Simulated Imagery

3.0 MAIN CONTENT

3.1 The Product or Goods Market Equilibrium

The goods or products market equilibrium is defined by equality between saving (S) and investment (I) - the condition that gave us the equilibrium level of income. At the level of income at which S = I (a simple two-sector economy), the leakage from the income stream into saving is exactly matched by offsetting investment spending; or at this income level, aggregate demands for goods just equals the aggregate supply of goods. There is, accordingly, goods market equilibrium at this level of income (Shapiro, 1974).

The product market is in equilibrium when desired savings and investment are equal. Saving is a direct function of the level of income.

S = s(Y)……….. ... (4.1) Investment is a decreasing function of interest rate,

I = I(r)………... (4.2) From equation (4.1) and (4.2), we have S = I

Equilibrium condition is s (Y) = I(r)………. (4.3) It is also assumed in the presents analysis that the price level is stable so that all changes in saving, investment and income (and in the interest rate as well) are real changes.

The set of equations maybe shown graphically as in Figure 1.1 below:

Part A gives the MEI (investment demand) schedule, showing that investment spending varies inversely with the interest rate. The straight line in part B is drawn at an angle 45⁰ from the origin. Whatever the amount of planned investment measures along the horizontal axis of part B, equilibrium requires that planned saving measured along the vertical axis of part B be the same. Thus, all points along the 45⁰ line in part B indicate equality of saving and investment. Part C brings in the saving function, showing that saving varies directly with income.

Fig. 1.1: Goods Market Equilibrium

SELF-ASSESSMENT EXERCISE

Explain the product market equilibrium.

3.5 The IS Curve

The IS curve or schedule reflects the equilibrium of the product market.

It is the locus of pairs of income and interest rate for which the expenditure sector is at equilibrium. That is, the expenditure (or goods) market equilibrium curve or IS curve shows combination of interest rates and levels of output such that planed spending equals income. It is that relationship that links the level of income and the interest rate such that investment demands plus government demand equals saving plus taxes.

I + G = S + T. Equivalently, the IS curve is the relationship between the level of income and interest rate which ensures that aggregate demand (consumption demand plus investment demand plus government demand ) is equal to the level of income:

Y = C + I + G or

Y = α + βy + I0 + I₁ (Y, r)……… (4.4) Thus, there exist a set of combinations for Y and r which provide equilibrium in the expenditure market, by equating expenditure plans with income. By implication those sets of Y and r also equate the planned levels of saving and investment that is satisfying the condition:

S = I or S₀ + S₁ (Y) = I₀ + I₁ (Y, r)……… (4.5) 3.2.1 Derivation of the IS Curve.

The IS curve which is negatively sloped can be derived as shown in Figure 1.1 above.

Quadrant (A) Part A shows the relationship between investment and interest rate hence yielding the marginal efficiency of investment (MEI).

Quadrant (B) Part B shows the saving–investment equality i.e. the demonstration of the equality of planned saving and planned investment.

Quadrant (C) Part C shows the saving schedule where savings are positively related to income.

Quadrant (D) Part D of the figure is the goods market equilibrium, yielding the IS curve.

Algebraically the IS curve can be derived from the following procedures:

Let’s assume that income is made up of only consumption and investment, where investment is dependent on income and interest rate.

Y = C + I C = α + βY I = I0 + I1Y – I2r

We then solve for the endogenous variable, Y in terms of the exogenous variables r

Y = α + βY + I0 + I1Y – I2r……… (4.6) Y = 1/1 – β – I1 [α + I0 - I2r]……… (4.7) This expresses the equilibrium level of income as a function of the rate of interest and it is referred to as the IS curve when shown graphically.

SELF-ASSESSMENT EXERCISE

What do you understand by the “IS curve”? Draw the IS curve both graphically and algebraically.

3.5 The Slope of the IS Curve

The IS curve slopes downward from left to right. This negative slope reflects the increase in investment and income as the rate of interest falls. The IS curve may be flat or steep depending on the sensitiveness of investment to changes in the rate of interest, and also on the size of the multiplier (1/1 – β – I₁).

If investment is very sensitive to the rate of interest, the IS curve is very flat. This is shown by the segment AB of the IS curve in Figure 1.2 where a fall in the rate of interest from r₁ to r₂ leads to a proportionate large rise in income from Y₁ to Y₂. The IS curve is interest elastic in the AB segment of the IS curve.

On the other hand, if investment is not very sensitive to the rate of interest, the IS curve is relatively steep in terms of Figure 1.2, when the rate of interest falls from r2 to r3, income increases by a relatively smaller amount Y₂ Y₃.

Fig. 1.2: The Slope of IS curve

The BC segment of the IS curve is less interest elastic. Any further fall in the rate of interest from r3 will led to no change in income because the IS curve is vertical in that range. It is interest inelastic. Algebraically, the negative slope of the IS curve can be obtained by taking the partial derivative of income, Y with respect to interest rate r of equation (4.7):

Y = 1/1 – β – I₁ [α + I₀ - I₂r]

dY/dr = -I /1 – β – I < 0……….(4.8)

SELF-ASSESSMENT EXERCISE

Discuss why the slope of IS curve is negative.

3.5 Shifts in the IS Curve

The IS functions shifts to the right with a reduction in saving. Reduction in saving may be the result of one or more factors leading to increase in consumption or increase in investment. Moreover, government expenditure and tax policies have the effect of shifting the IS function.

In all these cases, the IS function will shift to the right, equal to the decrease in the supply of saving times the multiplier or the increase in the investment times the multiplier. With the increase in the autonomous investment, the IS curve shifts from IS1 to IS2 and the new equilibrium is established at point E2 which indicates a higher level of income Y2 at a higher interest rate, as shown in Figure 1.3 below:

r

E2

E1 IS2

IS1

0 Incomes

Fig. 1.3: Shifts in the IS Curve

In the opposite case, when investment falls or saving increases, the IS function will shift to the left and the equilibrium will be established at a lower level of income and interest rate. This situation can be explained by assuming IS₂ as the original curve.

SELF-ASSESSMENT EXERCISE

Discuss the factors that can led to a shift in the IS function.

4.0 CONCLUSION

You have seen from the analysis that the basic concept of the product market equilibrium is essential for the derivation of the IS curve.

Equality of saving and investment is the basic element of equilibrium in the real sector or product market. Therefore it has been argued that the IS curve or function is the locus of pairs of interest rate and levels of income where the goods or the product market is in equilibrium.

5.0 SUMMARY

This unit has explained the product market and the derivation of the IS curve. Both the graphical and the algebraic derivation of the IS functions (curve) have been considered alongside the slope and shifts in the IS curve. In the next unit, you will be introduced to the money market and the LM curve.

6.0 TUTOR-MARKED ASSIGNMENT

1. Graphically and algebraically derive the IS functions including the slope of the IS curve.

2. What are causes of shifts in the IS curve?

7.0 REFERENCES/FURTHER READING

Anyanwu, J.C. & Oaikhenan, H.E. (1995). Modern Macroeconomics:

Theory and Applications in Nigeria. Onitsha-Nigeria: Joanee Educational Publishers Limited.

Dornbusch, R., Fischer, S. & Startz, R. (2008). Macroeconomics. (10th ed.). New York: MacGraw- Hill/Irwin.

Parkin, M. (1982). Modern Macroeconomics. Ontario: Prentice-Hall, Canada Inc.

Shapiro, E. (1974). Macroeconomic Analysis. (3rd ed.). New York:

Harcourt Brace Jovanovich, Inc.

UNIT 2 MONEY MARKET EQUILIBRIUM AND THE