ELEMENTOS PRINCIPALES DE LOS SECADORES VERTICALES

After having established the autarky equilibrium in which neither retailer undertakes FDI we now turn to the situation in which one of the retailers decides to enter the foreign market via FDI. We assume that the retail firm from country i enters the retail market in country j. While the retailer still acts as a monopolist on his home market he has to compete with the incumbent over market shares in the foreign country.

Consumers

Inverse demand in the home country is still given bypi =bi−xiiwherexii is the demand

facing retailer i on market i and bi is still consumer willingness to pay. Consumers in

4_{See Eckel (2009) for the interpretation of such costs. Note, however, that we include these costs}

the foreign market may now choose between two retail outlets to do their purchases: one operated by the incumbent retailerj, the other operated by the entrant retailer i.Hence, inverse demand facing a countryi-based retailer on the foreign marketj is represented by

pij =bj −xij −θxjj, 0< θ <1, (2.8)

where xij is the demand facing retailer i on market j, and xjj denoting demand facing

retailer j on his home market j. Parameter θ represents the degree of competition on the retail market under consideration. The closer θ to unity the fiercer the competition between the retailers, and vice versa.

Similarly, inverse demand facing the incumbent retailer in country j is given by

pjj =bj −xjj−θxij, 0< θ <1. (2.9)

Manufacturing

Again, only the supplier selling the final goods priced at average cost is listed on the retailers’ shelves. The manufacturing firms in country i now produce the products sold by the multinational retailer on both markets. Hence, the supplier price becomes

si =si(xii+xij) , and s0i <0. (2.10)

Accordingly, in country j suppliers sell their goods to the local retailer j at price

sj =sj(xjj), and s0j <0. (2.11)

The fact that the suppliers in countryj still only sell to the incumbent retail company is intuitive: as the retailer is aware of the scale economies realized by the suppliers he has no incentive to sell goods from the host-country manufacturer. Reducing the quantity sourced from his home-country supplier would increase the supplier price; in addition it would lead to an increase in competition on the foreign market which is not desirable

from the point of view of the entrant retailer.5 _{Note at this point that if x}

ij > 0 then si(xii+xij)< sA(xA) and xii> xA.

Retailing

The profits of the i-based retail MNE are given by

ΠR_i = [pii−si−γi]xii+ [pij −si−γi−t]xij −F, (2.12)

where the first term describes the profits generated by sales in the home country. Price pii includes again a mark-up over the marginal procurement and provision cost (si+γi),

and the second term represents the profits generated on the foreign market where price pij includes a mark-up, this time over the marginal procurement and provision cost

(si+γi+t). Note that t are trade costs accruing to each unit of the goods the retailer

orders from his home-country manufacturer. Parameter F represents the conventional fixed cost of setting up an affiliate in the foreign country.

The situation for the incumbent in market j changes as he, too, has to take the new competitor on his home market into account. His profits are given by

ΠR_j = [pjj−sj−γj]xjj (2.13)

Technically, the profits in (2.13) do not differ from the autarky profits (equation (2.4)), quantitatively, however, they are not the same as sj(xjj)6=sA(xA).

On the home market, retailer i still acts as a monopolist and maximizes his profits in (2.12) with respect to pii which yields the optimal sales quantity of

xii=

1

2[bi−si−γi]. (2.14)

However, the two retailers now located in market j compete over market shares in

5_{A similar argument applies to the manufacturer in countryiwho still only sells to the home-market}

Cournot-Nash fashion.6 _{Their profit-maximizing quantities are determined as best re-} sponse functions given the quantity of the rival and given the respective supplier prices:

xij = 1 2[bj−si−γi−t−θxjj], (2.15) xjj = 1 2[bj−sj −γj−θxij]. (2.16)

In equilibrium retail profits then amount to

ΠR_i = (xii) 2 + (xij) 2 −F, (2.17) ΠR_j = (xjj) 2 . (2.18)

Given that the fixed cost of setting up business in the foreign countryF is sufficiently small the multinational retailer’s profits clearly exceed the autarky profits depicted in equation (2.4) once xij >0: as explained in subsection 2.2.2, ifxij >0 thensA(xA)> si(xii+xij)

and xii > xA so that the first term in (2.17) already exceeds the autarky profits. As the

second term is the square of the equilibrium quantity retailer isells on the foreign market (2.15) this increases the profits further. The incumbent’s profits ΠR

j are lower than in

autarky as he now holds a smaller market share, and has to pay a higher supplier price.