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Math Help - Payoff Matrix

  1. #1
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    Payoff Matrix

    You inherit 10K prior to a presidential election and wish to invest it in solar energy and oil stock. An investment advisor provides you with a payoff matrix that indicates your probable 4-year gains depending on which party comes into office. How should you invest so you have the largest gains irrespective of how the election turns out?

    --------Rep DEM
    Solar 5000 1000
    Oil 4000 6000

    Invest how much in solar?

    Invest how much in oil?
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  2. #2
    Grand Panjandrum
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    Re: Payoff Matrix

    Quote Originally Posted by fcabanski View Post
    You inherit 10K prior to a presidential election and wish to invest it in solar energy and oil stock. An investment advisor provides you with a payoff matrix that indicates your probable 4-year gains depending on which party comes into office. How should you invest so you have the largest gains irrespective of how the election turns out?

    --------Rep DEM
    Solar 5000 1000
    Oil 4000 6000

    Invest how much in solar?

    Invest how much in oil?
    Well, if you invest x in oil and the rest in solar what are the gains for the two election outcomes?

    Then the solution is the value of x which gives the same return whatever the election outcome.

    CB
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  3. #3
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    Re: Payoff Matrix

    5x+4(1-x)=x+6(1-x)
    x+4=6-5x
    x=1/3
    Invest 1/3 in solar and 2/3 in oil. You now no longer care who wins.
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  4. #4
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    Re: Payoff Matrix

    I can't help but wonder why a republican winning would be better for "solar" over "oil" and vice-versa for a democrat!
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