Macroeconomic Theory

1. Macroeconomic Theory Chapter 2 Aggregate Demand, Aggregate Supply, and Business Cycles

2. Aggregate Demand • Note that the short run is a period where prices and wages are given. Why? • institutional arrangements, i.e., wages are reviewed periodically. • for prices, the costs associated with changing prices (menu costs) • The standard model used to summarize the way in which the level of output is determined by AD (with sticky wages and prices) is the IS/LM, where the goods market is labeled IS (equity between planned I and S), and the money market is labeled LM (equity between money demand (liquidity) and money supply (money) • At IS/LM equilibrium, output and interest rates are constant. The IS is useful to analyze: • shifts in C and I and changes in fiscal policy • On the LM side we can analyze: • shifts in MD and changes in monetary policy (ΔMS)

3. The goods market: the IS curve • AD refers to planned real expenditures on goods and services (yD). At equilibrium (y=real output): • yD = y it can be rewritten as (A is non interest rate): • yD = c(y ,t, wealth + I( r, A) + g (AD) • Using a linear function for consumption (other factors are summarized in autonomous consumption c0), • c = c0 + cy (y - t) • 0< cy < 1 is the marginal propensity to consume. • t is total tax revenue. The linear tax function • t = ty y • 0< ty < 1 by substitution: • c = c0 + cy (1 - t)y • It is clear that consumption is affected by current level of activity in the economy.

4. Investment is assumed to depend negatively on real interest rate and on expected future profitability (determined by factors proxied by A). • The idea is that firms are faced with an array of projects, which are ranked by their expected returns. When i ↓ some projects would be profitable than otherwise. If expected return increases, more projects will be undertaken. The investment function is • I = I (r, A). • The linear form is • I = A – ar . ( a is constant) • Expectational or confidence factors are often considered crucial determinants. Hence shifts in I due to A > than movements along the curve. • The IS curve is defined by the goods market equilibrium condition (yD = y) or using the linear versions of C & I above:

5. yD = c = c0 + cy (1 - t)y + A – ar + g (planned expenditure) • Rearrange using yD = y and replacing (1-cy) by the marginal propensity to save, sy, to define the locus of interest rate and output: • y =(co+A+g/1-cy(1-ty)-(a/1-cy(1-ty) . r • =(1/1-cy(1-ty) . [c0 + (A-ar) +g] • = 1/sy+cyty . [c0 + (A-ar) + g]1/sy+cytyis the multiplier • We know that savings and tax are leakages from the feedback • The IS curve is derived graphically in fig. 2.1 • Note that low r generates high I and high y, and vice versa

7. Using the IS curve equation we can separate the determinants of the slope and position of the IS into 3 groups: • Changes in the size of the multiplier will change the slope of the IS curve. e.g., ↑cy will make the IS flatter. • Any change in interest sensitivity of I will change the slope of the IS curve. Less sensitivity → steeper IS. • Any change in c0 or g0 will cause the IS curve to shift by the change times the multiplier. A change in A also shifts the IS • Policy can be used to manipulate IS through 1 and 3. e.g., if income tax is proportional (t=tyy). ↓ ty ↑ the multiplier and shifts the IS into a flatter curve. • Any change in g will shift IS as in 3 above. • Quantities adjust through the multiplier process to take the economy to a stable short run equilibrium. e.g., a fall in I → y ↓ → S ↓ to equal the low I. • The process can be shown, assuming ty=0, as follows;

8. Initially y falls by ΔI → ↓ Δc=cyΔI. This reduces y and in the next round by ↓ Δc=cy (cyΔI) and so on. Therefore; • Δy= ΔI+cyΔI+cy2ΔI+cy3ΔI+… • =(1+cy +cy2 +cy3 +…)ΔI • =(1/1-cy) ΔI • =1/syΔI = multiplier . ΔI • Another way of focusing on quantity adjustment to a new goods market eq is to characterize positionsoff the IS curve. Look at figure 2.2. At point x with yx there is an excess demand in the goods market (r is low), while planned expenditure is y1. stocks will fall and output will rise until y=yD.

10. Money market: the LM curve • Demand for money • Confusion between the decision to save and the decision to hold money. Saving is a decision about the use of the flow of income. The demand for money is a decision about the form in which to hold wealth (money or another asset). • Money is notes and other interest bearing accounts. Money is fairly liquid. In nominal terms money is capital safe. • Money and bonds • Bonds are not capital safe in nominal terms. If nominal interest iincreases the market value of bonds will fall. Why there is an inverse relationship. • If there is a bond with a face value $100 and pays a yield $5, if the market rate is 4%, the market value would be $x where .04x=$5 i.e., x=$5/.04=$125. if i is lower 2%, x=5/.02=$250 and vice versa with higher i. • It is clear that only i=5% where the face value equals the market value.

