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Managerial Economics/Math

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This is an MBA-level Managerial Economics course. I am working on a homework assignment and have a couple problems that I don't really know how to get started. Here is another:

Assume that a drug manufacturer sells a major drug in Europe and the U.S. Because of legal restrictions, the drug cannot be bought in one country and sold in another. The demand curve for the drug in Europe is:

Pe = 10 - Qe

where Pe is the price (in dollars per pound) in Europe and Qe is the amount (in millions of pounds) sold there. The demand curve for the drug in the U.S. is:

Pu = 20 - 1.5Qu

where Pu is the price (in dollars per pound) in the United Statees and Qu is the amount (millions of pounds) sold there. Marginal costs are a constant $2 for all quantities sold. Assume that fixed costs are zero.

a. Calculate the optimum price, quantity, and profit for the firm if price discrimination is not possible and Pe = Pu.

b. Now assume that the firm can price discriminate in the two markets and charge separate prices in the two markets. Compare optimum prices, quantities, and resulting profits. Compare the total profits for both cases. Provide an explanation for the different pricing strategies when price discrimination is possible.

If someone could at least tell me where to get started (i.e. how to approach the problem, etc.) I would greatly appreciate it. Thanks!

  • Managerial Economics/Math -

    First b)
    Always, always, always -- maximize profits where MC=MR. In Europe, MR is 10-2Qe. As MC=2, then 2=10-2Qe. Solve for Qe. Repeat for US, cept MR=20-3Qu

    Now then a gets a little tricky as there is a kink in the demand curve. For P above 10, the combined demand is simply the US demand curve. At 10, Q=6,66667. For each $ drop below 10, total output goes up by 2.5 So, the slope of the demand line is 1/2.5 = 0.4 -- which means that if extended back to the y-axis, the line would cross the y-axis at 10+(6.6667*.4) = 12.6667. So, MR for the combined case is 12.6667-5Q. Solve for Q

  • Managerial Economics/Math -

    Ok, so for Question B, would these answers be right?

    MC = MR
    2 = 10 - 2Qe
    2Qe = 8
    Qe = 4

    Pe = 10 - Qe
    Pe = 10 - 4
    Pe = 6

    10Qe - Qe^2 - 2Qe
    8Qe - Qe^2
    8(4) - 4^2
    32 - 16

    So, Europe should produce 4 million pounds of the drug & charge $6/pound. Total profit would be $64,000,000 ($16/pound x 4 million pounds).


    MC = MR
    2 = 20 - 3Qu
    3Qu = 18
    Qu = 6

    Pu = 20 - 1.5Qu
    Pu = 20 - 1.5(6)
    Pu = 11

    20Qu - 1.5Qu^2 - 2Qu
    18Qu - 1.5Qu^2
    18(6) - 1.5(6)^2
    108 - 1.5(36)
    108 - 54

    So, the US should produce 6 million pounds of the drug & charge $11/pound. Total profit would be $324,000,000 ($54/pound x 6 million pounds).

    I just wanted to make sure I used the information you gave me correctly on this part of the question. Thanks! :)

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