into upward sloping SRAS curve.

 

10. Explain what factors determine the slope of the short-run aggregate supply curve in the following models: (a) sticky wage; (b) workers misperception; (c) sticky prices; (d) imperfect information

 

 

Demand Management Policy

 

1. Provide several examples of time-inconsistency problem.

 

2. Suppose the policymaker tries to minimize social losses, represented by the following objective function: , where and is the natural rate of unemployment. Unemployment rate is determined by Phillips curve .

(a) Assuming rational expectations, find equilibrium inflation rate (denote it by ), unemployment rate () and corresponding value of loss function, . Comment on factors, affecting and . Illustrate equilibrium graphically.

(b) Suppose government can credibly precommit itself to target inflation so that . Calculate the value of the loss function and compare it with part (a). Is there time-inconsistency problem? Provide a graph.

(c) Show how inflation bias could be eliminated by

(i) setting for the central banker inflation target that is different from the socially optimal target;

(ii) reputation: find the values of (if any) for which Nash-reversion punishment strategies if and otherwise for all gives an equilibrium.

 

3. Consider a central bank with the following loss function . Assume that the Central bank has complete control over the short run interest rate and it estimates that the current inflation rate is given by . Calculate the optimal interest rate and compute the central bank loss under the optimal policy rule.

4. Analyze, whether the following statements are true or false:

(a) Time inconsistency provides a theoretical argument in favor of discretionary stabilization policy.

(b) The Lucas critique states that fiscal and monetary policy cannot affect the level of output.

(c) Government is corrupted and does not care about the welfare of society – this is the only reason of “time inconsistency” problem.

 

 

Inflation and Unemployment

 

1. Even if inflation is always and everywhere a monetary phenomenon, the end of inflation requires fiscal measures. Do you agree and why?

 

2. Analyze, whether the following statements are true or false:

(a) Economic agents cannot be rational if they make mistakes.

(b) Even anticipated inflation has economic costs.

(c) The policy ineffectiveness proposition states that fiscal and monetary policy cannot affect the level of output.

(d) Immigration lowers the long run inflation rate.

 

3. What is the sacrifice ratio? How might its value be affected by the credibility of monetary policy announcements?

 

4. Suppose that an economy can be described by the following system of equations:

(1)

(2)

(3)

where denotes the unemployment rate in year , denotes the rate of inflation, denotes the rate of money growth, denotes the growth rate of output. Suppose that initially (at ) the unemployment rate is equal to the NAIRU (non accelerating inflation rate of unemployment), and inflation is 20%. The Central Bank engages into a disinflationary program, which is meant to reduce the rate of inflation by 4 percentage points each year for 4 consecutive years, starting from the initial value of 20%.

(a) Give an economic interpretation of equations (1), (2), (3). Compute the NAIRU for this economy.

(b) Provide a table containing data on the implied evolution of , , , for .

(c) Provide an economic interpretation for the trajectory of each of these variables.

 

5. An economy is at the natural rate of unemployment and suffers from a rate of inflation, equal to 5% per year.

(a) Show the position of this economy in a Phillips curve diagram. Assume static expectations. Is this a stable situation?

(b) Suppose positive aggregate demand shock takes place and as a result the new inflation rate is 10%? Show the new short run equilibrium point in the diagram. Is this a steady state point? Indicate the new steady state equilibrium in the same diagram.

(c) Now instead of static, assume rational expectations. How your answer to part (b) will change if:

i. New wage contracts are signed immediately after the shock;

ii. Existing wage contracts will last another year after the shock.

 

6. Show that inflation rate depends not only on current rate of growth of money supply but also on the rate of growth expected in future (see Mankiw, appendix to Ch.6).

 

7. Consider Cagan money demand function under rational expectations. Let Central Bank announces at period that in some moment in the future money supply will be increased up to (in logs). How price level is affected by this announcement?

 

8. Consider an economy in which the current inflation rate equals the growth rate of nominal money and is given by . Money demand is given by , where and . Calculate the current level of seignorage. What is the inflation rate that maximizes seignorage?

 

 

Long run economic growth

1. Consider an economy whose production function is , where stands for the level of technological progress. Suppose it has a savings rate of 20%, a population growth rate of 2%, depreciation rate of 8%.

(a) Is per capita consumption maximised in the steady state?

(b) Determine what savings rate () would yield the golden-rule level of capital in this model. Would setting be a Pareto improvement?

2. Prove that in the Solow model if increases, then its growth rate diminishes (you are expected to provide analytical proof).

3. Consider Solow growth model without technological progress. Suppose the saving rate goes up. Draw time charts for the (i) growth rates of and ; (ii) k.

 

4. What stylized facts of economic growth can/cannot be explained by the Solow growth model without technical progress? Explain.

