Knoebels Amusement Park in Elysburg, Pennsylvania, charges a lump-sum fee, L, to enter its Crystal Pool. It also charges p per trip down a slide on the pool's water slides. Suppose that 300 teenagers visit the park, each of whom has a demand function of q 1equals6minusp, and that 450 seniors also vist, each of whom has a demand function of q 2equals3minusp. 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 L and p?
Part 2
With a two-part tariff, a firm charges a consumer a lump-sum fee (the first tariff) for the right to buy as many units of the good as the consumer wants at a specified price (the second tariff).
Part 3
When a monopoly must charge each type of consumer the same lump-sum fee, L, and the same per-unit price, p, it will either set L equal to the smaller of the two types of consumer surplus and maximize profits from the per-unit price when selling to both types of consumers or it will set L equal to the larger of two types of consumer surplus and maximize profits from the per-unit price when selling to only the high-demand type of consumer.
Part 4
The monopoly will set the lump-sum fee depending on which fee produces the greater profit.
Part 5
Specifically, if the monopoly sets the fee equal to the smaller of the two consumer surpluses and sells to both types of consumers, then its profit function will be
piequals300(6minusp)pplus450(3minusp)pplus(300plus450)L
where L equals the smaller of the consumer surpluses.
Part 6
If the monopoly sets the fee equal to the larger of the two consumer surpluses and sells to only the high-demand type of consumers, then its profit function will be
piequals300(6minusp)pplus300L
where L equals the consumer surplus of the high-demand type of consumer.
Part 7
When setting the lump-sum fee equal to the smaller of the two consumer surpluses, the optimal L and p are
Lequals$
  
enter your response here and pequals$
  
enter your response here. (Enter numeric responses using real numbers rounded to three decimal places.)