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.

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