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 ofBandGconsumed and produced in the Home country under autarky. What is the corresponding value ofp?
(b) Compute the equilibrium levels ofBandGconsumed 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 ofBfor theB-exportingcountry as a function ofp.
(e) Derive the import-demand curve ofBfor theB-importingcountry as a function ofp.
(f) What is the equilibriumpunder free trade? How muchBdoes Home import/export under free trade?
Hint :To findp,you need to solve a non-linear equation inp.You may not be able to do this using pencil and paper. You can use MS-Excel to do this. For example, suppose you have an equation that looks like this:ap3+bp2+cp+d= 0,wherea, b, canddare constants. Then pick a value forp.Create separate columns forap3, bp2, cpandd,and another column that has their sum. Then vary the value forpuntil the sum is equal to zero. The correspondingpvalue is a solution. Keep in mind that non-linear equations typically have more than one solution.