## Interconnected communications networks and home market effects

Again note that K is the number of designs developed by northern skilled labor while n is the number of firms operating in the North. Now consider the cost structure of the network service provision. One of the main assumptions is that the provision of a network involves only a fixed cost: F units of skilled labor. Throughout this chapter I will assume that F is exogenously given and simply use it as an index of communications technology. Because of average-cost pricing, communications costs per skilled labor are simply

g(H) = F__H , g(H *) = F___H*. (8.8)

This implies that communications costs per skilled labor fall as the total quantity of skilled labor increases, allowing more users to share the common cost of providing the network, F. The joint assumptions on factor supply (8.7) and communications costs (8.8) are summarized in the total number of designs within each country, given by5

K = H [1 – g(H )] = γH* – F, K* = H*[1 – g(H*)] = H* – F. (8.9)

These equations imply that the skilled labor-abundant country (the North) can develop new products relatively more efficiently [(K/H) > (K */H *)]. Through better cost sharing, each user of the northern network can provide more resources for product development activities. In contrast to firms, households are immobile, so that their incomes are geographically fixed even though firms are not. Since factor income for skilled labor is equal to payments for designs, the national income of each country can be obtained as follows (see (8.1)):

I = L + rK = L + r(γH * – F ), I* = L* + rK* = δL + r (H* – F). (8.10)

Now consider the location of firms. The product market equilibrium requires that supply equals demand for each variety produced in the North: x = c + tc*. Substituting (8.3), the southern counterpart to (8.4), and (8.10) into this condition yields the following equilibrium condition for a northern product and its southern counterpart:

x = α(L + rK)_________n + τn* + τα(L* + rK*)___________τn + n* , (8.11)

x* = τα (L + rK)__________n + τn* + α (L* + rK*)__________τn + n* , (8.12)

where τ ≡ t1-σ (τ ≤ 1) measures the freedom of trade. The total number of varieties, N, is fixed by the number of designs (K + K*). Thus by using (8.9),

N = n + n* = K + K* = (γ + 1)H* – 2F. (8.13)

In equilibrium, the world labor market must be cleared. A constant fraction of world income must be paid for the designs. Hence, at the world level, this implies that

α (I + I*)/σ = r (K + K*). (8.14)

Substituting national income (8.10) into (8.14) yields the equilibrium payment for a design:6

r = α _____σ – α (1 + δ )L____________(γ + 1)H* – 2F . (8.15)

The skilled labor income differential between countries is

r(K – K*) = α _____σ – α (1 + δ )L(γ – 1)______________γ + 1 – (2F/H*) . (8.16)

Assume that this skilled labor income differential is substantial and that northern income is larger than southern income (I > I *). Using (8.10), this implies that r(K – K *) > (δ – 1)L. It follows that a difference in skilled labor income must exceed that in unskilled labor income: the North’s advantage in skilled labor abundance outweighs the South’s advantage in unskilled labor abundance. If we use (8.10) and (8.15), the proportion of firms located in the North becomes

n__N = 1 – τ (I *________________I)/(1 – τ)[1 + (I */I)] . (8.17)

When the national income of the North is greater than that of the South (i.e., (I*/I) < 1), the above condition implies that (n/N) > (1/2) holds, which means that the location with the highest national income will house the majority of firms. While intra-industry trade occurs, the North becomes a net exporter of high-tech products. This result is the standard “home market effects” analyzed by Helpman and Krugman (1985, ch. 10).