Chapter 6: Labor Market So far in the short-run analysis we have ignored the wage and price (we assume they are fixed). Key idea: In the medium run, rising GD will lead to lower unemployment rate (more outputs requires more inputs, or workers). So workers will have more bargaining powers, and will ask for higher wages. This will increase the production costs. So firms have to increase prices. Higher prices means higher living costs. So workers will ask more raises in wages, and so on. To begin with, assume there is two-step procedure. In the first step, firms decide workers wages. In the second step, firms decide output prices. First, the wage setting (WS) equation is given by W = F(u, z), ( df df < 0, > 0) (1) du dz where W is the nominal wage (the dollar wage specified in the labor contract, say, $10,000 a year), is the price level, u is unemployment rate, and z is a catchall variable that represents anything that gives workers higher bargaining powers (such as unemployment insurance, minimum wage, or some forms of employment protection). Everything else equal, rising means (higher lower) living cost. So workers will ask for (higher lower) nominal wage. Rising u means it is (easier harder) for firms to find replacements for current workers. So current workers have (more less) bargaining power, and they will ask for (higher lower) nominal wage. This explains df du < 0. Rising unemployment insurance means the cost of losing job (due to asking for higher wage) is going (up down). As a result, workers have (more less) bargaining power, and will ask for (higher lower) nominal wage. This explains df > 0. dz We can rewrite (1) as W = F(u, z) (2) where W is called real wage. It is the amount of goods and service that nominal wage can buy. Workers effectively care about (real nominal) wages. According to (2), rising u leads to (higher lower) real wage. Next let s consider how firms determine the output price. For simplicity, assume constant return to labor in production Y = AN (3) We see Y doubles after N doubles. Also note that the marginal product dy = is (constant, rising, diminishing). dn Q1: how to modify (3) to allow for diminishing marginal product of labor? The profit of a competitive firm (price taker, not price maker) is revenue cost = Y WN = AN WN By taking the first derivative with respect to N and letting it equal zero, we have The economic interpretation of above equation is 1
Finally, if the output market is not perfectly competitive, then the firm can charge a higher price. So the price setting (S) equation is given as = (1 + m)w A or W = A 1 + m (4) where m is called markup: m = 0 when the firms are price-takers (or the output market is competitive); m > 0 when the firms are price-makers (or the output market is NOT competitive). The equilibrium in labor market is obtained by solving (2) and (4) jointly. We can do that by substituting W in (2) with (4): F(u, z) = A 1 + m (5) The value of u that solves (5) is denoted as u n, called the natural rate of unemployment (NROU). It is the unemployment rate that clears the labor market for given z and m (z and m are exogenous). Using graph, we can put real wage W on the vertical axis, and unemployment rate u on the horizontal axis. The S line is because it does not involve u. The WS line is (upward downward) sloping since df < 0. The intersection of du the two lines gives Q2: Using WS-S diagram to show what happen to u n if markup rises (the whole economy becomes less competitive). Q3: Using WS-S diagram to show what happen to u n if the minimum wages rises. 2
Chapter 7: AS-AD Model Key Idea: We consider labor market, goods market and money market simultaneously. (1) Labor Market AS Curve: We first generalize the wage setting (WS) equation as W = e F(u, z) (1) We use expected price e because workers are forward-looking. When they sign the labor (wage) contract, they take future price into account. Under rational expectation, e =. The price setting equation is unchanged: Replacing W in (2) using (1) leads to = (1 + m)w (2) = e (1 + m)f(u, z), df du < 0 (3) Q1: how will change if e rises? How about rising m? What is the intuition? Q2: What happens in labor market when = e? What will workers do if e? Eq(3) shows the price level and unemployment rate u have (positive negative) relationship because