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    Expected Market Price & Profits

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    You are the manager of a firm that sells a commodity in a market that resembles perfect competition, and your cost function is C(Q)=Q+2Q^2.Unfortunately, due to production lags, you must make your output decision prior to knowing for certain the price that will prevail in the market. You believe that there is a 60 percent chance the market price will be $100. and a 40 percent chance it will be $200.

    a. Calculate the expected market price.
    b. What output should you produce in order to maximize expected profits?
    c. What are your expected profits?

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    Solution Preview

    a. Calculate the expected market price.

    Expected Market price = sum of [price x probability]

    E(p) = sum of [$100 x 60% + $200 x 40%]

    = $60 + $80

    = $140 ...

    Solution Summary

    The solution gives fully-displayed calculations for finding the expected market price and profits as well as determining the output necessary to maximize those profits.