As the manager of Smith Construction, you need to make a decision on the number
ID: 1209475 • Letter: A
Question
As the manager of Smith Construction, you need to make a decision on the number of homes to build in a new residential area where you are the only builder. Unfortunately, you must build the homes before you learn how strong demand is for homes in this large neighborhood. There is a 60 percent chance of low demand and a 40 percent chance of high demand. The corresponding (inverse) demand functions for these two scenarios are P = 300,000 – 400Q and P = 500,000 – 275Q, respectively. Your cost function is C(Q) = 140,000 + 240,000Q.
How many new homes should you build, and what profits can you expect?
Number of homes you should build:
Number of homes you should build:
Profits you can expect:Explanation / Answer
Low demand curve: P = 300,000 – 400Q (probability 60%)
High demand curve: P = 500,000 – 275Q (probability 40%)
Total demand curve:
0.6(300,000 – 400Q) + 0.4(500,000 – 275Q) = 180,000-240Q+200,000-110Q = 380,000-350Q
Derive MR from the demand equation = 380,000-700Q
Total cost: 140,000+240,000Q
Derive MC from the total cost equation = 240,000
Being a monopolist, set MR=MC to find profit-maximizing output and prices.
That is, 380,000-700Q = 240,000
Upon solving, Q* = 200; P* = $310,000
Profits = PQ-TC = (310,000)(200) – (140,000+240,000(200)) = $13860000
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