Question

The management at MooseWoods Park concluded that they will install flush toilets if the total surplus is greater than $50 in relation to the number of flush toilets at the equilibrium and the cost per campsite per night. Installing flush toilets will involve an increase in the cost per campsite per night. Researchers have calculated the demand and supply curves for flush toilets at this park and discovered that they are both perfectly straight lines. At $35 per campsite per night, no one will want flush toilets. At $0 per campsite per night, campers will demand seven flush toilets. Managers are willing to supply no flush toilets at the current campsite cost of $5 per night, but are willing to supply eight flush toilets at $25 per campsite per night. Please use the supply, demand and total surplus information to answer the three questions.

a What is the number of flush toilets desired at the equilibrium point?
b What is the total surplus?
c Will the managers install the number of flush toilets determined in the first question?nonot enough information to determineyes

Answer 1

a. The number of flush toilets desired at the equilibrium point is 5.5.

b. The total surplus is $164.

c. Yes, the managers will install the number of flush toilets determined in the first question.

Step-by-step explanation:

a. Number of flush toilets desired at the equilibrium point

The equilibrium point is where the supply and demand curves intersect. To find this point, we need to set the supply and demand equations equal to each other:

Supply: Q = 8 - 25P

Demand: Q = 7 - 15P

Solving for Q, we get:

8 - 25P = 7 - 15P

10P = 1

P = 0.10

Now that we know the equilibrium price, we can plug it back into either the supply or demand equation to find the equilibrium quantity. Let's use the demand equation:

Q = 7 - 15(0.10)

Q = 5.5

Therefore, the number of flush toilets desired at the equilibrium point is 5.5.

b. Total surplus

The total surplus is the sum of the consumer surplus and the producer surplus. The consumer surplus is the difference between the maximum price that consumers are willing to pay and the equilibrium price. The producer surplus is the difference between the equilibrium price and the minimum price that producers are willing to accept.

To calculate the consumer surplus, we need to find the maximum price that consumers are willing to pay. At $35 per campsite per night, no one will want flush toilets, so the maximum price is $35. The consumer surplus is then:

Consumer surplus = (35 - 0.10) * 5.5

Consumer surplus = 190.50

To calculate the producer surplus, we need to find the minimum price that producers are willing to accept. At $5 per campsite per night, managers are willing to supply no flush toilets, so the minimum price is $5. The producer surplus is then:

Producer surplus = (0.10 - 5) * 5.5

Producer surplus = -26.50

The total surplus is the sum of the consumer surplus and the producer surplus:

Total surplus = 190.50 - 26.50

Total surplus = 164

Therefore, the total surplus is $164.

c. Will the managers install the number of flush toilets determined in the first question?

Yes, the managers will install the number of flush toilets determined in the first question. This is because the total surplus is greater than $50. As stated in the question, the managers will only install flush toilets if the total surplus is greater than $50. In this case, the total surplus is $164, which is well above the threshold of $50.

Therefore, the managers will install 5.5 flush toilets at MooseWoods Park.