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S_CHAPTER11 - Chapter 11 Preliminaries Interest Rates and...

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Chapter 11. Preliminaries: Interest Rates and Capital Valuation Throughout this book, we have underlined the role of investment in the growth process. Until now, however, we have considered that the decision to invest was either exogenous (independent of any variable in the system) or driven by the general aim of maximizing a sum of discounted utility °ows, as we have described it in our chapters on optimal growth theory. But so far we have left aside the essential role played by the rate of interest, the price of loanable funds which is both a cost to investors in capital goods and a reward to those agents who are willing to supply those funds. For investors, we know from general economic principles that their decision to invest depends both on expected future rewards and on the rate of interest. Along a growth process, four prices are in search of an equilibrium: the spot price of any capital good, its future price, the rental rate, and the rate of interest. Those four prices are linked in a fundamental equation developed formally for the ±rst time by Irving Fisher (1896). This equation will turn out to be of central importance: it has far reaching, surprising consequences. In particular, we will demonstrate that if competitive equilibrium enforces it, society maximizes the sum of all future discounted consumption °ows it can acquire. Before showing this, we have to be very precise about the nature of the interest rates and the process by which equilibrium can be reached simulta- neously on the capital goods market and on the loanable funds market. But even before doing so, we should ask the question: ²Why do interest rates exist in the ±rst place?³ We will also explain how both lenders and borrow- ers alike bene±t from the very existence of an equilibrium interest rate. We will then turn to the various concepts of interest rates, their fundamental properties, and their intimate links. 1 1 To do this we have relied in the ±rst part of this chapter on some of our previous work. Section 1 borrows from chapter 1 of our book ² Bond Pricing and Portfolio Analysis - Protecting investors in the Long Run ³, MIT Press, Cambridge, Mass., 2003, pp. 10-13; section 2 is adapted from our chapter ³Protecting Investors against Changes in Interest Rates³, in ² Asset and Liability Management ³, W. Ziemba and S. Zenios, eds., Elsevier North Holland, 2006, pp.69-138. Note: authorizations will have to be requested from the publishers. 1
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1 The reason for the existence of interest rates Most people, when asked the innocuous-looking question about the reason why interest rates should exist in the ±rst instance, respond that since in°a- tion is a pervasive phenomenon common to all places and times, it is therefore only natural that lenders will want to protect themselves against rising prices; borrowers might well agree with that, therefore establishing the existence of an equilibrium rate of interest.
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