By substituting this into the production function (1), we get the following
supply function:
q* (p, w) ≡ k (αp∕w)1-α (5)
Suppose the sector is open, and the production in the country does not
affect the output price in the world. However, the wage is determined in the
national labor market.
With N identical producers, the sectoral demand for labor in the country
is Nl*. Each worker supplies one unit of labor inelastically, and there are
L > 0 sector-specific workers in the country. In equilibrium, Nl* = L or
equivalently
w* (N, L) ≡ αp (Nk∕L)1-α (6)
which suggests that the wage is decreasing in labor supply and increasing in
the number of producers.
By substituting the supply function (5), the labor demand (4) and the
equilibrium wage (6), we get
π* (N,L) ≡ (1 - α) pl*αk1-α - rk (7)
where l* = L∕N. The first term is the sum of the first and the second
terms in (2), which simply indicates that a fraction α of the total revenue is
distributed to workers.
The profit function (7) suggests the following:
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