Consider two countries, Home and Foreign, each of which produces two goods, butter (B) and guns (G), using labour and capital. The production possibility frontier at Home is given by B2+G2= 1,while that at Foreign is2B2 +1G2= 1.The preferences of consumers in both 2vp countries are identical and captured by the following utility function:U=BG.LetB=p pG be the relative price of butter.
(a) Compute the equilibrium levels of B and G consumed and produced in the Home country under autarky. What is the corresponding value ofp?
(b) Compute the equilibrium levels of B and G consumed and produced in the Foreign country under autarky. What is the corresponding value ofp?
(c) Based on your answers to parts (a) and (b), if the two countries open up, what will be the pattern of trade?
(d) Derive the export-supply curve of B for the B-exportingcountry as a function of p.
(e) Derive the import-demand curve of B for the B-importingcountry as a function of p.
(f) What is the equilibriumpunder free trade? How muchBdoes Home import/export under free trade?