a = capital's cost share in the production of A
    (1-a) = labor's cost share in the production of A
        b = capital's cost share in the production of B
    (1-b) = labor's cost share in the production of B

    Assume:
    1. A is capital-intensive compared to B => a > b; (1-a) < (1-b)
    2. A and B are competitive industries which use L and K to produce output. As a result, output-price changes depend on input-price changes as follows:
        %chPA = a %chPK + (1-a) %chPL
        %chPB = b %chPK + (1-b) %chPL

    Situation: The production of A rises, and the production of B falls. (In class this is the result of the home country opening up to trade, but the reason doesn't really matter; the results are the same.)

    Choose from the list -- %chPA, %chPB, %chPK and %chPL -- to fill in the blanks below, based on the specified resource and cost conditions of the two industries.

    1. Labor and capital are drawn out of industry B and into industry A. Based on the differing resource requirements of the two industries, compare the input-market effects:

        ______ > ______

    2. As noted under assumption 2 above, input-price changes cause output-price changes. Based on the differing cost shares of the two industries, compare the output-market effects:

        ______ > ______

    3. Note that output-price changes are a weighted average of input-price changes. Use this last piece of information to help you rank all four price changes:

        ______ > ______ > ______ > ______

    Is there an unambiguous winner and/or loser from the shift in the nation's production? If so who, and how can you tell? If not, why are you unable to tell?

Given:
        a = capital's cost share in the production of A
    (1-a) = labor's cost share in the production of A
        b = capital's cost share in the production of B
    (1-b) = labor's cost share in the production of B

    (1) %chPA = a %chPK + (1-a) %chPL
    (2) %chPB = b %chPK + (1-b) %chPL

        A is capital-intensive compared to B => a > b

Step 1: Compute %chPK as a function of %chPA and %chPB
                    1
    (1) => %chPL = --- [%chPA - a %chPK]
                   1-a

                    1
    (2) => %chPL = --- [%chPB - b %chPK]
                   1-b

     1                       1
    --- [%chPA - a %chPK] = --- [%chPB - b %chPK]
    1-a                     1-b

     1           1           a           b
    --- %chPA - --- %chPB = --- %chPK - --- %chPK
    1-a         1-b         1-a         1-b

                              a - b
                          = ---------- %chPK
                            (1-a)(1-b)

            1-b        1-a
    %chPK = ---%chPA - ---%chPB
            a-b        a-b

Step 2: Determine when %chPK exceeds %chPA.
            1-b        1-a
    %chPK = ---%chPA - ---%chPB > %chPA
            a-b        a-b
        => (1-b) %chPA - (1-a) %chPB > (a-b) %chPA (since a > b)
        => (1-b) %chPA - (a-b) %chPA > (1-a) %chPB
        => (1-a) %chPA > (1-a) %chPB
        => %chPA > %chPB

    Relevance to trade: When a capital-abundant country moves to free trade, PA will rise relative to PB. PK will therefor rise relative to both PA and PB. Symmetrically, PL will fall relative to both PA and PB. In other words, the real income of capital rises and the real income of labor falls.