Similar to the case of unrestricted choices a higher wag gap rises the cost of technology and implies lower levels of technology in production and, consequently, a lower productivity.
However, the downgrade is somewhat dampened by the factor εK¯T < κ as the lower technology level in the constrained case requires relatively less high-skilled labor. In a similar vein, lower barriers imply more sophisticated production techniques that require relatively more high-skilled workers.
In the case of heterogeneous firms, high-productivity firms’ use of technology in production is more efficient than low-productivity firms’ whereas the former’s optimal technology choice is constrained in contrast to the latter’s. In particular, this case emerges when low-productivity firms manage to influence politics to protect their vested interests. Resulting e.g. from a reform in regulations, lower barriers to technology adoption enableh-firms to use more sophisticated production techniques and increase their productivity while having no impact onl-firms when wages are exogenous. As an immediate result, the productivity gap rises proportionally to κh −εK¯T. That is, akin to ∂T∂φ, increases in the productivity gap abate if T approaches high-productivity firms’ optimal technology level.
On the other hand, h-firms have to employ relatively more high-skilled labor due to the complementarity of technology and skills. They will suffer more in terms of productivity from a skill premium increase. The relative loss is again proportional to εK¯T −κl and, thus, smaller than in the unconstrained case as restricted h-firms employ relatively less high-skilled labor than they would in optimum.
the latter has various implications for wages and welfare which are explored subsequently in detail.
The representative household has a CES-utility function
u=
Z M 0
Yiβdi
!β1
, 0< β <1,
and supplies low- and high-skilled labor (Ls, Hs) inelastically. There exists a continuum of final goods Yi, with i ∈[0, M], that are produced by a homogeneous mass M of firms that are all of technology type κ. The elasticity of substitution between final goods is
1
1−β >1. The above taste for variety preferences imply the demand function Yi =
pi PI
−1−β1 A
PI (2.14)
where pi is the price of final good i, A are aggregate expenditures, and PI ≡
RM 0 p−
β 1−β
i di
!−1−ββ
is the price index of final goods. Since PI is defined as the numeraire (PI ≡ 1) the implied demand function for each firm, Ap−
1 1−β
i , in Section 2.3.2 becomes identical to (2.14). In combination with optimal firm choices in Section 2.3.3and market clearing, equilibrium is defined as:
Definition 2.1 Equilibrium in an economy with homogeneous firms is given by a set of prices {p, wH, wL}, quantities {Y, H, L}, and level of technology N such that with free entry of firms consumers choose consumption of each final good optimally, firms choose output, level of technology and labor inputs optimally, and labor and product markets clear.
Note that intermediate inputs do not show up in the definition of equilibrium. However, they are produced within each firm with high- and low-skilled labor that are aggregated on the firm-level to firm-specific high- and low-skilled labor demands. Furthermore, when technology choices are constrained and thus given by the barrier, the set of equations defining the equilibrium is reduced by the optimal firm decision on technology.
2.4.1 Wages Levels, Skill Premium, and Firm numbers
There is free entry of firms and each firm has to incur f units of low-skilled labor to set up production. Adding these market entry cost to production low-skilled labor demand results in a firm’s total low-skilled labor demand: L+f. The free entry condition,
pY −C(Y)−wLf = 0 ⇐⇒ (1−β)pY =wLf, (2.15) fixes the wage level given a firm’s revenue. The latter is derived by multiplying the optimal price (2.8) by the optimal output (2.7) and using the expression of average unit costs ¯KN:
pY =β1−ββ AN1−βκβ w
β β−1
L w¯µ(β−1)N β (1−εK¯Nσ)σ(β−1)β . (2.16) Plugging this expression into the free entry condition (2.15) and considering total labor income (wLLs+wHHs =A) results in the wage level
wL=βNκw¯−Tµ(1−εK¯Nσ)−1σ (1−β)(Ls+ ¯wHs) f
!1−ββ
(2.17) which is a function of labor endowments, parameters, the barrier to technology adoption, and the skill premium.
The wage gap and, implicitly, the high-skilled wage are derived from setting relative labor supply equal to relative labor demand, using production labor demands ((2.11) and (2.12)) and the zero profit condition (2.15) in a firm’s revenue where pY =Apβ−1β :
HS
LS = M H
M(L+f) = 1
¯ w
εK¯N
ln ¯w
β −εK¯N
. (2.18)
If the barrier does not constrain the technology choice, the above skill premium equa-tion collapses to HLSS = w1¯ ln ¯wκ
β −κ exhibiting the properties presented in the first chapter.
