Uncertain Productivity Growth and the Choice between FDI and Export

Uncertain Productivity Growth

2 THEORETICAL FRAMEWORK

demand function of variety i is then derived as

- = p^-t" γξt
^it ∕' " ∙ Pt

(3)

with η = i----,

1

n nt       ∖ ^1-η

Pt = IX ' I

jt

where Pt denotes the foreign country’s price index and η the elasticity substitution. The investor
insinuates that the expenditure share γξ spent on Q and the price index P do not change over
time. Therefore, equation (3) represents the investor’s perceived demand function and the inverse
demand for the relevant variety Xi can be written as

1

—

Pt = ZXt ^η

(4)

η-1       1

with Z = P—(γξ) n,

where the considered variety’s subscript i is omitted, as the investor intends to serve the foreign
market only with this distinctive brand. Furthermore, there is no strategic interaction among
firms. Depending on the country specific elasticity of substitution, the investor possesses a varying
degree of market power. The mark-up of price over marginal costs

- = Z ( η

w ∖η — 1

(5)

with w as the equilibrium wage rate, results from the investor’s profit maximization problem as
a monopolist. Defining ν as the inverse of the mark-up with

η — 1

ν =---

^η

the inverse demand function can be reformulated as

p = ZX^ν-1.                                     (6)

In a country, where ν is close to 0, the elasticity of demand is close to 1 which represents a
scenario where the investor has a high monopoly power, since the substitutability between the
varieties of good Qt is very low (ρ → 0). In contrast, for a country with ν close to 1, the elasticity