Chapter 7: 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 dz > 0. 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 1
The economic interpretation of above equation is 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 (4): in (2) with 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 8: hillips Curve Key Idea: We consider labor market, goods market and money market simultaneously. 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. 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. hillips curve is just another way of describing the labor market. 3
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. 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 Q4: what happens to modified hillips curve when minimum wage rises? Q5: 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). 4
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. 5