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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) = 2Q + 3Q2.

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) = 2Q + 3Q2. 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 70 percent chance the market price will be \$200 and a 30 percent chance it will be \$600.

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

a) C(Q) = 2Q + 3Q2
Expected market price = (0.7×200) + (0.3×600)
= 140 + 180
= \$320
b) Expected profit (π) = 320Q – 2Q – 3Q2
= 320 – 2 – 6Q = 0
Or, 6Q = 318
Q* = 53
c) Expected profit =...

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