Consider a very simple labor market model described by the equations below. L s

Question

Consider a very simple labor market model described by the equations below.

Ls = ¯a w + ¯l(little letter of L) Ld = ¯f w(1 + ) where w is the wage rate, ¯l is the household’s taste for work (could be positive or negative), a¯ represents the sensitivity of labor supply to the wage rate and ¯f represents the productive capacity of the firm. The tax is a payroll tax paid by the firm. Taxes are taxen as given and may vary across time and countries. When the market is in equilibrium Ls = Ld

a. (1 pt) Which variables in this model are endogenous, which variables are exogenous and which variables are parameters?

b. (1 pt) Solve for equilibrium wage,w* , and employment, L* , as a function of the parameters.

Explanation / Answer

a. Endogenous variables are wage rate and employment rate. Exogenous variables are household’s taste for work and productive capacity of the firm. Parameters are tax and sensitivity of labor supply to the wage rate.

b. Ls = Ld

or, ¯a w + ¯l = ¯f w(1 + )

or, ¯a w + w(1 + ) = ¯f - ¯l

or, w[¯a + (1 + )] = ¯f - ¯l

or, w* = ( ¯f - ¯l)/[¯a + (1 + )]

L* = ¯f [( ¯f - ¯l)/{¯a + (1 + )}](1 + )

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