Globalization, Divergence and Stagnation



derived from (4) is:


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

(5)


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) .

(6)


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
speci
fication 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).

(7)


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:

p (г)

P (j)


Г А (j) f
И (г)


(8)


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:

j А (г)в(е-1)


1∕β(e-1)


(9)




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