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Q. Consider the search model in Pissarides (2000), i.e. suppose that

U˙ (t) = λ[L − U(t)] − M(U(t), V (t)) where U(t) is the number of unemployed people at instant t, V (t) is the number of posted, unfilled vacancies at instant t, and λ > 0 is the separation rate. Suppose, moreover, that the matching function is given by M(U, V ) = U αV 1−α where 0 < α < 1 is a parameter. For simplicity, suppose the labour force L is constant and equal to one. 1

(a) Derive the steady-state Beveridge curve, i.e. solve for V in terms of U and parameters when U˙ = 0.

(b) Draw (the qualitative features of) the steady state Beveridge curve. Hint: Consider what happens as U → 0 and U → L.

(c) Suppose U <˙ 0. Show that the Beveridge curve shifts to the right relative to when U˙ = 0 and explain why.

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