Question

An amusement park has estimated the following demand equation for the average park guest

Q=16-2P

Where Q represents the number of rides per guest and P the price per ride. The total cost of providing rides to a guest is

TC=2+0.5Q

If a one-price policy is used, how much should it charge per ride if the park wishes to maximize its profit?

What is the park's profit for each guest?

If a two-part tariff policy is used, what admission fee should the park charge to maximize its profit?

What is the park's profit for each guest?

(please show work as I am confused. Thanks!!)

Answer 1

The demand equation for the average park guest Q = 16 – 2P. The total cost of providing rides to a guest is

TC=2+ 0.5Q. Inverse demand function is 2P = 16 – Q or P =8 – 0.5Q. This gives MR = 8 – Q. MC = 0.5

If a one-price policy is used, how much should it charge per ride if the park wishes to maximize its profit?

The park uses MR = MC rule

8 – Q = 0.5

Q = 7.5 rides

P = 4.25 per ride

What is the park's profit for each guest?

Profit = TR – TC = 4.25*7.5 – 2 – 0.5*7.5 = 26.125

If a two-part tariff policy is used, what admission fee should the park charge to maximize its profit?

It will charge a price which is equal to its marginal cost. Hence per ride price is $0.5. Fee for entering the park is the consumer surplus at this price. When price is 0.5, Q = 16 – 2*0.5 = 15 rides. CS = 0.5*(8 – 0.5)*15 = 56.25. Under two part tariff, fixed fee is 56.25 and per ride charge is $0.5

What is the park's profit for each guest?

It is $56.25 as there are no profits on rides.