Col. Tom Barker is about
to open his newest amusement park,

Elvis World. Elvis World features
a number of exciting attractions: you

can ride the rapids in the
Blue Suede Chutes, climb the Jailhouse Rock

and eat dinner in the
Heartburn Hotel. Col. Tom argues that
Elvis World

will attract 1,000 people
per day, and each person will take

*x*= 50*−*50*p*
rides, where

*p*is the price of a ride. Everyone who visits Elvis World is
pretty much the same and
negative rides are not allowed. The marginal

cost of a ride is
essentially zero.

*(a)*What is each person's inverse demand function for rides?

*(b)*If Col. Tom sets the price to maximize profit, how many rides will be

taken per day by a typical
visitor?

*(c)*What will the price of a ride be?

*(d)*What will Col. Tom's profits be per person?

*(e)*What is the Pareto efficient price of a ride?

*(f)*If Col. Tom charged the Pareto efficient price for a ride, how many

rides would be purchased?

*(g)*How much consumers' surplus would be generated at this price and

quantity?

*(h)*If Col. Tom decided to use a two-part tariff, he would set an admission

a. The inverse demand function puts P, price, on the left side of the equals sign. Thus, P = 1 - x/50

b. Find the profit function as total revenue minus total cost then find profit max at the point where marginal revenue equals marginal cost. TR = (1-x/50)x; 1x-x^2/50; 1-2X/50 = 0; 50-2X=0; X = 25

C. 1 - X/50 = 1-25/50 = 1-.50 OR .50.

d. Each person will ride 25 rides at 50 cents so profit will be 12.5.

e. The Pareto efficient price will be where no one can be made better off. This happens at a price of Zero.

f. He would sell 50 rides per customer.

g. take one-half base times height. (.50 x 50)/2 =12.5

h. Colonel Tom would have to capture all of the consumers surplus. So he would charge $12.5 to enter and charge $0 per ride.

If you find errors, please comment.

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