is certain, but 772 is uncertain. The firm maximizes expected profits and, for simplicity, the interest rate is zero.

(a) Suppose the Arms only choices are to undertake the investment in period 1 or not to undertake it at all. Under what condition will the firm undertake the investment?

(b) Suppose the firm also has the possibility of undertaking the investment in period 2, after the value of is known; in ttiis case the investment pays off only 772. Is it possible for the firms expected profits to be higher if it does not invest in period 1 than if it does even if the condition in (a) is satisfied?

(c) Define the cost of waiting as 771, and define the benefit of waiting as (7 2 < I)E\I - 772 I 772 < I]- wfiy thcsB represent the cost and the benefit of waiting. Show that the difference in the firms expected profits between not investing in period 1 and investing in period 1 equals the benefit of waiting minus the cost.

8.12. The Modigliani-Miller theorem. (Modigliani and Miller, 1958.) Consider the analysis of the effects of uncertainty about discount factors in Section 8.6. Suppose, however, that the firm finances its investment using a of equity and risk-free debt. Specifically, consider the financing of the marginal unit of capital. The firm issues quantity b of bonds; each bond pays one unit of output with certainty at time f -1- for all > 0. Equity holders are the residual claimant; thus they receive MKit + T))-batt + for all > 0.

(a) Let P(t) denote the value of a unit of debt at , and V(t) the value of the equity in the marginal unit of capital. Find expressions analogous to (8.29) for P(f) and V(f).

(b) How, if at all, does the division of financing between bonds and equity affect the market value of the claims on the unit of capital, P(r)b -1- V(r)? Explain intuitively.

(c) More generally, suppose the firm finances the investment by issuing n financial instruments. Let d, (t + r) denote the payoff to instrument i at time r-i-t; the payoffs satisfy di(f-i-t)H---4-d„(f-i-t) = 77(X(f - )),butare otherwise unrestricted. How, if at all, does the total value of the n assets depend on how the total payoff is divided among the assets?

(d) Return to the case of debt and equity finance. Suppose, however, that the firms profits are taxed at rale , and that interest payments are tax deductible. Thus the payoff to bond holders is the same as before, but the payoff to equity holders at time f -t- is now (1 - )[ { (r + )) - h]. Does the result in part (b) still hold? Explain.

Chapter 9

INFLATION AND MONETARY POLICY

9.1 Introduction

Inflation and unemployment are two of the main subjects of macroeconomics. They are among the principal concerns of policymakers and the public, and they have been the subject of large amounts of research. In our hivestigations of fluctuations in Chapters 4 through 6, we encountered various possible sources of short-run movements in both variables. Yet we said little about what determines their average levels over longer periods. This is the focus of the final two chapters. This chapter considers inflation, and Chapter 10 considers unemployment.

Inflation varies greatly both across countries and over time. In Germam and Japan, for example, the price level has risen an average of just a few percent per year over the past few decades, whereas in Italy and the United Kingdom it has risen an average of over 10% per year. In the United States during this period, annual inflation increased slowly and irregularly from around 1% in the late 1950s to almost 10% at the end of the 1970s; it then fell rapidly to less than 5%, and has remained between 2% and 5% since then.

If we consider periods before the past few decades and countries outside the industrialized world, there is even more variation in inflation. Many countries experienced large deflations-that is, dechnes in prices-after World War 1 and at the beginning of the Great Depression. And some developing countries, such as Bahrain, Burma, and Singapore, have average inflation rates in recent decades that are simflar to Germanys and Japans. At the other extreme, several countries have recently experienced hyperinflations (traditionally defined as inflation greater than 50% per month). In Argentina, for example, prices rose by a factor of 600 between Ma> 1989 and March 1990, and in some months the price level almost tripled. And many other countries have undergone episodes of triple-digit annual

The all-time record inflation appears to have occurred in Hungary between August 1945 and July 1946, when the price level rose by a factor of approximately 10. During the peak month of this inflation, prices on average tripled daily (Sachs and Larrain, 1993).

inflation. Yet many of the countries that have experienced hyperinflations or very high inflations have also had extended periods of low inflation.

This chapters main subject is the causes of inflation. Sections 9.2 and 9.3 explain why inflation is almost always the result of rapid growth of the money supply; they also investigate the effects of money growth on inflation, real balances, and interest rates.

We then turn to the deeper question of what causes growth of the money supply. Most economists beheve that average rates of inflation in most countries in the postwar period have been higher than is socially optimal. Since inflation stems mainly from money growth, this suggests that there is some type of inflationary bias in monetary policy. There are two main sets of explanations for such a bias.

The first set emphasizes the output-inflation tradeoff. If monetary policy has real effects (or if policymakers beheve that it does), policymakers may increase the money supply in an effort to increase output. Theories of how inflation can arise from this tradeoff particularly theories that emphasize the dynamic inconsistency of low-inflation policy-are discussed in Sections 9.4 through 9.6. Section 9.6 also considers several related policy questions that arise when monetary policy has real effects, particularly the issues of how much importance policymakers should attach to stabilizing real output versus keeping inflation low and of how monetary pohcy should be conducted when the economy is subject to shocks.

The second set of explanations of rapid money growth focuses on seignorage-the revenue the government gets from printing money. These theories, which are more relevant to less-developed countties than to industrialized ones, and which are at the heart of hyperinflations, are the subject of Section 9.7.

All of this analysis presumes that we understand why inflation is costly and how large its costs are. hi fact, however, these are difficult issues. Section 9.8 is therefore devoted to the costs of inflation. This section not only describes the various potential costs of inflation, but also attempts to understand the basis for the intense concern about inflation among pohcymakers, the business community, and the public.

9.2 Inflation, Money Growth, and Interest Rates

Inflation and Money Growth

The simple diagram from Chapter 5 showing aggregate supply and aggregate demand, which is reproduced as Figure 9.1, provides a framework