The 20 residents of the village of Towneburg are considering hosting a fireworks show next summer.The total cost of the show is estimated to be $1,000 + $10 per unit.Each resident's demand for fireworks is identical: P = 50 - 2 * units as shown below:
Suppose 10 fireworks units have been set off.What is the marginal cost of providing one more unit at the fireworks show?

Question

The 20 residents of the village of Towneburg are considering hosting a fireworks show next summer.The total cost of the show is estimated to be $1,000 + $10 per unit.Each resident's demand for fireworks is identical: P = 50 - 2 * units as shown below: 
Suppose 10 fireworks units have been set off.What is the marginal cost of providing one more unit at the fireworks show?

Quizplus · Accepted Answer

The total cost function for the fireworks show is: 
TC = 1,000 + 10 * units

If 10 fireworks units have already been set off, then the current total cost is: 
TC = 1,000 + 10 * 10 = 1,100

To find the marginal cost of providing one more unit, we need to find the derivative of the total cost function with respect to units: 
MC = dTC/dunits = 10

Therefore, the marginal cost of providing one more unit at the fireworks show is $10.

As for the best choice(s), it depends on what the residents are trying to maximize or minimize. If they want to maximize their total consumer surplus (the difference between what they are willing to pay and what they actually pay), they should set the price equal to each individual's willingness to pay, which is P = 50 - 2 * units. Setting this equal to the marginal cost of $10, we can solve for the optimal number of units: 
50 - 2 * units = 10 
2 * units = 40 
units = 20

Therefore, the best choice would be to set off 20 fireworks units at a price of $10 per unit. However, if the residents are trying to maximize their total revenue or their profit, the best choice would be different.

The 20 Residents of the Village of Towneburg Are Considering