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9 You are the manager of a firm that sells a^\"commodity^\" in a market that res

ID: 1208654 • Letter: 9

Question

9

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 + 3Q^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 70 percent chance the market price will be $200 and a 30 percent chance it will be $600. Calculate the expected market price. What output should you produce in order to maximize expected profits? What are your expected profits?

Explanation / Answer

Calculations:

a. Expected Market Price is calculated as follows:

Ep = .7* ($200) + .3 *($600)

Ep = $320

b. In order to maximize expected profits, the output will have to be calculated as follows:

Set Ep = MC

C = 2Q + 3Q2

MC = dC/dQ

MC = 2+6Q

2+6Q = 320

6Q = 320-2

6Q = 318

Q = 318/6

Q = 53 units

c. The expected profits are calculated as follows:

(Ep)Q – C(Q) = $320(53) – (2(53) + 3(53)2)

= 16960 - (106 + 3(2809))

= 16960 - (106+8427)

= 16960 - 8533

Expected Profits are = $8427