Following Brander and Spencer 1983 and 1985, consider two countries denoted by i = X; Y , each of which has one firm producing a homogeneous product only for export, to be sold in the international market. Both firms compete a la Cournot in international market. The inverse demand function in the international market is P = 15 - 0:5Q. In addition, assume that preinnovation unit cost of each rm is c = 4. Let ri denote the amount of R&D sponsored by the government in country i.
Assume that when the government i undertakes R&D at level ri, the unit production cost for the firm producing in country i is reduced to c-ri, i = X; Y . Finally, the total cost to government i of engaging in R&D at level ri, is TC(ri) = (ri)sq/2 .
(a) Identify countriesbest response function.
(b) What is the Nash equilibrium R&D level for each country? Discuss your results.