F is (increasing decreasing) function in u. We can extend (3) to show relation between and aggregate output Y. First we assume Y = AN (constant marginal product of labor). By definition of unemployment rate and labor force: u = U L = L N L = L Y/A L = 1 Y AL (4) Make sure you understand each step in the above derivation. By replace u in (3) using (4), we get the aggregate supply (AS) equation: = e (1 + m)f (1 Y, z) (5) AL As Y rises, the unemployment rate u goes (up down), the nominal wage W will go (up down), and the price level will go (up down). So and Y have (positive negative) relationship (from the perspective of labor market), and the two variables move in the (same opposite) directions. (Optional) Alternatively, by applying the chain rule of Calculus, we can show d dy = Thus the AS curve is (upward downward) sloping and looks like 3
Note that the AS curve goes through a special point where = e. On that point, the actual price level is equal to, and unemployment rate and output are at, denoted by u n and Y n, respectively. When Y > Y n, e. Workers (overestimate underestimate) the price level. In the next period, the worker will revise (upward downward) the expected price level. This will shift AS curve (upward downward). Lesson 1: AS curve shifts when workers adjust the expectation of price level e. (2) Goods and Money Markets AD Curve: The AD curve is derived from the IS-LM model (or goods and money markets): suppose the price rises, the real money balance or stock M will (rise fall). On the money market, this will (increase decrease) the interest rate: In the IS-LM diagram, this will shift (IS LM) curve (up down): Output will (rise fall) because the investment will (rise fall). Now we see that and Y have (positive negative) relationship (from the perspective of goods and money markets), and the two variables move in the (same opposite) directions. ut differently, AD curve is (upward downward) sloping and looks like: Q3: lease show what will happen to AD curve when government expenditure G rises. How about rising money supply M? Mathematically, the AD curve can be represented as Y = Y ( M dy, G, T), d ( M ) > 0, dy dy > 0, dg dt < 0 (6) 4
The AD-AS Model consists of equations (5) and (6). The exogenous variables are and the endogenous variables are. In short run, the equilibrium of three markets is at intersection of AD and AS curve. As long as Y Y n, the AS curve will shift because. In the medium run, the AS curve will keep shifting until. See Figure 7-6. Lesson 2: In medium run, Y = Y n. The AD-AS model is very useful to analyze policy and understand business cycle. Consider monetary policy first. Suppose the economy is at natural level at the beginning. Now the money stock M rises (expansionary monetary policy is used). The AD curve will shift (right left). Why? In the short run, the new equilibrium output is (greater less) than the natural level. So e will (rise fall). This will shift AS curve (up down). This adjustment will continue until. See Figure 7-8. Now we see monetary policy can affect output only in run. In the medium run, the output and interest rate all go back to the natural levels. We call this the neutrality of money. Q4: Is there any variable that can be affected by rising money supply even in medium run? By how much? Q5: If we put output on the vertical axis, and time on the horizontal axis. Can you draw the dynamic response of output to the change in money stock? This graph is called impulse-response. How about interest rate and price? Q6: lease draw AD-AS diagram to show what happens when the crash in housing market reduces consumer s confidence, with and without the intervention of Fed. 5
