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Unformatted text preview: 10 M ONEY , I NTEREST , AND I NCOME FOCUS OF THE CHAPTER This chapter introduces the IS-LM model the heart of short-run macroeconomic theory. The simple model of Chapter 9 is extended to include the interaction of goods and money markets, which, together, uniquely determine both the interest rate and the position of the AD curve. Both investment and the interest rate are now endogenous variables: investment is a function of the interest rate, which is determined by the equilibrium conditions for goods and money markets. SECTION SUMMARIES 1. The Goods Market and the IS Curve This section derives the IS curve . The IS curve shows all of the combinations of income and the interest rate for which the goods market is in equilibrium (Y = AD). This equilibrium turns out to be a function of the interest rate because AD is now a function of the interest rate: We develop an investment function, which shows that the level of investment falls when interest rates increase. Our investment function is written as follows: I = I - bi , where i is the real interest rate, I is a constant which represents autonomous investment , and b is a coefficient which measures the responsiveness of investment spending to changes in the interest rate. If we imagine that firms borrow the money that they use for investment, it is easy to see why their investment decisions should be affected by the interest rate: higher real interest rates mean 99 100 C HAPTER 10 more expensive loans, and therefore lower returns on investment opportunities. When we incorporate this investment function into our AD schedule, we find that AD is now a function of the interest rate as well: ( 29 G bi) I ( cY C AD +- + + = or, allowing both income taxes and transfers, [ ] ( 29 bi t)Y c(1 A G bi) I ( TR t)Y (1 c C AD-- + = +- + +- + = where R T c G I C A + + + = . A , as before, represents autonomous spending. As before, we can find the level of output for which the goods market is in equilibrium by imposing the requirement AD Y = . The only difference now is that there will be one of these equilibria for each value of i , the real interest rate. We derive the IS curve by allowing the interest rate to vary, and plotting the combinations of i and Y for which the goods market is in equilibrium. This is done graphically in Figure 101. It is also done algebraically, below: bi A t))Y c(1 (1 bi A t)Y c(1 Y bi t)Y c(1 A Y- =---...
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- Spring '09