# EFFICIENT UNEMPLOYMENT INSURANCE: A Model of Job Search

Preferences and Technology

There is a continuum 1 of identical workers, each with the von Neumann-Morgenstern utility function u(c) over final consumption, и is twice continuously differentiable, strictly increasing, and weakly concave. All workers are endowed with initial wealth Л0, which they may either store or invest in a mutual fund. The absence of aggregate risk ensures that the mutual fund’s gross rate of return is equal to the return from storage, R = 1. Worker z’s consumption is therefore equal to his assets A0, minus lump-sum taxes r, plus net income from wages or unemployment benefits y,-, so his utility is

u(A + yi),

where A = A0 — r is after-tax assets. In most of the paper, we will think of UI as provided by the government and financed by taxes, but it could also be provided by a private insurance firm or the worker’s family.

There is a larger continuum of potential firms, each with access to a production technology / : (0, oo) —> (0, oo) that requires one worker and capital к > 0 to produce f(k) units of the consumption good. / is continuously differentiable, strictly increasing, and strictly concave, and satisfies standard conditions to ensure an interior solution: lim^o/W = 0, limfc_K) f(k) > 1, and there exists к such that f'(k) = 1. The price of capital is normalized to R = 1, and since workers own a diversified portfolio, firms maximize expected profit. The large number of potential firms ensures free-entry, so aggregate profits are zero in equilibrium.

Workers and firms come together via search. At the beginning of the period, each firm j decides whether to buy capital kj > 0. If it does, the firm is active, and posts a wage Wj} In the next stage, each worker observes all the wage offers and decides where to apply. That is, worker i seeks jobs with a wage e W where W = {Wj, for all j active} is the set of wage offers. If he is hired, he earns yi — wi. Otherwise he is unemployed and obtains UI yi = z. A firm that hires a worker produces /(&), while an unfilled vacancy produces nothing and its capital remains idle. online payday loans direct lenders only