Gehrke: Macroeconomics Winter term 2012/13. Exercises

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1 Gehrke: Macroeconomics Winter term 2012/13 Questions #1 (National accounts) Exercises 1.1 What are the differences between the nominal gross domestic product and the real net national income? 1.2 Why must savings always equal investment in a closed economy without a government sector? What relationship exists between savings and investment in an open economy with a government sector? 1.3 An economy produces three goods: cars, computers, and oranges. Quantities and prices per unit for years 2006 and 2007 are as follows: Quantity Price Quantity Price Cars 10 $ $3.000 Computers 4 $ $ 500 Oranges $ $1 (a) What is nominal GDP in 2006 and 2007? By what percentage does nominal GDP change from 2006 to 2007? (b) Using the prices for 2006 as the set of common prices, what is real GDP in 2006 and 2007? By what percentage does real GDP change from 2006 to 2007? (c) Using the prices for 2007 as the set of common prices, what is real GDP in 2006 and 2007? By what percentage does real GDP change from 2006 to 2007? (d) Why are the two output growth rates constructed in (b) and (c) different? Which one is correct? Explain your answer. 1.4 Explain the construction of a chain-type price index. Questions #2 (Goods market) 2.1 In a closed economy the following equations hold: ( ) ( ), (a) Determine the associated savings function algebraically and numerically. (b) Compute the equilibrium income. (c) Show graphically that savings equal investment at equilibrium income. 2.2 Consider the following equation for equilibrium GDP:

2 ( ) (a) By how much does increase when increases by one unit? (b) By how much does decrease when increases by one unit? (c) Why are your answers to (a) and (b) different? (d) Suppose that the economy starts with a balanced budget and that and are increased by one unit each. Using your answers in (a) and (b), what is the change in equilibrium GDP? (e) How does the specific value of the propensity to consume affect your answers to (a) and (b)? Why? 2.3 Explain the so-called paradox of saving. 2.4 Consider the following equations: ( ). (a) Determine and in equilibrium. (b) Determine the new equilibrium GDP when government expenditures are increased to 650. (c) Compute the net government budget in equilibrium. Explain your result. (d) Why does fiscal policy act as an automatic stabilizer in this model? Questions #3 (Financial markets) 3.1 How is the effective interest rate on bonds affected by an expansive open market operation of the central bank? Explain your answer. 3.2 The demand for money is given by ( ) ( ). Suppose real GDP is and the price level is. Suppose the Central bank fully controls the money supply. (a) Determine the equilibrium rate of interest when the money supply is. (b) Suppose the economy under consideration is in a recession. In order to raise aggregate output and employment, the central bank decides to lower the level of the rate of interest to 2%. By how much does it have to raise the money supply in order to achieve this goal? (c) The policy measure of the monetary authorities is successful and leads to an increase in real GDP by 10% at a constant price level. By how much must the central bank change the money supply in order to keep the rate of interest constant? (d) In order to check inflationary tendencies the central bank decides in the following year to reduce the money supply by 20 units. Compute the new equilibrium rate of interest and show the money market equilibrium graphically. 3.3 Consider the money market model with financial intermediaries (banks), using the symbols for reserves, for demand for currency, and for deposits, with:. (e) Compute the reserve ratio θ. (f) Explain how the rate of interest is affected by an increase of the federal funds rate. (g) Determine the money supply and the amount of high-powered money. (h) Compute the money multiplier.

3 Questions #4 (IS curve) 4.1 Explain the meaning of the IS curve. Show how it can be derived from the goods market equilibrium. 4.2 Determine the slope of the IS curve when one of the following investment functions holds: (i) investment is given exogenously ( ); (ii) investment is only affected by changes in income, but not by changes in the rate of interest ( ( )). 4.3 Explain the meaning of ( ) combinations which are off the IS curve. Show the corresponding excess supply/excess demand situation on the goods market. 4.4 Consider the following model: ( ). (a) Determine the equation of the IS curve. (b) Determine the equation of new IS curve when government expenditures are increased from 300 to 450 units. Questions #5 (LM curve) 5.1 Explain the construction and the meaning of the LM curve. 5.2 Explain the situation on the money market when the rate of interest is higher (lower) than the equilibrium rate. Show the location of the corresponding point in the ( ) diagram. 5.3 How is the location and/or the slope of the IS and/or the LM curve affected, when (i) the demand for money is less interest elastic; (ii) the demand for money is more income elastic; (iii) the marginal propensity to consume increases; (iv) income rises. 5.4 Consider the following model: ( ) There is a balanced budget and the money supply is. Determine the equations for the IS curve and the LM curve and construct the corresponding diagram. Compute the equilibrium income. Questions #6 (IS-LM model) 6.1 Show graphically that the effect of expansionary fiscal and monetary policy measures on equilibrium GDP depends on the interest elasticity of investment. Determine the effect for the case of zero interest elasticity. 6.2 Assume the following: ( ). Moreover:. (a) Calculate the equilibrium rate of interest and determine it graphically.

