EFFICIENT UNEMPLOYMENT INSURANCE: A Dynamic Model Without Wealth Effects 4

Analysis

Using the value functions derived above, we can define an equilibrium. Let V be the set of market participants.
w6686-13

his is a generalization of the definition of equilibrium in the static model. To understand the expression for firm profits, observe that from free entry, the expected present value a vacant firm’s profits equals the cost of creating a new vacancy, k/(l — /3). The value of a vacant firm comes from the possibility of creating a job, yielding profit f{k) — w for the infinite future, and the continuation value if it fails to create a job. Then in steady state, if к e JC, w € W{k), and q — Q(w), к = rj(q) (f(k) – w) -f (1 – rj(q)) (3k. http://get-instant-loans.com/

Next, Optimal Application and Participation use the fact that the relationship between t/, J, and N does not depend on asset levels A. Also, notice that if there is a unique queue length q in steady state, then the end-of-period unemployment rate is
w6686-14
w6686-15
As in the static model, we call a {&*, w*, q*, ф*} that solves this program an equilibrium.

The first part of this proposition is the analog of Proposition 1 in the static model (for the case where z < z) and its proof is omitted. Unemployed workers choose w and q to maximize J(A,w,q), subject to firms making zero profits. From equation (9), this is equivalent to maximizing dissavings while unemployed, ф, subject to (8), so that the rate of dissavings must be optimal, given the wage w and hiring probability fi(q).