11. Demand for money versus bonds • money is needed to carry out transactions which is a function of income, but holding assets as money will entail a cost, the foregone interest income. The demand for money is; • MD/P = L(y, i) where; • dL/dy >0, dL/di <0 • The linear demand for money is: • asset demand transactions demand • Where , vT and li are positive constants. The term reflects the asset motive and term reflects the transactions motive for holding money. vT is the transactions velocity.

12. In the quantity theory output is the only determinant of money demand; i.e.; MD/P =1/v .Y, the overall relationship between money demand and output is not constant, it will vary with changes in interest rate. • Asset and speculative motives • Two of the explanations of the –ve relationship between MD and i is the asset motive and the speculative motive. For speculative demand Keynes argued that if an individual believes that the current interest rate is above normal he expects it to fall to normal in due course. He then will choose to hold financial assets over money required for transactions in the form of bonds. As there is a chance for a capital gain on bonds when i falls such that there is an inverse relationship between i and the demand for speculative balances.

13. A more general rationale was provided by Tobin, instead of assuming that each individual is certain about what he expects the future rate of i on bonds, Tobin focused on the implications of investor uncertainty. Individuals allocate their portfolio between riskless asset (money that pays no i) and risky assets that pay i. • The individuals utility depends positively on the return and negatively on risk. To maximize their utility individuals will hold a mixture of the two assets trading off benefits of expected return against the associate risk according to his preferences. • Money market equilibrium • MD/P = MS/P • It is assumed that the supply of money is fixed by monetary authorities at . Hence the equilibrium condition is: • L(y, i) =

14. We can define an upward slopping LM curve as at low levels of y the transactions demand is low which must be correspondent with a high asset (or speculative) money demand. A low i will ensure this since the return from bonds relative to the risk is low, and vice versa when income is high and interest is high. • Fig 2.3, shows how shifts in MD or changes in i sensitivity of MD or changes in MS affect the LM. In step one look at the levels of MS and corresponding MD for transactions and interest sensitive MD in order to have an equilibrium in the money market. • Having done that, the second step is to calculate y that is consistent with that level of transactions demand for money as: Y=vT. transactions demand at i. • By joining points X and Y the LM curve is drawn.

16. From the derivation of the LM there are four ways in which the position/slope of the LM can be affected 1. a change in transactions velocity of circulation. If vT↑ will make LM flatter. 2. a change in interest sensitivity of asset demand for money. High sensitivity will produce a flatter LM. A special case arise when interest sensitive money demand is horizontal, where no one believes that interest will fall below actual interest rate, the speculation demand for money will be perfectly elastic. This is known as the liquidity trap case. 3. a change in MS. ↑ MS shifts LM to the RHS. 4. a change in P. ↑ P given i will mean that available transaction balances can only finance a lower y. the LM shifts to the LHS.

17. Look at fig 2.4. at point X, y is y0 and i is ix MS is too high for money market equilibrium. This excess MS can be eliminated if y rises, or i falls. Excess MS will raise the demand for bonds, bond prices will increase and i will go down. • The converse situation is true at point Z.

19. Putting together the IS and the LM • Real and nominal interest rates • r is defined in terms of goods and i in terms of money. Thinking of goods and r, how much extra of one good would have to be paid in order to have one of that good today i.e., Today 1 goodt=(1+r)goodt+1. • i is how much extra in $ would have to be paid in the future in order to have one $ today i.e., 1$t=(1+i)$t+1. • If goods prices remain the same it is clear that r and i are the same. If you lent $1 today would be able to buy (1+r) goods in the future. In general • 1+r = (1+i).p/pE1+1. • If we use the following of definition of expected inflation • πE=(PEt+1-P)/P then • P/PEt+1 = 1/(1+ πE) • By rearranging it follows that • (1+r) = (1+i)/(1+ πE) and therefore r = (i- πE)/(1+πE)

20. When πE is low, the denominator is close to 1 and the standard approximation of the relationship between i and r is • i = r + πE. • The IS/LM model • To avoid the problem that the IS depends on r and LM on i we shall assume that r = i, i.e., inflation equals zero. • The path adjustment of the economy will depend on the speed of adjustment in each market. The money market diseq is cleared rapidly (through the bond prices) than the goods market since it involves the adjustment of production and employment. • Look at fig 2.5, there are two examples of government policy changes. The first is ↑G, the new IS(g1), y and r is higher, higher y will mean a higher MD, but since monetary policy is unchanged, (LM stays the same) r will be higher to dampen the higher asset demand for money.