However, whenever firms’ optimal technology choice is restricted by the barrier, the im-plied wage gap in (2.18) depends on the barrier which has important repercussions in the following.
Plugging the free entry condition (2.15) into the equality of household income and total
expenditures (wLLs+wHHs =M pY) results in the number of firms M = 1−β
f (Ls+ ¯wHs).
Clearly, firm numbers rise in the absolute supply of labor and decrease in fixed costs.
They depend on the barrier to technology adoption when the latter determines the skill premium, i.e. when firms are restricted in their technology choice. Note further that a higherM increases variety and, as a consequence, welfare of the representative household.
2.4.2 Determinants of Technology Restriction
The relative endowment of high-skilled labor and the scope for technology in production determine the skill premium and, simultaneously, a firm’s technology level. Whether the latter is chosen optimally or restricted by the barrier to technology adoption is analyzed in the following proposition.
Proposition 2.4 If and only if it holds that HS
LS >exp −2κµT 1−κσ
! 1−κσ
2 β
µ
T −1 +κσ (2.19)
firms’ technology choices are constrained by the barrier to technology adoption. In partic-ular, the latter precludes the use of better technologies if it is rather restrictive, high-skilled labor is relatively abundant, firms are endowed with a rather great scope for technology in production, or the elasticity of substitution between final goods is relatively small.
The proof is given in Appendix 2.7.5. A more restrictive barrier to technology adoption is, ceteris paribus, more likely to constrain a firm’s technology choice14. A smaller range of feasible production techniques decreases firms’ chances to adopt the most efficient technologies. On the other hand, a country’s labor endowments have an indirect impact on the fact whether the barrier is binding or not. A greater relative endowment of high-skilled labor implies ceteris paribus a lower skill premium which, in turn, decreases costs
14AsT ≤µ, a firm cannot choose a ‘not defined’ technology level ofN > µ. See the first chapter for an analysis ofN ≤µin the unconstrained case.
of technology adoption. Firms would choose a higher optimal level of technology in production and would be more prone to become restricted by the barrier. In the same line, a higher scope for technology in production increases the benefits of more sophisticated production techniques. The optimally chosen technology level rises and, consequently, being restricted in their technology choice becomes more likely for firms. A different mechanism applies to the elasticity of substitution between final products. A less elastic demand (i.e. a smaller β) implies greater operating profits what induces more firms to enter the market. As fixed costs are paid in units of low-skilled labor, relative skill demand decreases and the skill premium shrinks. This reduces the cost of technology adoption as in the case of a greater relative skill endowment and raises the level of the optimally chosen technology.
2.4.3 Impact of Lower Barriers to Technology Adoption on Firms and Welfare
Beside vested interests of groups, inefficient institutions and bureaucratic regulations are often the underlying causes of barriers to technology adoption (Parente and Prescott, 2002). Their removal requires dedicated policy reforms which are usually tackled step-by-step. My model follows this process by analyzing the marginal impact of a reduction in barriers on a country’s economic variables.
Proposition 2.5 The skill premium, a firm’s productivity, the number of firms, total labor income, and a country’s welfare increase when the barrier is lowered (i.e. if T increases).
The proof is given in Appendix 2.7.5. If firms are not restricted in their choice of tech-nology, the barrier has no impact on any firm decision or aggregated variable. However, if the barrier constrains effectively firms’ decisions, it has severe consequences. Instead of choosing their optimal level of technology in production,N∗, firms’ production techniques are restricted toT < N∗. When the barrier is lowered, i.e. through a policy change, firms adopt higher and more efficient levels of technology that boost their productivities. How-ever, the implementation of more sophisticated production techniques is relatively more
high-skilled labor intensive. As a result, relative high-skill demand increases and, as labor supply is fixed, necessarily the skill premium. Nevertheless, the total impact on firm-level productivity is positive since gains from more advanced technologies outweigh the labor costs increase that results from a combination of higher skill intensity and a widening wage gap. Furthermore, the rise in productivity increases firms’ revenues and makes market entry more profitable. As a consequence, more firms enter the market and set up produc-tion. However, perfect competition on labor markets imply that higher productivities are passed on to workers via higher wages resulting in greater total labor income. An inherent property of models having a representative consumer with CES utility is that total labor income directly translates into the representative household’s utility or, in other words, into welfare. As a result, a gradual improve in a country’s regulatory framework that implies lower barriers to technology adoption increases overall welfare.