DMP Economic Assingment Help With Solution
1. Consider a worker who lives forever, discounting the future at rate r: While unemployed, this worker enjoys áow utility b and receives job o§ers, which are iid draws from a known exogenous wage o§er distribution F(w);
at Poisson rate : Jobs end at exogenous Poisson rate .
(i) Derive the comparative statics of the reservation wage with respect to the job destruction rate, i.e., Önd dR=d:
(ii) Let u denote the fraction of time that this worker is unemployed. The unemployment rate u can be derived from the steady-state condition, (1 F(R))u = (1 u):
Derive the comparative statics of the unemployment rate with respect to the job destruction rate, i.e., Önd du=d: You should Önd that the sign of du=d is ambiguous.
2. Sketch the comparative statics of an increase in in the basic DiamondMortensen-Pissarides (DMP) model. That is, how does an increase in a§ect the equilibrium level of labor market tightness, the wage rate, and the
unemployment rate? To answer this question, you should draw the graphs that represent the equilibrium conditions of the model and then explain how the increase in shifts these curves.
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3. Consider the following extension of the basic DMP model. Unemployed workers meet vacant jobs according to the constant-returns-to-scale contact function, M(u; v); just as in the basic model. However, not all contacts lead
to a match. When a worker and Örm meet, a match-speciÖc productivity, y; is drawn from an exogenous distribution function, F(y): These matchspeciÖc productivity draws are independently and identically distributed
across all worker-Örm meetings.
If y R; the match goes forward, and the worker receives a wage w(y) = y + (1 )rU; while the Örm receives yw(y); so long as the match lasts. Otherwise, the worker and Örm continue to search. Matches end at exogenous Poisson rate ; again just as in the basic model.
In this extension, the key endogenous variables are (i) labor market tightness; (ii) the reservation productivity, R; and (iii) the unemployment rate, u: The corresponding equilibrium conditions are (i) free entry of vacancies,(ii) zero net surplus at y = R; and (iii) the Beveridge curve. The free-entry condition is more complicated than it is in the basic model because a Örm doesnít know in advance what value of y will be realized when it meets a worker; that is, ex ante, a Örm with a vacancy can only compute the expected value of meeting a job applicant. The zero net surplus condition is J(R) = 0 or, equivalently, N(R)U = 0: Here J(R) is the value to a Örm of Ölling a job when the productivity of the match is y = R; and similarly for N(R): (In general, the value to a Örm of a Ölled job is J(y); i.e., depends on the productivity of the match; similarly, the value to the worker is N(y):)
Finally, the Beveridge curve condition needs to account for the fact that not all contacts lead to a match.
Write down (and explain) the equations that describe the equilibrium of this extended version of the basic DMP model. Sketch the comparative statics of an increase
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