This application shows the predicted steady state wages, market tightness, vacancies, and unemployment for a perfect foresight, rational-expectations version of the labor search and matching model, a-la Diamond, Mortensen and Pissarides. This version of the model is based on the presentation in Chapter 1 of EQUILIBRIUM UNEMPLOYMENT THEORY, second edition, by Christopher Pissarides, assuming (1) no capital and (2) a Cobb-Douglas matching function.
Recall that \(w\) is wages,\(v\) and \(u\) are vacancies and unemployment, \(\theta \equiv v/u \) is market tightness, \(z\) is match productivity, \(k \) is the vacancy post cost, \(\delta\) is the exogenous rate of separation, \(\beta = \frac{1}{1+r} \) is the discount rate for payoffs where \( r \) is the real interest rate, \(a \) is the bargaining weight parameter in the Nash bargaining problem for wages, and \(\alpha \) is the Cobb-Douglas matching elasticity Wages and market tightness, in steady state, are determined jointly by a job creation condition $$ w = z - \frac{k}{e \cdot m \left(\frac{1}{\theta}, 1\right)} (r + \delta) $$ and a wage curve $$ w = b + a( z- b + k \theta)$$
Below you can pick different values for each parameter of the model. and for the Cobb-Douglas parameter in the matching function, and compare the steady states