Respuesta :
Answer:
New houses build =200
Profit =$13,860,000
Explanation:
In this particular question there are 2 scenarios for demand function,
i.e. (a.) 60 percent chance of low demand, [tex]P_{60} = 300,000-400Q[/tex]
(b.) 40 percent chance of high demand, [tex]P_{40} = 500,000-275Q[/tex]
∴ Expected demand function = 60%×(300000-400Q) + 40%×(500000-275Q)
= 380,000-350Q
[tex]P_{D}[/tex] =380000-350Q
Revenue = (380000 - 350Q)×Q = 380000Q - 350[tex]Q^{2}[/tex]
Here, the no. of new homes build will depend on maximizing profit
∵ Profit = Revenue - Cost
π = (380000 - 350Q)×Q - (140000+240000Q)
π = 380000Q - 350[tex]Q^{2}[/tex] - (140000+240000Q)
In order to maximize profit , we will
[tex]\frac{\delta P_{\pi}}{\delta Q}[/tex] = 0
[tex]\frac{\delta P_{\pi}}{\delta Q}[/tex] = 380000-350*2*Q-240000
∴ 380000-350×2×(Q-240000) =0
Q=200
So number of houses that they should build =200
π = 380000Q - 350[tex]Q^{2}[/tex] - (140000+240000Q)
π = 380000-(350×[tex]200^{2}[/tex]) - (140000+(240000*200))
π =$13,860,000
New houses to be build =200
Profit =$13,860,000
