Robert J. Gordon, Macroeconomics, 10 th edition, 2006, Addison-Wesley

1. Robert J. Gordon, Macroeconomics, 10th edition, 2006, Addison-Wesley Chapter 3 Spending, Income, and Interest Rates

2. Spending, Income, and Interest Rates • Business Cycles and the Theory of Income Determination • Remember that minimizing fluctuations in real GDP is important. Revise the volatilia and stabilia cases. • Business cycles in USA Figure 3-1 • Note that the goals of monetary policy is to dampen business cycle fluctuations and ensure a steady growth of real GDP. • This is, as shown in the above figure, is far from reality. • Ups and downs in real GDP are basically caused by changes in shocks to aggregate demand (a significant change in desired spending by consumers, business, government and foreigners).

3. Figure 3-1 Real GDP Growth in the United States, 1950–2004 Note that expansions in general lasts longer than recessions. Why?

4. Improved performance of anti-cyclical fluctuations can be due to: • - demand shocks are smaller and less important • - monetary and fiscal policies become more effective • - a change in the conditions that make fiscal and monetary policies more effective. • Income determination, unemployment and the price level • Income determination and the price level • Shocks to AD can change either real GDP, the price level or both. • Changes in AS depends mainly on costs among other factors.

5. Suppose that the price level is fixed in the short run. All changes in AD cause changes in real GDP by the same amount in the same direction, since; ∆ real GDP = ∆ AD/fixed price level (1) • Is there any evidence to support the assumption that prices are fixed in the short run? • Price labels are printed and expensive to reprint • Prices of mail order catalogues are set for the entire season • Wages and salaries usually change every year and perhaps in more than that. • Therefore, changes in AD are directly translated into changes in real GDP.

6. What we explain and what we take as given? • The variables to be explained in a model are called endogenous, while those which are taken as given are called exogenous. • What we will consider as exogenous: • The key instruments of monetary (money supply) and fiscal policies (G & Tax rates), exports and other potential causes of changes in demand shocks such as consumer and business confidence about the future are assumed to be exogenous. • We know that: E ≡ C+I+G+NX (2) • Now let us consider the components of E

7. The consumption function • Starting with C as the only endogenous variable, C depends on disposable income (Y-T) such that, C = Ca + c(Y-T) (3) • The fixed amount Ca is autonomous consumption, which is completely independent of disposable income. • The change in C due to the change in (Y-T) depends on marginal propensity to consume (c). • c(Y-T) is the induced consumption. e.g., C = 500 + .75 (Y-T)

8. Figure 3-2 A Simple Hypothesis Regarding Consumption Behavior Break-Even-Point

9. This function is shown in figure 3-2 below. • Note that: • When disposable income is zero, total consumption consists of the autonomous part only Ca. • For any extra disposable income, C changes by .75 of that extra disposable income. • Induced saving and the marginal propensity to save: • Look at figure 3-2 again and note that. • The distance between the consumption function and the 450 line is the total saving. • To the right of point F saving is positive as (Y-T)>C.

10. To the left of point F saving is negative as (Y-T)<C, i.e., people either withdraw from their saving accounts or borrow in order to consume. Note: S=(Y-T)-C = (Y-T)- Ca-c(Y-T) S=-Ca+ (1-c)(Y-T) • In our example S=-500+.25(Y-T) • (1-C) is the marginal propensity to save

11. Autonomous consumption, the interest rate and the stock market • There are other factors that cause a change in autonomous consumption. These factors are: • Interest rates; Ca rises when interest rate falls, and falls when interest rate rises. • Household wealth (the market value of houses, stocks, bonds and bank accounts minus liabilities); as wealth rises people will consume more even with fixed income (lower their savings). See figure 3-3 • The economy in and out of equilibrium • To see how income is determined note that expenditure is not always what is desired or planned. • If some expenditure is unplanned, business firms will adjust production until the unplanned component is eliminated.

12. Figure 3-3 Consumption, Saving, and Disposable Income, 1929–2004

13. Total spending that is planned is Ep, while the rest is unplanned or undesired (E – Ep). Assume that Investment is the only component that can contain an unplanned component, while the rest are always equal to their planned levels. Ep = C + Ip + G + NX • Or Ep = Ca +c(Y-T) + Ip + G + NX • The word parameter is a value taken as given or known within a particular analysis. In the consumption function Ca and c are parameters,

14. Autonomous planned spending • Autonomous planned spending (Ap) is the spending that does not depend on total income (Y); i.e., Ap = E – cY = Ca – cTa + Ip + G + NX (cY induced consumption) • -cTa is autonomous taxes that affect C (note that so far we consider taxes as autonomous). • So Ap excludes induced spending only (Ca – cTa + Ip + G + NX) • Assume that Ip = 1200, NX = -200, T=0, G=0, Ap equals Ap = 500 – 0.75(0) + 1200 + 0 – 200 = 1500

15. Now we have learned that Ep has two parts Ap and cY, i.e., Ep = Ap + cY Ep = 1500 + .75 Y • When is the economy in equilibrium • Only when Y equals Ep, the economy will be in equilibrium, i.e., households, business firms, the government and the foreign sector want to spend exactly the income generated by current level of production. • If the economy is out of equilibrium, (out of line with planned expenditures) business firms will be forced to change their production. At equilibrium production and income are equal to their planned levels.

