ABSTRACT
Note that P measures the minimum cost to obtain one unit of D: welfare gains are measured by a reduction in P. The Home consumers’ derived demand for a Home service is
c = td = t(tp)–σPσ – 1µλL, (10.3)
where µ is the share of spending devoted to differentiated services. Similarly, the derived demand for a Foreign service from Home consumers is
c*´ = t´*d*j = t´(t´p*)–σPσ – 1µλL. (10.4)
A producer of a differentiated service has to commit α units of labor as a fixed cost and has constant marginal input β. With the total number of services available to consumers being very large, each producer chooses its constant mark-up price as
p = p* = (σβ )/(σ – 1). (10.5)
It is important to note that, as the degree of differentiation rises (i.e., the smaller σ is), producers are able to charge higher prices. Free entry ensures that the equilibrium output per service, x, is constant, common across countries, and independent of the level of delivery costs:
x = [α (σ – 1)]/β. (10.6)
Before turning to the trading equilibrium, we must draw attention to the autarky equilibrium (i.e., the equilibrium when t´ is prohibitively high due to the lack of communications networks). In autarky, the number of differentiated services in each country is given by
nA = (µλL)/ασ , n*A = [µ(1 – λ)L]/ασ , (10.7)
where A refers to the value in autarky equilibrium. Autarky equilibrium levels of price indices become
PA = [(nA)t1 – σp1 – σ ]1/(1 – σ ),
P*A = [(n*A)t1 – σp*1 – σ ]1/(1 – σ ).