 

5. Assume an economy is characterized by production function . The capital stock is 1000 and the current net investment is 90. If the growth rate of total factor productivity is 3%, and growth rate of labor is 1%, what is the current growth rate of per person output? Explain.

 

6. Assume an economy has an aggregate production function , the savings ratio is 0.3, depreciation rate is 0.05 and there is no technical progress. The rate of population growth depends on the level of per capita income. If per capita income does not exceed 2.5 then , and if per capita income is above 2.5, then . Assume that economy is initially in the steady state where . The International Monetary Fund is prepared to give this country financial assistance in the form of grant. What is the minimum size of the per capita capital transfer necessary in order for it to be effective in the long run? What happens if this per capita transfer is smaller than required?

 

7. What stylized facts of economic growth can/cannot be explained by the Solow growth model with technical progress? Explain.

 

8. Use the Solow model (without technological progress) to incorporate the government. Assume that an income tax at the rate t is levied and that, accordingly, saving per capita is equal to s(1-t)y. The government spends the tax revenue on government purchases of goods and services.

(a) Derive the capital accumulation equation. Explain each step carefully.

(b) Analyze the impact of an increase in the tax rate on the steady-state per capita output level and capital/labor ratio.

(c) Draw a chart of the time paths of (i) the growth rate of per capita output, (ii) the growth rate of output and (iii) per capita output.

(d) Derive the golden rule of capital accumulation for considered economy and illustrate graphically. Explain each step carefully.

 

 

Consumption

 

1. Consider a household that lives for two periods and earns (or expect to earn) $100 in the current period and $220 in the future period. . Utility function is .

(a) How would the budget constraint change if the household could lend but could not borrow? If his preferences stay the same, will the household be better off or worse off?

(b) Let . Compare the short run MPC (out of current income) with and without liquidity constraint.

 

2. An unexpected lottery prize of $40000 would have a stronger impact on current savings than an annual increase in labour income by $2000 for 20 years. True or false? Explain your answer.

 

3. In most developing countries, the share of young people in the total population is larger than in most developed countries. However, developed countries have higher saving rates than do less developed ones. Discuss how this observation may be reconciled with the hypothesis that the young tend to save more than the old.

 

4. Which of the following stylised facts are consistent with the permanent income-life-cycle hypothesis? Where the facts are not consistent with the theory, can you suggest some reasons for inconsistency?

(a) The marginal propensity to consume out of current income is less for old people than for middle-aged people.

(b) The marginal propensity to consume out of current income is less for farmers than for most other occupations.

(c) Most countries in Western Europe have both more extensive social welfare systems for older people and higher saving rates than does the USA.

(d) The amount of wealth in the economy is far greater than what current wage earners will consume in their retirement.

(e) In most countries the national saving rate is procyclical (that is, falls during a recession and rises during an expansion).

(f) Russian economy was characterised by high saving rates in 1990-s.

 

5. (a) Suppose the assumptions required for Ricardian Equivalence to hold are satisfied. Suppose further that the government unexpectedly announces a future reduction in government spending, but leaves current fiscal policy unchanged. What will be the impact on the current consumption and savings choices of private individuals?

(b) Outline why Ricardian Equivalence might not hold if there are borrowing constrains. When this is the case, analyze the implications for current consumption of a cut in taxes.

(c) “Given that all people die’, Ricardian Equivalence is a concept of little practical importance. Evaluate this statement.

 

6. Consider infinite horizon intertemporal choice model with the following budget constraint

.

Let for every . Assume that and diminishing marginal utility. Calculate the level of consumption in each period.

 

 

Investment

 

1. The simple accelerator model predicts that net investment will be positive if output is increasing but that net investment will fall if successive increases in output diminish. True or false? Explain.

 

2. Suppose that production function in the economy is , capital stock at the beginning of the period is 20 and the relative price of capital is 1. The real interest rate is 5%, physical depreciation of capital is 60%, and used capital looses 40% of its value every year. Let purchase of capital is subsidized at a rate of 20%. If the economy fully adjusts during the period to the new optimal capital stock, what is the net investment in this period?

 

3. Suppose investment depends not only on the real interest rate, but also on the level of output.

(a) Would you expect, the effect, of output on investment to be positive or negative? Explain.

(b) If the effect is assumed to be positive, how would the value of the multiplier be affected'?

(c) If the effect is assumed to be positive, how would the slope of the IS and Aggregate Demand curves be affected?

 

4. Consider each of the following changes and describe how it might affect firms’ investment decisions. Be sure to indicate which theory/theories of investment you are using in your answers:

(a) an earthquake destroys part of the capital stock

(b) a sudden surge in economic growth

(c) a fall in stock prices

(d) immigration increases the size of the labour force

 

5. Assume that an asset paying zero dividend is being traded. If agents are rational, is it possible that the price of this asset is grater than zero?