Explain more B and ii in more depth Page 10 of 11 Suppose that there is no unemp

Question

Explain more B and ii in more depth

Page 10 of 11 Suppose that there is no unemployment benefits (b-0), that each match produces 2 units (z-2), and that the bargaining power of workers is the same as that of firms (a-0.5). Show that the equilibrium wage is equal to1 a) b) Following on the previous question (a), suppose in addition that M ein (Q.)-0.4Q1/2 /2, and that the cost of posting a vacancy is k-A2. i. Show that the equilibrium probability of filling a vacancy is Pr-0.2 ofz_w) = 0.2 implies that pf-0.2 ii. Show that the equilibrium labor market tightness is j- 4. 0.2 implies that pf-MA-em(QA)/A-em(Q/A)-0.4 (OA)^(1/2) AO 22-4

Explanation / Answer

(ii) Show that the equilibrium labor market tightness is j = 4.

We know that, the probability of filling a vacancy is given as -

pf = 0.2

(M / A) = 0.2

em (Q, A) / A = 0.2

em (Q / A) = 0.2

(0.4) (Q / A)1/2 = 0.2

(Q / A)1/2 = (0.2) / (0.4)

(Q / A)1/2 = (1 / 2)

squaring on both sides & we get -

(Q / A) = 1 / 4

rearranging an above eq.

(A / Q) = 4

where, A / Q = j = labor market tightness

Then, we have

j = 4

Hence, Proved.

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