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2. Consider the search model in Pissarides (2000), i.e. suppose that
30‘) = ML - [103)] - M(U(t), V(‘»‘)) 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 /\ > 0 is the separation rate. Suppose, moreover, that
the matching function is given by M(U, V) = URI/1"” where 0 < a < 1 is a parameter. For simplicity, suppose the labour force L is constant
and equal to one. (a) Derive the steady-state Beveridge curve, i.e. solve for V in terms of U and parame-
ters 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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