How Are Output and the Interest Rate Determined Simultaneously in the Short Run?

Output and the interest rate are determined by simultaneous equilibrium in the goods and money markets. In the short run, we assume that production responds to demand without changes in price (i.e., price is fixed), so output is determined by demand.

II. Why the Answer Matters

The determination of output is the fundamental issue in macroeconomics. The interest rate affects output (through investment) and output affects the interest rate (through money demand), so it is necessary to consider the simultaneous determination of output and the interest rate.

III. Key Tools, Concepts, and Assumptions

Tools and Concepts

i. The chapter introduces the IS-LM framework.

ii. The chapter introduces the concept of policy mixes to achieve macroeconomic goals.

iii. The chapter introduces the use of “+” and “-” below the argument of a function to indicate the effect of an increase in the value of the argument on the value of the function.

Assumptions

i. This chapter maintains the fixed price assumption of previous chapters, but relaxes the assumptions that investment is independent of the interest rate (assumed in Chapter 3) and that nominal income is fixed (assumed in Chapter 4). Investment is also allowed to depend on output. The point of this chapter is to show how goods and financial markets are related and thus how output and the interest rate are simultaneously determined.

ii. The chapter continues to assume that inventory investment is zero and that the economy is closed.

IV. Summary of the Material

The Goods Market and the IS Relation

First, relax the assumption that investment is endogenous. In terms of the framework developed thus far, investment should depend on two factors: sales and the interest rate. A firm facing an increase in sales will need to purchase new plant, equipment, or both to increase production. Thus, investment increases when sales increase. An increase in the interest rate will increase the cost of borrowing needed to purchase new plant and equipment. Thus, investment decreases when the interest rate increases. This discussion describes an investment function of the following form:

I=I(Y , i). (5.1)

+ -

Although the discussion suggests that investment should depend on sales, rather than income, the chapter continues to assume that inventory investment is zero, so income equals sales.

With the revised investment function, the closed economy, goods market equilibrium condition becomes

Y=C(Y-T)+I(Y,i)+G. (5.2)

For a fixed interest rate, the Keynesian cross analysis of Chapter 3 holds with two caveats. First, demand for goods and services (the RHS of equation (5.2)) is no longer assumed to be linear. Second, an additional assumption is required to ensure an equilibrium (i.e., that the ZZ curve intersects the 45°-line). A sufficient assumption for this purpose is that the sum of the (marginal) propensity to consume out of income and the (marginal) propensity to invest out of income is less than one.

Equation (5.2) is called the IS relation, because (as shown in Chapter 3) goods market equilibrium is equivalent to the condition that investment equals saving. To trace out an IS curve, start with a Keynesian cross with a given interest rate, then vary the interest rate. A decrease in the interest rate increases the level of investment for any level of output, so the ZZ curve shifts up and output increases. Therefore, the IS curve has a negative slope in Y-i space (Figure 5.1).