CLASS #13: EQUILIBRIUM IN THE LABOR MARKET

• How is equilibrium determined?
• How do labor taxes affect the equilibrium?
• Unemployment
• The relationship between output and unemployment: Okun's law

Labor Market Equilibrium

There is an equilibrium level of real wages w^* such that labor demand is equal to labor supply. When w<w^* there is excess demand for labor, which induces firms to bid wages up. When w<w^* there is excess supply of labor, which induces firms to bid wages down.

Labor Taxes and Equilibrium Wages and Employment

If firms have to pay 10 % of the wage as, say, social security contribution, their perceived cost of labor is 10% higher: the labor demand curve shifts down.

$$(1-\alpha) A K^{\alpha} N^{-\alpha} = (1+\tau_f)w$$

or

$$\frac{(1-\alpha) A K^{\alpha} N^{-\alpha} }{1+\tau_f}= w$$

If workers have to pay a 10% tax on their income, their perceived earnings are 10% lower: the labor supply curve shifts up.

$$U_C(C,L)w(1-\tau_w)=U_L(C,L)$$

or

$$w=\frac{U_L(C,L)}{U_C(C,L)(1-\tau_w)}$$

Taxes are equivalent to increase the marginal utility of leisure from U_L to $\frac{U_L}{1-\tau_w}$, and therefore induce people to work less, for any given pre-tax wage. $\rightarrow$ social security contributions and income taxes lower equilibrium employment.

Unemployment

Measuring unemployment: Labor force= number of employed + number of unemployed Labor force participation rate=Labor force/Adult population (66% in US) In order to be considered unemployed one has to be actively looking for a job. Discouraged workers are not counted as unemployed, but just dropped from the labor force. Frictional unemployment Job search: people looking for the "right" job (example: tenant and landlord). Structural unemployment Low skilled workers: cannot find a job at any wage. Full employment We have full employment when the only kind of unemployment is structural or frictional (no pressure on wages). Natural rate of unemployment= structural + frictional Cyclical unemployment= actual unemployment - natural rate =$u-\bar{u}$

Okun's law

How much does output decrease in % terms when cyclical unemployment increases? Okun's law is an empirical relationship:

$$\frac{\bar{Y}-Y}{\bar{Y}}=2.5\times (u-\bar{u})$$

when cyclical unemployment rises:

• labor force declines (discouraged workers)
• hours per worker decline
• productivity declines

Modeling the natural rate

Why should we be interested in modeling the natural rate? Because it changes over time and, more importantly, it changes a lot across countries.

	Unemployment (%)			Long term unemployment
	%			% of total unemployment
	74-79	80-89	96	79	89
Germany	3.2	5.9	8.9	19.9	49
France	4.5	9	12.4	30.3	43.9
Spain	5.2	17.5	22.1	27.5	58.5
UK	5	10	8.2	24.5	40.8
US	6.7	7.2	5.4	4.2	5.7

A model of the natural rate

Define U= number of unemployed people;
E= number of employed people;
L= U+E= total labor force; f= job finding rate;
fU= unempl. become empl.; (1-f)U= unempl. stay unempl.;
s= job separation rate; sE= empl. become unempl.
So the law of motion for Unemployment is:

U_t+1=(1-f)U_t+sE_t

or

U_t+1=(1-f)U_t+s(L-U_t)

At the steady state (long run) U_t+1= U_t=U_s Solve for U_s and obtain:

$$\frac{U_s}{L}=\frac{s}{s+f}$$

As f increases, $\frac{U_s}{L}$ decreases Obtain that the natural rate is a function of the separation rate (s) and of the finding rate (f). What happen when Unemployment Insurance programs are very generous? Incentives to look for a job decrease. But UI programs in Europe were very generous back from the 50's. Why are differences in natural unemployment rates appearing only in the 80's? Sargent and Ljungqvist: human capital story + changes in technology.