Question

Score: 0 of 1 pt 12 of 17 (17 complete) HW Score: 61.76%, 10.5 of 17 pts Text Question 5.2 Question Help Knoebels Amusement Park in Elysburg, Pennsylvania, charges a lump-sum fee, L, to enter its Crystal Pool. It also chargesp per trip down a slide on the pool's water slides. Suppose that 400 teenagers visit the park, each of whom has a demand function of q1 6-p, and that 400 seniors also vist, each of whom has a demand function of q2 5-p. Knoebels's objective is to set L and p so as to maximize its profit given that it has no (non-sunk) cost and must charge both groups the same prices. What are the optimal Land p? The optimal L and p are and p $ L = $ (Enter numeric responses using real numbers rounded to three decimal places.)

Answer 1

If you wish to have both kind of consumers, you would set a cover charge L which is equal to the consumer surplus of lower demand group, the seniors. Then the price per trip will be P.  Find the price that will be charged per trip by finding the maximized profit function

Profit function = 800 x F + (P - MC)*(400Qstudents + 400Qseniors)

= 800 x 0.5*(5 - P)Qseniors + 400(P)*(Qstudents + Qseniors)

= 800 x 0.5*(5 - P)*(5 - P) + 400(P)*(11 - 2P)

= 400*(25 + P^2 - 10P) + 400*(11P – 2P^2)

= 10000 + 400P^2 - 4000P + 4400P – 800P^2

= 10000 – 400P^2 + 400P

Profit is maximum when

800P = 400

P* = 0.5

Hence the price per trip is P = $0.5.

Fees amount is L = 0.5*(5 – 0.5)*(5 – 0.5) or L = $10.125