21. The adjustment process : ↑G → excess demand → unplanned inventory depletion, if the rise in AD is sustained ↑ employment. The economy moves from A to B. • This boosts the MDT and → excess MD. At B bonds are sold causing bond prices to fall and r to rise (B to C). This dampens excess demand and → I ↓. At C there remains some excess demand due to ↑ consumption associated with the multiplier effect. The adjustment process continues until A’. The full multiplier expansion doesn’t occur because there is a fiscal expansion without any change in MS, as the rise in r causes interest sensitive spending to fall. • The second example is CB ↑MS. The LM curve shift to the right LM(MS1/P). Lower r will be associated with higher I and y (A’). • The adjustment process: there will be an excess MS, leading to more demand for bonds and r↓. The economy moves from A to B. the fall in r creates excess demand ↑ AD and investment which ↑y and employment raising y from B to C. adjustment of output will continue until A’.

23. Fig 2.6 shows why expansionary monetary policy may not raise y even in the short run. If interest is ihat the LM is flat. People believe that i will rise they will sell bonds, bond prices will fall. • The economy is in liquidity trap, the CB is powerless to use monetary policy to shift y higher. • The liquidity trap plays a role in the long Japanese slump in 1990s.

25. Aggregate supply Equilibrium in the competitive labor market. • Demand and supply of labor depend on real wage. Given capital stock • Y=f(E), E=employment • The standard assumption is that the production function is characterized by diminishing returns. i.e., ∂y/ ∂E (MPL) declines as E rises. • The demand for labor under perfect competition is MPL, as firms employ up to the point where MPL=w. • The supply of labor is upward slopping and is driven from households optimization as they allocate their time between work and leisure. • At eq the market clears. Any temporary displacement of the economy from eq. is assumed to be eliminated by w. The only unemployed people are those voluntarily unemployed. The competitive unemployment rate is UCE/L, where L is the labor force.

27. Supply side in the imperfect competition model. • In an imperfect competition market, the wage is set either by employers or unions. Wage setting • Under imperfect competition there is an upward slopping wage setting (WS) curve which is the counterpart of the labor supply curve, which is above the competitive labor supply curve. In fig 2.8, if wage = w1, the competitive market employment is E1, but with imperfections it is E0, and additional workers (E1-E0) would be prepared to work at that wage. Again if E=E0 a higher wage w1 is set for that level of employment. • Conditions in the labor market are the key determinants of the wage setting real wage. The money wage equation is • W=P.b(E) b is a rising function of employment.

29. When wage is set it is the nominal wage that is fixed, workers will evaluate wage offers in terms of the real wage they are expected to deliver, i.e., the money wage relative to expected price level. • If expected and actual price levels are equal, the wage equation can be written in terms of the real wages to define the upward sloping ws cuve as: • wWS=b(E), wage setting real wage • wWS=W/P, • The excess of w on the WS curve above that on the labor supply curve is the mark up per worker. Two common interpretations of this mark up: • Wage setting by unions. • The simplified model is “Monopoly union”, the union set the wage. It aims to strike a balance between (i) too high a wage, which decreases employment and (ii) too low a wages, which lowers living standards of employees. This results in a union setting a wage higher than the competitive wage.

30. Efficiency wage setting by firms • Here the firms set wages. Firms will set a wage above the minimum voluntarily. By setting a higher wage, the employer is able to retain well qualified and cooperative workforce, i.e., to allow the firm to efficiently solve its motivation, recruitment, and/or retention problems. Employer sets a higher wage and this efficiency wage arises as unemployment falls. • Price setting • Under perfect competition • P = MC = W/MPL • → W/P = MPL. • Under imperfect competition, firms set a price to max profits. The mark up will depend on elasticity of demand. As elasticity rises the mark-up falls until we get the special case of perfect competition where elasticity of demand is infinite.

31. In the simplest case of monopoly, profits are maximized when MR=MC. If ɛ is constant then the mark up is constant and greater than one of (ɛ/ɛ-1) • The standard monopoly pricing formula is • P = (ɛ/ɛ-1) . (W/MPL) • And the price-setting real wage is • (W/P) = (ɛ-1/ɛ) . (W/MPL) • Fig 2.9 illustrates the PS curve in the monopoly case: because (ɛ-1/ɛ)<1, the PS real wage is a fraction of MPL. • More generally any type of product market imperfection causes the PS curve to lie below the competitive labor demand curve. The excess is supernormal profits per worker. We shall use a horizontal rather than downward-sloping PS curve. Some additional assumptions are required.

33. The flat PS curve offers a useful simplification (firms do not change P in response to fluctuations in output). This is consistent with the sticky prices assumption. • In this baseline case, we assume a constant MP and a constant mark-up. Firms thus set prices to deliver a specific profit margin. The fixed output per worker is split into profits per worker and w per worker. w is therefore constant and the PS curve is flat. • Price setting can then be summarized as the marking up of unit labor cost by a fixed percentage ( ) on unit labor costs.

