Consider a standard Ricardian model with two countries, France and Brazil. Each country can produce two goods: coffee and wine. All consumers in both countries have the following utility function: U(Dc, Dw) = log Dc + 2 log Dw (1) where Dc and Dw denote quantities demanded of coffee and wine respectively. Labour is the only factor of production and all workers are identical. In France, each unit of coffee requires 2 worker and each unit of wine requires 10 workers. In Brazil, each unit of coffee requires 4 workers and each unit of wine requires 40 workers. France has 12,000 workers and Brazil has 19,200 workers, and no workers are allowed to migrate to the other country.
(a) Suppose that initially, countries cannot trade with each other. Find the autarky equilibrium prices and quantities produced and consumed in each country.