Question

The city of Ventura would like to build a seawall to protect the city from the threat of tsunamis. Each additional inches of height further protects the city and the 100 residents are each willing to pay $5 per inch of seawall height, regardless of how many inches are provided. The cost of building a wall that is inches high is given by c(i)= 7i^2. What is the Pareto Optimal height for the seawall?

Answer 1

The Pareto Optimal height for the seawall is 35.71 inch

Step-by-step explanation:

According to the given data we have the following:

marginal benefit=$5 per person and there are 100 resident s

Therefore, total marginal benefit=500

Pareto optimal height for the sea wall is at a point where the total marginal benefit of an inch of building equals to marginal cost

The cost of building a wall that is inches high is given by c(i)= 7i^2, therefore MC= MC=14i

Therefore in order to calculate the Pareto Optimal height for the seawall we would have to calculate the following formula:

optimal height i=total marginal benefit/MC

optimal height i=500/14

optimal height i=35.71 inch

The Pareto Optimal height for the seawall is 35.71 inch