34. The marking up rule is: • P = (1+ ) (W/λ) λ = labor productivity • Let μ = / (1+ ) then the pricing rule can be written as: • P=(1/1- μ).(W/ λ)μ = mark up. • As the extent of competition increases, the size of the mark-up falls. Divide both sides by P and rearrange λ = μ.λ + W/P Output per head=real profit per head + real wage per head • In other words given μ, λ and W, the price level set by firms implies a specific value of the real wage. This is the price setting real wage. • wPS = W/P = λ . (1- μ ) (price setting real wage) • See fig 2.10

36. Equilibrium in the labor market under imperfect competition • The labor market is characterized by an upward sloping WS curve and a flat or downward sloping PS curve. At eq. • wWS = wPS • b(E) = λ . (1- μ) (labor market eq, imperfect competition) • See fig. 2.11. the eq level of employment is EICE, the associated eq rate of unemployment is ERU=UICE/L.

38. The contrast between competitive and imperfectly competitive eq rates of unemployment is shown in fig. 2.12. WS lies above the labor supply to reflect imperfection. The PS lies beneath MPL (firms make supernormal profits). Unemployment will include some involuntary unemployment. There are people who would be willing to work at WICE, but are not employed at eq level EICE. Involuntary unemployment UICE is not ideal.

40. Aggregate demand and aggregate supply • Aggregate demand: from the IS/LM to AD curve. Look at fig. 2.13, if the economy is at A, if we hold M constant and lower P to P0, the new money market eq is shown by LM(MS/P0), the increase in the value of (M/P) creates disequilibrium in the money market. Households will buy bonds, and r falls. This is know as the Keynes effect. The new eq at B with higher y. the combined goods and money market eq for different price levels produce the AD curve. Shifts in the IS or LM curves, apart from a change in P shifts the AD curve. • The AD represents two sets of equilibrium conditions. When P changes, it disturbs the eq in the money market, which changes r, which creates diseq in the goods market and output changes as eq is restored. • In the liquidity trap case, shits of LM do not change r, and falling prices fail to stimulate the economy.

42. Aggregate Supply: from the labor market to the AS curve • Look at fig. 2.14, a rise AD due to a rise in A would be associated with labor market eq. only at the unchanged yCE or yICE. The economy moves from A to Z. • This special case of immediate adjustment of w and P is summarized by the AD curve combined with vertical AS curve. This economy will face fluctuations in y only as a consequence of changes in the supply side, as changes in AD will affect prices not output or employment. • We will return to fig. 2.14 later

44. Two approaches to business cycles • The Real business cycle model: Supply shocks • Fluctuations are due purely to supply side factors in RBC model such as changes in technology. In fig. 2.15 the economy is initially at A. a positive technology shock shits the MPL to the right and the economy moves to B (boom). The opportunity for workers to earn higher wages leads them to supply more labor, i.e. to move up the labor supply curve. B is therefore a position of labor market eq. • A negative supply shock (sudden scarcity in a raw material) takes the economy into recession as MPL shifted left and eq is at C, workers choose to supply less labor voluntarily, i.e., they shift the timing or the labor supply in response to shifts in demand by working more in good times and less in bad times. This is called the inter-temporal substitution of labor. Technological progress plays the key role in explanations of the long run growth of living standards. However, it seems less plausible that technical progress lie behind the pattern of booms and recessions that characterize economies.

46. As the economy recovers from a recession productivity rises relative to long term trend, and the reverse in recession, this does not mean that technological change that is causing the boom and recession. • A simpler explanation consistent with AD-view of the business cycle is that when AD falls firms hold on to workers (it is costly to hire and fire), hence productivity will fall in recession (fall in y is > fall in employment) and vice versa. • Fig. 2.15, shows that RBC mechanism is able to explain the substantial changes in employment over the BC. A small change n w must lead to a large change in labor supply. However, this does not fit empirical evidence, that inter-temporal elasticity of labor supply is low.

47. Business Cycles: aggregate demand shocks plus sticky wages and prices • Suppose that wages and prices do not adjust at all in the short run. In fig. 2.14 this means that the economy does not move directly from A to Z in response to an AD shock. The short run adjustment due to the shift of IS to the RHS is shown in the bottom panel as the movement from A to B with unchanged w and P in the top panel. The middle panel shows that the labor market is not in equilibrium when employment is at E1. • The prevailing w (w0) is neither on the labor supply and demand in competitive market, nor on WS or PS in the imperfectly competitive interpretation.