If immigrants and native workers
are indeed perfect substitutes, then over time the increased profits earned by
firms and its future profitability will attract capital flows into the
marketplace, as current firms will expand while new firms take advantage of the
lower wage by entering the market. This increase in the capital stock then
leads to an increase in the demand for labour which will thus shift the labour
demand curve to the right, which would diminish the “negative impacts of the
initial labour supply shock” (Borjas, 2010, p.169). However, a question which
should be explored is how much will the labour “demand curve shift to the right
in the long run?” (ibid, p.169). To help explain and illustrate the ‘extent’,
the Cobb-Douglas production function can be used: q = AK?L1-?, A (constant),
? (parameter between 0 and 1). This Cobb-Douglas production function can be
seen as accurate in relation to a country such as the United States which is
susceptible to waves of immigrants, as it possesses the property of constant
returns to scale, with this: if labour and capital is doubled, then output is
doubled. In a competitive labour market, the factor demand concept states that
the price of capital is “given by the value of the marginal product of capital”
(MPK) (ibid, p.170) plus, the value of the marginal product of labour (MPL) gives
the level of wage. For this example, the price of output will equate to $1. Using
mathematical manipulation, the value of both the MPK and MPL equations are
given by: r = $1 x ?AK?-1L1-?
and w = $1 x (1-?)AK?L-?. By manipulating these equations
algebraically we get:
r = ?A(K/L)?-1 (equation 4) and w = (1-?)A(K/L)? (equation 5). As stated before an increase in
the amount of workers in the workforce is the short-run effect of immigration. From the
equation 4 and 5, they show as the number of workers increase, the rate of
return to capital ‘r’ is subsequently raised, which lowers the wage rate ‘w’.
Immigration in the long run would also lead to an increase in the size of
capital stock ‘K’. When assessing equation 5, if the capital-labour ratio (K/L)
is constant in the long run, then the wage rate must also be constant in the
long run. Therefore,
when immigration lowers the wage, in the long run the capital stock will
increase as employers make use of the cheaper workforce, however after this,
the capital stock adjusts completely to set the economy to its original point
with the same rate of return to capital and wage rate.
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