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For latter reference it is useful to define Ma as the highest number of a firms compatible with the steady state requirements. The number Ma is such that 7ra = 0 in an economy with no b firms:
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Consider first the case in which we start the economy with Ma> 0 and Mb = 0. Lemma 2.2 implies that there will be no entry of b firms; the labor force will be divided equally among firms in sector a and profits will be given by:
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Suppose now that we start the economy with Ma > 0 and Mb > 0, so the fixed costs of setting up Mb firms in sector b have already been incurred. Will the firms in sector b remain in operation? There are two possibilities. Figure 2.1 depicts the case in which firms of type b survive in the steady state. In this case the steady state set is determined by the intersection of the areas defined by the following four conditions: тга > 0, тгь > 0, тга < <£>r* and тгь < фг*. This set includes elements in which both Ma and Mb are positive. We call these “non-specialized steady states”. Figure 2.2 depicts the “specialized steady state” case. In this case there are no elements of the steady state set such that Ma> 0 and Mb> 0. Points in which b firms would be willing to continue producing because 7r6 > 0 will trigger entry of firms in the a sector to the point where b firms will become unprofitable and be driven to exit.
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To determine whether we will have a specialized steady state we ask whether a marginal incumbent in the b sector would survive when the number of a firms is the lowest number consistent with sector a’s no-entry condition. This value of Ma is determined by the condition 7га = фг*. A value of Ma lower than the one implied by this condition would mean lower wages and hence higher profits in the a sector. The present value of profits in the a sector would then rise above the entry cost ф, thus triggering entry of a firms. The profits of a marginal firm in sector b in this scenario can be determined using equation (2.10):
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Figure 2.2: Specialized Steady State
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