4 (b) Suppose the money supply is increased by 400 units to equilibrium levels of income and interest rate. Compute the new (c) Solve (a) and (b) using the alternative investment hypothesis. Explain why the changes in and which emanate from the increase in money supply differ from the previous case. 6.3 Propose a combination of fiscal and monetary policy measures in order to achieve the following goals: (i) An increase in GDP at a constant rate of interest; (ii) a reduction of the budget deficit with a constant GDP. What happens to the rate of interest and the level of investment? 6.4 Consider the following IS-LM model: ( ), with The government budget is balanced and taxes are exogenous. Money demand is given by, with and. The exogenous money supply is and the price level is. (a) Solve both algebraically and numerically for the equilibrium level of equilibrium level of private consumption. and. Compute also the (b) Compare the effects of two alternative policy measures: a tax reduction of 600 units and a simultaneous tax and government expenditure reduction of 600 units. Calculate the effects of the two policy measures on the equilibrium levels of GDP and private consumption. (c) Which of the two measures is to be preferred when the welfare measure is aggregate income? What is your answer when the welfare measure is private consumption? Questions #7 Labour market, AS-AD model 7.1 Consider the wage setting equation ( ) and the price setting equation ( ) (a) Explain why the expected price level affects the current wage setting. (b) How is the real wage rate affected by an increase of the unemployment rate? (c) Why does the WS curve exhibit a negative slope? (d) Give three examples for changes which shift the WS curve to the left. (e) Why does a higher mark-up change the real wage rate? (f) How are prices related to costs under perfect competition? 7.2 Why are firms willing to pay nominal wages above the reservation level? 7.3 Consider the following AS-AD model: Goods market equilibrium:

5 Money market equilibrium: with. ( are arbitrary constants.) (a) Determine the AD curve algebraically and show that the relationship is negative. (b) Determine the AD curve graphically in a diagram with four quadrants, showing respectively: the goods market equilibrium (Keynesian cross), the money market equilibrium, the short run equilibrium (IS-LM diagram), and the medium run equilibrium (AS-AD diagram). (c) Explain by means of your diagram how the AD curve changes when (i) the central bank increases the money supply by means of expansionary monetary policy, (ii) the government increases government expenditures, (iii) the marginal propensity to consume falls, (iv) the price level rises. (d) Explain how a reduction of the parameter (e) Explain how a reduction of the parameter affects the slope of the AD curve. affects the slope of the AD curve. 7.4 Consider the following AS-AD model: (IS) (LM) (AS) ( ) In initial equilibrium, the money supply is. The natural level of income is. Assume adaptive expectations, that is,. (a) Compute the price level in medium run equilibrium. (b) The central bank increases the money supply to equilibrium price level.. Determine the new medium run (c) Explain the adjustment process from the initial equilibrium (a) to the new equilibrium (b). How do change in the course of the adjustment process? Questions #8 Phillips curve 8.1 Suppose that the AS relationship is given by ( ) ( ), with. The relationship between nominal wages, the rate of unemployment and the other structural factors is given by ( ), with and. (a) Compute the Phillips curve relationship algebraically and numerically. (b) Interpret the Phillips curve relationship. (c) Discuss how an increase of the parameter rate of unemployment? If so, why? affects the Phillips curve. Does it change the natural 8.2 The short run Phillips curve is given by.

6 (a) Compute the so-called natural rate of unemployment. (b) Suppose that in the past up to period the rate of unemployment was always and the rate of inflation was always. Determine the rate of inflation for periods, at which it would be possible to reduce the rate of unemployment permanently to 3% when expectations formation assumes one of the following forms: (i) (ii) θ (iii) (c) How plausible are the various assumptions on expectations formation in connection with the policy measure under consideration? (d) Suppose that a fraction of the wage contracts are indexed to the current price level. Compute the new equation for the short run Phillips curve. 8.3 Suppose that the Phillips curve is given by, where. Suppose that inflation in year t-1 is zero. In year t, the monetary authorities decide to keep the unemployment rate at 4% forever. (a) Compute the rate of inflation for years t, t+1, t+2, and t+3. (b) Now suppose that half the workers have indexed labour contracts. What is the new equation for the Phillips curve? (c) Re-compute your answer to part (a). (d) How does wage indexation affect the relationship between and? 8.4 What reasons can be given for international differences in unemployment rates in view of the Phillips curve? Why might the natural rate of unemployment have increased over time in some European countries in the past two or three decades?