The Snow City Ski Resort caters to both out-of-town skiers and local skiers. The
ID: 1222463 • Letter: T
Question
The Snow City Ski Resort caters to both out-of-town skiers and local skiers. The demand for ski tickets for each market segment is independent of the other market segments. The marginal cost of servicing a skier of either type is $12. Suppose the demand curves for the two market segments are: Out of town: Qo = 60 - P Local: Ql = 60 - 2P
a. If the resort charges one price to all skiers, what is the profit-maximizing price? Calculate how many lift tickets will be sold to each group. What is the total profit?
Please show all work.
Explanation / Answer
First found the total demand curve by adding the two demand curve, we will get
Q = 120 - 3P
Now by manupulating we will get,
P = 40 - Q / 3
Now to found profit maximizing price and quantity, first we have to set marginal revenue = marginal cost
Marginal revenue is found by differentiating total revenue.
Total revenue = P * Q
TR = 40Q - Q2/ 3
MR = 40 - 2Q / 3
Now MC is given as $12. So,
40 - 2Q / 3 = 12
2Q / 3 = 28
Q = 14 * 3
Quantity = 42.
Putting this into demand curve we will get ,
Q = 120 - 3P
3P = 78
Price = $26.
Tickets sold for out of town skiers is = 60 - 26 = 34
Tickets sold for local skiers is = 60 - 52 = 8.
Total Profit = Total Revenue - Total Cost
Total Profit = (P * Q) - (Marginal Cost * Q)
Total Profit = ($26 * 42) - ($12 * 42)
Total Profit = $588.
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