Optimal unemployment compensation with unobservable wage offers Consider an unemployed person…
Optimal unemployment compensation with unobservable wage offers Consider an unemployed person with preferences given by
Where β ∈ (0, 1) is a subjective discount factor, ct ≥ 0 is consumption at time t, and the utility function u(c) is strictly increasing, twice differentiable, and strictly concave. Each period the worker draws one offer w from a uniform wage distribution on the domain [wL, wH ] with 0 ≤ wL H L, wH]. After the worker has accepted a wage offer w, he receives the wage w per period forever. He is then beyond the grasp of the unemployment insurance agency. During the unemployment spell, any consumption smoothing has to be done through the unemployment insurance agency because the worker holds no assets and cannot borrow or lend.
a. Characterize the worker’s optimal reservation wage when he is entitled to a time invariant unemployment compensation b of indefinite duration.
b. Characterize the optimal unemployment compensation scheme under full information. That is, we assume that the insurance agency can observe and control the unemployed worker’s consumption and reservation wage.
c. Characterize the optimal unemployment compensation scheme under asymmetric information where the insurance agency cannot observe wage offers, though it can observe and control the unemployed worker’s consumption. Discuss the optimal time profile of the unemployed worker’s consumption level.
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