16. Figure 3-4 How Equilibrium Income Is Determined

17. See figure 3-4 • At point B income equals planned expenditure, (no pressures to change). • What happens out of equilibrium • The economy is out of equilibrium all points other than B. at point J, income is 8000. planned expenditure are 7500 (Autonomous planned spending 1500 + Induced consumption spending 6000), i.e., there will be 500 of unsold products. • Though this is counted as investment, businesses do not desire it. (unintended inventory investment Iu). For this reason, they will cut production and income which moves the economy back to B. • Note: Y ≡ E ≡ Ep + Iu

18. The economy will be at equilibrium when Iu = 0, i.e., businesses produce exactly the amount that is demanded, or Y = Ep Table 3-1 Comparison of the Economy’s “Always True” and Equilibrium Situations

19. Determining equilibrium real GDP. • take cY from both sides of the above equation (Y = Ep) Y – cY = Ep – cY (remember Ep-cY=Ap) (1-c)Y = Ap • Note that mps (s) = (1-c), hence; sY = Ap (.25Y=1500) • Induced saving equal autonomous planned spending. Since this equation is obtained from equilibrium condition we can divide both sided by s to solve for equilibrium income such that; Y = Ap/s or Y = 1500/.25 = 6000 • 1500 of induced savings are required to balance 1500 of autonomous planned spending.

20. The multiplier effect. • Any change in Ap will cause a change in equilibrium income. • Suppose that businesses raise their investment by 500, i.e., Ap increases from 1500 (Ap0) to 2000 (Ap1). • Calculating the multiplier • New equilibrium Y1 = Ap1/s = 2000/.25 = 8000 • Subtract from old Y0 = Ap0/s = 1500/.25 = 6000 • Equals change in income ∆Y = ∆Ap/s = 500/.25 = 2000 • The multiplier k is ∆Y over ∆Ap Multiplier k = ∆Y/∆Ap = 1/s ∆Y/∆Ap = 1/.25 = 4 • Look at the figure and note that k = ∆Y/∆Ap = RJ/RB = 1/s k = 2000/500 = 4

21. Figure 3-5 The Change in Equilibrium Income Caused by a $500 Billion Increase in Autonomous Planned Spending Point B is no longer an equilibrium point

22. Example of the multiplier effect in action • If planned expenditure rises, real income must rise by 1/s as much. • suppose that an airway company bought 4 billion of boeing aircrafts. This will raise Boeing workers income by 4 billion, out of which they will soon spend .75 on goods and services, that will raise output by 3 billion of consumer goods in the second round. A rise in income by 3 billion will raise spending by 2.25,….., and so on. • Total change in income = 4 x 1/.25 = 16 billion

23. Sources of shifts in planned spending • What might cause actual real GDP to decline below the desired level?. A drop in planned investment is a major cause of actual real world recession and depressions. • All other components of autonomous planned spending, can change, (Ca, cTa, Ip, G, and NX). • Government spending and taxation • The government can adjust its expenditures and taxes to offset fluctuations in real GDP caused by movements in autonomous consumption, in planned investment and net exports. We know that; Ap = E – cY = Ca – cTa + Ip + G + NX

24. A change in autonomous planned spending is; ∆Ap = ∆Ca – c ∆Ta + ∆Ip + ∆G + ∆NX • A $1 change in Ca changes Ap by $1 in the same direction • A $1 change in Ta changes Ap by $1 in the opposite direction • A $1 change in Ip changes Ap by $1 in the same direction • A $1 change in G changes Ap by $1 in the same direction • A $1 change in NX changes Ap by $1 in the same direction • Once a change in Ap is calculated, the multiplier determines the resulting change in income. ∆Y = ∆Ap/s

25. Fiscal expansion • Suppose that the desired level of income is 8000. If the autonomous spending Ap = 1500, real income is 6000, as shown at point B, but this is unsatisfactory as actual real GDP is 2000 lower than desired. • How fiscal policy correct for this situation through control over G? From 3.14, an increase in real income by 2000 is achieved by any action to raise Ap by 500. There are two possibilities: • raise G by 500 • reduce autonomous tax revenue by 667 • A 500 rise in G will have the same impact as any other 500 increase in Ap. kfor ∆G is the same

26. The government budget deficit and its financing • Any change in G or tax revenue has a consequence for the budget. We know that T-G ≡ I + NX – S (recall the magic equation) • and ∆T-∆G ≡ ∆I + ∆NX – ∆S 3.17 • Assume that ∆Ca = ∆I = ∆NX = 0, and ∆T = 0, such that the only elements of 3.17 that are changing ∆S and ∆G. • ∆G is the value of fiscal stimulus. Now • ∆T - ∆G = ∆I + ∆NX – s(∆Y - ∆T) • 0 - ∆G = 0 + 0 – .25(∆Y - 0) • 0 - 500 = 0 + 0 – .25(2000 - 0) = -500 (There is a deficit of 500)

