Suppose that a car dealer has a local monopoly in selling Volvos. It pays w to V
ID: 1114284 • Letter: S
Question
Suppose that a car dealer has a local monopoly in selling Volvos. It pays w to Volvo for each car that it sells, and charges each customer p. The demand curve that the dealer faces is best described by the linear function Q=30-p, where the price is in units of thousands of dollars.
What is the profit-maximizing price for the dealer to set? At this price, how many Volvos will the dealer sell and what will the dealer's profit from selling the cars be?
Now let us think about how the situation looks from the car manufacturer's point of view. If Volvo charges w per car to its dealer, calculate how many cars the dealer will buy from Volvo. In other words, what is the demand curve facing Volvo? Suppose that it costs Volvo $5,000 to produce each car. What is the profit-maximizing choice of w? What will Volvo's profits be? What price p will the dealer set and what profit will the dealer earn at Volvo's profit-maximizing choice of wholesale price w? Now suppose Volvo operates the dealership and sells directly to its customers. What will be Volvo's profit-maximizing price p? What will Volvo's profit be
Explanation / Answer
The demand function faced by the monopolist Q = 30- P => P = Q +30
TR = PQ = Q^2 +30Q
MR = 2Q + 30
MC = w
In equilibrium MR = MC =>2Q + 30 =w => Q =(w- 30)/2
1.
Profit maximising price = 30+ Q = 30 +(w- 30)/2 = 15 + w/2
2. The number of volvos to be sold by the dealers are (w- 30)/2
3.
TC = wQ
Therefore, profit = TR - TC= Q^2 +30Q- wQ = Q (Q+30-w)
= (w-30)/2*[((w-30)/2) + 30- w]
= (w-30)/2* ((w- 30+60-2w)/2
= (w-30)/2* (30-2w)/2
= (w-30)/2 * (15-w)
This is the amount of profit.
4. The volvo manufacturer is the firm operating in the competitive market.
AR would be its demand curve.
= TR/ Q =(Q^2 +30Q)/Q = Q + 30= AR is the demand curve of the volvo.
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