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In both sectors production is organized in firms as in Hopenhayn (1992). To set up a firm it is necessary to make a one-time investment of ф units of good a. If this cost is paid at time t the firm will be able to operate at time t -f 1. Plants produce according to the following technology:
where Ylt denotes the output of sector i and Nit the number of units of labor that this sector employs. To simplify we assume that the production functions in the two sectors differ only with respect to the level parameter 2*. The elasticity of production with respect to labor (a) is assumed to be identical in both sectors.

In every period each firm must pay a overhead cost of units of good a. This cost plays two roles. First, it keeps the number of firms bounded. Given the presence of decreasing returns to scale the equilibrium number of firms would be infinite with Ф — 0. Second, the overhead cost will induce firms to exit in response to a sufficiently large deterioration in the relative price of their product. With ф = 0 firms would never exit since they would always earn positive profits.
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At the end of every period, a firm can choose to produce or to discontinue its operation. To simplify we assume that a firm which discontinues its operations for one period cannot resume its operations in future periods and has a liquidation value of zero. The problem facing an incumbent firm in sector г can be described in terms of the following dynamic programing problem, where rHt represents time-t maximal profits in the г sector: