Consider two countries Home and Foreign each of which produces two goods butter

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= 1while 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?(1.5 points)(b) Compute the equilibrium levels ofBandGconsumed and produced in the Foreign country
under autarky. What is the corresponding value ofp?(1.5 points)
(c) Based on your answers to parts (a) and (b) if the two countries open up what will be the
pattern of trade? (1 point)(d) Derive the export-supply curve ofBfor theB-exportingcountry as a function ofp.(2
points)
(e) Derive the import-demand curve ofBfor theB-importingcountry as a function ofp.(2
points)(f) What is the equilibriumpunder free trade? How muchBdoes Home import/export under
free trade? (2 points)
Hint :To findpyou 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= 0wherea b canddare constants. Then
pick a value forp.Create separate columns forap3 bp2 cpanddand 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.