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Expected Market Price & Profits

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?

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.