Chapter 8: hillips Curve Key Idea: hillips curve shows the relation between unemployment rate and inflation rate based on the AS curve. To begin with, let s repeat labor market equation (3) here = e (1 + m)f(u, z) (3) For simplicity, assuming F is a linear function: F = 1 au + z, and using the math fact that ln(1 + m) m, ln(1 au + z) au + z. After taking log of both sides of (3), we get ln( t ) = ln( t e ) + (m + z) au t (4) We add the time subscript t to show dynamics. The inflation rate and expected inflation rate are defined as By subtracting ln( t 1 ) on both sides of (4) we get π t t t 1 t 1 ln( t ) ln( t 1 ) ; π t e ln( t e ) ln( t 1 ) π t = π t e + (m + z) au t (5) Equation (5) is called the expectation augmented hillips curve. Lesson 3: hillips curve is just another way of describing the labor market. Q1: Suppose the price level has been stable, so π t j =, (j = 1, 2 ). The workers expectation about inflation π t e =. In that case, (5) reduces to π t = (m + z) au t (Old hillips Curve) A.W. hillips originally observed that there was a (positive negative) relationship between inflation rate π t and unemployment rate u t using UK data from 1861 to 1957. If inflation rate rises, the old hillips curve implies that the unemployment rate will go (up down). The old hillips curve looks like: This result seems to be important for policymakers. If they desire low unemployment, they can (increase decrease) inflation rate by (increasing decreasing) money supply. However, both inflation rate and unemployment rate went up in US in 1970s. This phenomenon is called stagflation. The old hillips curve (can cannot) explain the stagflation. Q2: How to use AS-AD diagram to explain stagflation? 6
Q3: Suppose the inflation rate has been stable, so π t 1 = π t 2 = 0. The workers expectation about inflation π t e =. This is called adaptive expectation. In that case, (5) reduces to π t π t 1 = (m + z) au t (Modified hillips Curve) The modified hillips curve shows that there is (positive negative) relationship between unemployment rate u t and the change in inflation rate π t π t 1. The modified hillips curve looks like Q3: what happens to modified hillips curve when minimum wage rises? Q4: Recall that = e when u = u n. This is equivalent to saying when u = u n, π t e = π t. So another way to define the natural rate of unemployment rate u n is that it is the rate such that the actual inflation rate is equal to the expected inflation rate. lease find u n using (5). Now using this formula for u n we can rewrite the modified hillips curve as π t π t 1 = a(u t u n ) (6) If u t > u n, π t π t 1 0. The inflation rate is (rising falling). If u t < u n, π t π t 1 0. The inflation rate is (rising falling). The inflation rate is stable only when. So u n is also called non-accelerating inflation rate of unemployment (NAIRU). A Numerical Example: Suppose π t π t 1 = 2(u t 0.05) and currently, u t = u n = 0.05, π t = 0, π t 1 = 0, t = 100 If u t+1 = 0.04, π t+1 = t+1 = If u t+2 = 0.04, π t+2 = t+2 = If u t+3 = 0.04, π t+3 = t+3 = So in order to maintain an unemployment rate that is below its natural level, the inflation rate will keep going up (accelerating). The price level will go up at (constant increasing decreasing) rate. 7
Neutrality of Money Again Now we know in the medium run u = u n That means Y =. Recall the AD curve Y = Y ( M, G, T) So in the medium run M will remain a constant. In other words, the percentage change of real balance is zero in medium run. Using the math fact that we have 0 = M% % or ( A ) % = A% B% B π = g M (inflation rate = rate of money growth) Milton Friedman put it this way: Inflation is always and everywhere a monetary phenomenon. In the medium run, the rate of inflation is determined by the rate of money growth. Disinflation In early 1980s, aul Volcker was the chairman of Fed, and his task was to cut the high inflation rate (called disinflation) at that time. Let a = 0.5 in (6). In order to reduce inflation rate from 10% to 4%, the unemployment rate has to be greater than its natural level by. That means a (high low) cost for disinflation. Because of this, many economists suggested a gradual rather than sudden disinflation. 8
Discuss questions for Chapter 9 1. Why was the interest rate so low before 2006? 2. Why was there big increase in house price before 2006? 3. How to tell there is bubble on the housing market? 4. What will the home owners do if the value of house (price) is below the value of mortgage (debt)? 5. What will happen to the balance sheet of a bank if the home-owner defaults? 6. What will happen to interest rates if banks reduce the amount of loan? 7. What will happen to IS, LM, AD and AS curve? 8. What policies were used to fight the Great Recession? Can you show that using IS-LM and AD-AS diagram? 9. What is the liquidity trap? 10. What has happened to federal budget? 11. What are leverage ratio, securitization, Libor rate and quantitative easing? 9