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a) Define the concept of "money". b) What are the essential functions of money? c) Is it possible to establish a connection between "money in the utility function" and the cash-in-advance constraint (= Clower constraint)? Hint: If is desired consumption, and is actual consumption, then the cash-in-advance constraint implies = min( ) where is money holding, and is the nominal price. d) "Classical representative agent monetary macroeconomics suggests that money is neutral and superneutral. Hence, according to this kind of theory, the rate of money growth is irrelevant." Discuss whether these statements are valid. e) "The Sidrauski model contains a satisfactory micro-based theory of money demand". Do you agree? Why or why not?

f) "According to the Sidrauski model, hyperinflation driven by expectations cannot occur in general equilibrium." Evaluate this statement. g) List some cases where money is not superneutral. h) "According to Keynesian Economics, money is neutral, but not superneutral." Evaluate this statement. i) What is meant by the "Friedman zero interest rule" or the "Friedman money satiation result"? j) A controversial question in monetary theory is whether the Sidrauski model and similar classical (or new classical) models are a suitable or not suitable framework for the design of monetary policy. Briefly discuss this question!

Money in the long and short run (comparing Keynesian and classical views) Consider the Keynesian money demand hypothesis, = ( ) 0 0 (*) where 0 is the general price level (in terms of money), () is a real money demand function ("" for liquidity), is aggregate production per time unit, and 0 is the nominal interest rate on short-term bonds. Let time be continuous and define the short-term real interest rate by where (the inflation rate). Since asset markets move fast, it is natural to assume that the money market clears continuously, i.e., = ( ) for all 0 where is the money supply. Let the growth rate of any positive variable be denoted Abstracting from fluctuations around the trend, suppose that = and = both constant, and that the real interest rate is a constant, a) Briefly, interpret the signs of the partial derivatives of the money demand function in (*). b) Show that if the money demand function is specified as ( ) = () where 0 () 0 then a constant long-run inflation rate, is consistent with the model and that this satisfies a simple equation where also and enter. Relate to your empirical knowledge. 67 Recall that the (income) velocity of money is defined as Classical monetary theory (the Quantity Theory of Money) claims that for given monetary institutions the velocity of money is a constant and thus independent of the nominal interest rate. c) What is the prediction implied by the classical theory concerning the long-run inflation rate, given and ? Comment in relation to the above Keynesian result. We now consider a short time interval, say a month, where the level of the money supply is practically constant, apart from level shifts implemented by the central bank, through open market operations as part of its monetary policy. Suppose the money supply in this way shifts from to 0 d) According to the classical monetary theory (which is more or less shared by the "monetarists", like Milton Friedman, and also to some extent by the "new classical" theorists like Robert Lucas), which variable will respond in the short run and how? e) What is the likely further effect on aggregate demand, output, and employment as long as the rate of inflation does not respond very much? f) Now answer d) and e) from the point of view of Keynesian theory where and even are "sticky" in the short run? Figure 8.1 is taken from Stock and Watson: "Business Cycle Fluctuations in US Macroeconomic Time series", Handbook of Macroeconomics, vol. 1A, 1999, p. 51. Based on US data 1921-1996, the authors estimate the regression log() = + log + + (where is the "commercial paper rate", an unsecured promissory note with a fixed maturity of no more than 270 days) and find the following estimates and standard errors: = 0868 (0070) = 0094 (0018) g) Discuss the relationship between the data and the mentioned theories. VIII.4 Short questions a) Briefly describe different monetary transmission mechanisms. Make sure that both classical and Keynesian-style monetary transmission channels are included in the list. Briefly discuss.

b) To combat the sharply rising unemployment in the U.S., the Obama government decided to increase government spending substantially and the U.S. now has a huge government budget deficit. In response to this policy, economist Robert Barro from Harvard University declared that the policy was likely to raise expected future taxation considerably and as a result of this there would not be any stimulating effect on current aggregate demand and production. Briefly discuss. c) "According to Sidrauski's monetary Ramsey model, the long-run growth rate in the money supply is irrelevant for welfare." True or false? Why?

Consider the following model in continuous time for a closed economy: = (( ) + ) (1) 0 0 1 0 1 0 = ( ) 0 0 (2) = 1 (3) 1 + = (4) (5) = (6) where the superscript denotes subjective expectation. Further, = output, = real price of a consol paying one unit of output per time unit forever, = government spending on goods and services, = money supply, = output price, = real long-term interest rate, = nominal short-term interest rate, = real short-term interest rate, and = rate of inflation. The variables and are exogenous positive constants. The initial values 0 and 0 are historically given. In questions a) - f) we assume that the central bank maintains the real money supply, at a given constant level, by letting the (nominal) money supply grow at a rate equal to the rate of inflation. a) Briefly interpret the model including the parameters.

Suppose expectations are rational and that speculative bubbles never arise. b) To characterize the movement over time of the economy, derive from the model a dynamic system in and . Draw the corresponding phase diagram and illustrate the path that the economy follows for an arbitrary 0 0. Comment. Now we will consider effects of shifts in policy. Suppose that the economy has been in its steady state until time 0 0 c) Then, at time 0 an unanticipated downward shift in occurs. But after this shift everybody rightly expects to remain unchanged forever. Graphically illustrate by means of a phase diagram. Comment. Hint: the following formula may be helpful for intuition: = 1 = 1 R d) Suggest a "free" interpretation of and the downward shift in such that the result under c) can be seen as a "rough" picture of events in the wake of the financial crisis 2008-2009. e) What is the sign of the slope of the yield curve immediately after the shock to ? Comment. We now consider a different monetary policy. Suppose that the central bank applies the short-term nominal interest rate as the monetary policy instrument and does so in accordance with the following rule: = max(0 + ) (*) where and are constants, f) Maintaining the interpretation from d), briefly answer question c) under these circumstances. g) Compare the output stabilization capability of this policy rule to that of the original monetary policy above. Hint: compare the slope of the = 0 locus under the two alternative policies. Suppose that the economy is close to a steady state and that the government finds the level of economic activity (output and employment) unsatisfactorily low.

h) In this situation the government decides to raise the level of spending to 0 . So, at time 1 0 the government announces a shift to 0 to be implemented at time 2 1 and maintained forever. After this announcement everybody rightly expect this fiscal policy to be carried out as announced. Graphically illustrate by means of a phase diagram what happens to and for 0 Comment. i) Given the intension of the government: 1) Is it a good or bad idea to let the time interval (1 2) be short? Why? 2) Is it a good or bad idea to have the monetary policy (*) replaced by the interest rate targeting policy = for a while? Why? IX.2 In this problem we change the policy regime in the model of Problem IX.1 so that becomes the instrument and equal to a positive constant, , as long as the monetary authority does not decide to change it. Now is endogenous. a) To characterize the movement over time of the economy, derive from the model a dynamic system in and . Draw the corresponding phase diagram and illustrate the path that the economy follows. Comment. Suppose that the economy has been in its steady state until time 0 b) Then an unanticipated downward shift in occurs, but after this shift everybody rightly expect to remain unchanged forever. Graphically illustrate by means of a phase diagram and time profiles what happens to and Comment. c) Assume instead that at time 0, the monetary authority credibly announces a downward shift in the instrument variable to take place at time 1 0 After this shift everybody rightly expect to remain unchanged forever. Graphically illustrate by means of a phase diagram and time profiles what happens to and for 0 Comment. d) Briefly discuss the model.