You are the manager of a firm that sells a “commodity” in a market that resemble

Question

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?

Explanation / Answer

a) expected market price = 0.6*100+0.4*200 = 140 ($) (ANSWER) b) C = Q + 2Q^2 MC = dC/dQ = 1 + 4Q P = 140 ($) MR = P*1 = 140 For max profit, MR = MC So, 140 = 1 + 4Q Q = 139/4 = 34.75 = (say) 35 . (ANSWER) Expected profits = R - C = 35*140 - (35+2*35^2)= (4900 - 2485) = 2415 ($) (ANSWER)

Related Questions

Navigate

• Browse (All)
• Browse Y
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.