Consider that you own a construction company and you need to make a decision on

Question

Consider that you own a construction company and you need to make a decision on how many homes to build in a new residential area. It is estimates that there is a 20 percent chance of a recession, a 60 percent chance the economy will remain as it is, and a 20 percent chance there will be an economic upturn. If a recession hits, your inverse demand curve for new homes will be P = 105,000 - 4Q. If things remain as they are, your inverse demand curve will be P = 115,000 - 3Q. If economic growth occurs, your inverse demand curve will be P = 130,000 - 2Q. Your cost function in all three scenarios is C(Q) = 80,000 + 1.8Q + 0.5Q2 (MC = 1.8 + Q). If you are risk neutral, how many homes will you start?

Explanation / Answer

The expected demand curve (P) = 0.2(105,000 - 4Q) + 0.6(115,000 - 3Q) + 0.2(130,000 - 2Q)

= 21,000 - 0.8Q + 69,000 - 1.8Q + 26,000 - 0.4Q

P = 116,000 - 3Q

Total Revenue(TR) = P * Q = 116,000Q - 3Q2

Expected Marginal Revenue(MR) = 116,000 - 6Q

Equating expected MR and MC yields:

116,000 - 6Q = 1.8 + Q

=> 7Q = 115,998.2

=> Q = 115,998.2 / 7 = 16571.17

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