Hardware H, and Software, S, are perfect substitutes. Consumers combine a unit of hardware with a unit of software to obtain a laptop, so that consumers have a Leontief utility function of the form U(H, S) = min{H, S}. Hardware and Software are produced both in England and in Portugal using labor as the only production factor. England is endowed with 800 units of labor, while Portugal is endowed with 400 units of labor.
Labor productivity is described in the following matrix:
Hardware: England 1/10, Portugal 1/40
Software: England 1/30, Portugal 1/20
(Namely, one unit of labor in England produces one tenth of Hardware, etc.)
(a) Does either of the two countries have an absolute competitive advantage? Does England have a comparative advantage? In which sector? What about Portugal?
(b) How many laptops are produced in England under autarky? How many laptops are produced in Portugal under autarky? How many units of labor are employed in the production of Hardware in the two countries? What are the relative autarky prices?
(c) Suppose free trade is now allowed between England and Portugal. Is either of the two countries fully specializing? What is the number of Hardware and Software units produced in Portugal and in England? What is the free trade equilibrium relative price?