Question

Using Supply and Demand to Analyze Markets — End of Chapter Problem

The Ministry of Tourism in the Republic of Palau estimates demand and supply for its scuba diving tours is given by ??=6,000−20?, where ?Q is the number of divers served each month and P is the price of a two-tank dive. The supply of scuba diving tours is given by ??=30?−2,000QS=30. The equilbrium price is $160, and the equilibrium quantity is 2,800 customers diving each year. The Ministry of Tourism also knows that if the price is $300 or greater, no tourist will want to dive, and if the price is $66.67 or less, no dive companies will want to offer services. Find consumer and producer surplus.

a. Consumer surplus = $

b. Producer surplus = $

Suppose the demand for scuba diving in the Republic of Palau increases, and the new equilibrium price is $180 and the new equilibrium quantity is 3,400. Now, if the price is $350 or greater, no tourists will want to dive. Find the new values for consumer and producer surplus.

c. New consumer surplus = $

d. New producer surplus = $

e. When demand for scuba diving tours increased, how did it affect the consumers and producers?

1) Consumers are better off, but producers are worse off because now they have to work additional hours and offer more dives to meet demand.

2) Producers are better off, but consumers are worse off because they now have to pay a higher price.

3) Both consumers and producers are worse off, because deadweight loss is not included in the example.

4) Both consumers and producers are better off because each received increases in their corresponding surpluses)

Answer 1

a. $196,000
(CS = area of triangle = (1/2)*base*height = (1/2)*(Qe)*(Pmax-Pe) = (1/2)*(2800)*(300 - 160) = 1400*140 = 196,000)

b. $130,662
(PS = area of triangle = (1/2)*base*height = (1/2)*(Qe)*(Pe-Pmin) = (1/2)*(2800)*(160 - 66.67) = 1400*(93.33) = 130,662)

c. 289,000
(CS = area of triangle = (1/2)*base*height = (1/2)*(Qe)*(Pmax-Pe) = (1/2)*(3400)*(350 - 180) = 1700*170 = 289,000)

d. 192,661
(PS = area of triangle = (1/2)*base*height = (1/2)*(Qe)*(Pe-Pmin) = (1/2)*(3400)*(180 - 66.67) = 1700*(113.33) = 192,661)

e. 4) Both consumers and producers are better off because each received increases in their corresponding surpluses
(As CS and PS has increased so they are both better off.)