that suppose Professor Knight opens a widget retail store-which, luckily for him
ID: 1115661 • Letter: T
Question
that suppose Professor Knight opens a widget retail store-which, luckily for him, is the only widget store in town. He purchases widgets from a local wholesaler for $20 each, and he has no other costs, as he sells widgets out of the trunk of his mother's car. The demand for widgets on the retail market is characterized by the following inverse demand curve: P-100-2Q where Q is the quantity of widgets demanded from Professor Knight's retail "shoppe," and P is the per- widget price. Part (): Identify the profit-maximizing quantity of widgets that Professor Knight will sell, q', and per- widget price that he will charge, p. Part Identify the maximum amount of profit that Professor Knight can make from his widget "business." Part (ii):Suppose that Professor Knight can buy his widgets from a wholesaler in North Carolina for $10 per-widget. Assuming that he chooses to resell these cheaper widgets, identify the profit-maximizing quantity of widgets that Professor Knight will sel.q40, and per-widget price that he will charge Part (iv; Assuming that he chooses to resell these cheaper widgets, identify the maximum amount cof profit that Professor Knight can make from his widget "business. Part (v!: If Professor Knight had to pay his sketchy friend, Karlye, a flat fee to transport the cheaper widgets from North Carolina to Gainesville, what is the maximum fee that he would be willing to pay her? Explain your answerExplanation / Answer
Demand: 100-2Q
MR = dPQ/dQ = 100-4Q
MC = 20
A)
Set MR = MC
100-4Q = 20
Q* = 20
P* = 100-2(20) = $60
B)
Profit = (P-MC)Q = (60-20)20 = $800
C)
New condition: MR = MC'
100-4Q = 10
Q' = 22.5
P' = 100-2(22.5) = $55
D)
Profit = (P-MC)Q = (55-30)22.5 = $562.5
E)
Maximum amount that can be offered = (60-55) = $5
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