Globalization, Divergence and Stagnation

^χ (г) = [(ι - β) p (г) lχ (г)]^1/в А (г)^l (г) ,

where χ (г) is the price of machine ʃ(i). Machines in each sector are produced by
a monopolist. The unit cost of producing any machine is normalized to (1 — β)².
Together with isoelastic demand (2), this implies that the monopolist in each sector
charges a constant price, χ (г) = (1 — β). Substituting χ (г) and (5) into (4), yields
the quantity produced in sector г as a linear function of the level of technology А(г)
and employed labor l (г):

_y (г) = p (г)^(1-в)/в А (г) l (г) .

The linearity of y (г) in А (г) is crucial for endogenous growth, but it is not a sufficient
condition. As it will become clear later on, an expansion of y (г) can reduce its price
р(г) and this can effectively generate decreasing returns. Given the Cobb-Douglas
specification in (4), the wage bill in each sector is a fraction β of sectoral output.
Therefore, equation (6) can be used to find the relation between equilibrium prices
and the wage:

w = βp (г)^1/в а (г).

Since there is perfect mobility of labor across sectors, the wage rate has to be equal-
ized in the economy. Dividing equation (7) by its counterpart in sector j delivers
the equilibrium relative price of any two varieties:

Intuitively, sectors with higher productivity have lower prices. Using (7), integrating
over the interval [0,1] and making use of (3) shows that the equilibrium wage rate
is a CES function of sectoral productivity:

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