27. The extra saving of 500 are to be used to buy government bonds that the government must sell to finance its 500 deficit, in order to raise real GDP BY 2000. • The tax multiplier • As an alternative to using G by 500, the government can reduce taxes by 667 to have the same impact. Thus; ∆Y = ∆Ap/s = -cTa/s ∆Y=-(.75)(-667)/.25 = 500/.25 = 2000 • The multiplier for a change in taxes is the income change divided by ∆Ta: ∆Y/∆Ta = ∆Ap/s∆Ta = -c∆Ta/s∆Ta = -c/s ∆Y/∆Ta = -.75/.25 = -3.

28. Financing the tax cut • To see how the budget deficit due to a tax cut is financed we use the same equation: • ∆T - ∆G = ∆I + ∆NX – s(∆Y - ∆T) • -667 - 0 = 0 + 0 – .25(2000 – (-667)) • - 667 = -.25(20667) = -667 (There is a deficit of 667) • The tax cut of 667 raised disposable income by 2667 or 667 extra savings is available for households to buy 667 government bonds.

29. The balanced budget multiplier • The government can stimulate the economy even if it needs to maintain a balanced budget. To see this add the G and T multipliers • Balanced budget multiplier 1/s + -c/s = 1-c/s = 1 • this states that the balanced multiplier is one no matter what the value of c is. • How can monetary policy affect planned spending • For the time being we will take the interest rate as given, while converting autonomous consumption from an exogenous into an endogenous variable, but interest rate is still an exogenous variable.

30. Functions of interest rate • Interest rates help the economy allocate saving among alternative uses. For consumers it is the reward from abstaining from consumption, the higher the interest rate the greater the incentive to save. Also people will borrow less and purchase fewer goods. • Interest rates are central to the role of monetary policy, the government can affect the cost of funds to private borrowers by affecting interest rates • Types of interest rates. • Deposits short term interest rates; for deposits of 3 months or less; while long term interest rates; for a year or more. • Borrowed funds rates: short term rates on funds borrowed by the government (treasury bill rate), by business (commercial paper), and by banks (federal funds rate). There are long term rates on funds borrowed by the government (Treasury bond rate), by businesses (corporate bond rate) and by households (the mortgage rate).

31. The relation of autonomous planned spending to the interest rate • Ip depends on interest rates, since business firms attempt to profit by borrowing in order to buy investment goods. business can stay in the business only if earnings are enough to pay the interest on borrowed funds. • Example of an airline’s investment decision • If earnings on Boeing jet airliner is 10 m, while its cost is 50 m (interest, fuel, food...etc). • Earnings are 20% rate of return (10/50). If interest rate is 10%, return is sufficient to pay the interest expense. • Look at figure 3-6 which shows the rate of return on 1-5 planes • The first plane earn more because it is operated on the most profitable routs, compared to the second…etc. • Up to the third plane can be bought.

32. Figure 3-6 The Payoff to Investment for an Airline and the Economy

33. Interest rate and the rate of return line. • Figure 3-6 shows the relationship between interest rates and real private autonomous planned spending. Determination of the level of Ip + Ca is a two step process. First we plot the rate of return line. Second we find the level of Ip+Ca at the point where the rate of return crosses the interest rate level. • Business and consumer optimism • Can purchases change when interest rate is held constant? Certainly an increase in business and consumer optimism about expected payoff of additional purchases can shift the entire rate of return line to the RHS. See figure 3-7.

34. Figure 3-7 Effect on Autonomous Planned Spending of an Increase in Business and Consumer Confidence

35. The demand for autonomous planned spending • We know that autonomous spending is composed of 5 components. There is a negative relationship between interest rates and Ip+Ca, the other 3 do not depend on interest (G-cTa+NX). See figure 3-8. • Shifts in the Ap demand schedule • A change in G, T and NX shift the Ap demand schedule. A shift in business expectations, and improvement in consumer confidence will also shift the Ap demand schedule.

36. Figure 3-8 Relation of the Various Components of Autonomous Planned Spending to the Interest Rate

37. The IS curve • Ap depends on interest rate. Real GDP and real income depend on Ap, therefore, real GDP and real income depend on interest rate. The IS curve shows the different combinations of interest rate and real income that are compatible with equilibrium. • How to derive the IS curve. • the LHS OF figure 3-9 shows the demand for Ap at different levels of interest rates. Assume that there are no G, T, and NX, so that Ap consists of Ip + Ca, both is negatively related to interest rate. Given a multiplier of 4, at different points of Ap, real income is determined.

38. Figure 3-9 Relation of the IS Curve to the Demand for Autonomous Spending

39. What the IS curve shows • The IS shows different combinations of interest rate (r) and income (y), at which the market is in equilibrium when y = Ap. At any point out of the IS the economy is out of equilibrium.