Question

A local golf course’s hired-gun econometrician has determined that there are two types of golfers,frequent and infrequent. Frequent golfers’annual demand for rounds of golf is given by Qf = 24–0.3P, where P is the price of a round of golf. In contrast, infrequent golfers’ annualdemand for rounds of golf is given by Qi =10–0.1P. The marginal and average total cost of providing a round of golf is $20. If the golf course could tell a frequent golfer from an infrequent golfer, what price would it charge each type? How many times would each type golf? How much profit would the golf course generate?

Answer 1

The golf course should charge $46.67 to frequent golfers and $180 to infrequent golfers. Frequent golfers would golf approximately 7.11 times a year and infrequent golfers would golf approximately 2 times a year. The golf course would generate a profit of $2404.44.

Step-by-step explanation:

To determine the price that the golf course should charge each type of golfer, we need to set the demand equations equal to the marginal cost:

Frequent golfer: 24 - 0.3P = 20

Infrequent golfer: 10 - 0.1P = 20

Solving these equations, we find that the price for frequent golfers should be $46.67 and the price for infrequent golfers should be $180. The corresponding quantities can be calculated by substituting the prices into the demand equations. The profit can be calculated by multiplying the difference between the price and average total cost by the quantity and summing it for each type of golfer.

Therefore, the golf course should charge $46.67 to frequent golfers and $180 to infrequent golfers. Frequent golfers would golf approximately 7.11 times a year and infrequent golfers would golf approximately 2 times a year. The golf course would generate a profit of $2404.44.

Answer 2

To determine the price the golf course should charge each type of golfer, we need to set the quantity demanded equal to the quantity supplied. The golf course would not generate any profit as no golfers would play.

Step-by-step explanation:

To determine the price the golf course should charge each type of golfer, we need to find the equilibrium price for each demand equation. To find the equilibrium price, we need to set the quantity demanded equal to the quantity supplied. When Qf = Qs, we can solve for Pf, the price for frequent golfers: 24-0.3Pf = 24-0.1Pf-100 -> 0.2Pf = 76 -> Pf = 380. Therefore, the price for frequent golfers would be $380. Similarly, we can solve for Pi, the price for infrequent golfers: 10-0.1Pi = 24-0.1Pi-100 -> 0.1Pi = -66 -> Pi = -660. Since the price cannot be negative, we conclude that no infrequent golfers would play.

To find the number of times each type would golf, we substitute the equilibrium price for Pf in the quantity demanded equation: Qf = 24-0.3Pf -> Qf = 24-0.3(380) -> Qf = 24-114 -> Qf = -90. As Qf cannot be negative, we conclude that no frequent golfers would play as well.

For profit calculation, we need to find the total revenue and total cost. Total revenue is given by TR = P * Q, where P is the price and Q is the quantity. Total cost is the sum of fixed cost (FC) and variable cost (VC). Given that variable cost is given as $20, total cost (TC) = FC + VC = 20 * Q.

However, since no golfers would play, the golf course would not generate any profit.