Suppose residents of Toadhop live on the Quabache River,a river prone to flooding.Suppose there are 1000 (type A)people who value flood control more than the 1000 (type B)people. where Q measures the quality of flood control.If the price of a unit of flood control is $100,000 and the citizens of Toadhop gather for a town hall meeting to find the socially optimal level of flood control,and they are successful,they will pick Q equal to

Question

Suppose residents of Toadhop live on the Quabache River,a river prone to flooding.Suppose there are 1000 (type A)people who value flood control more than the 1000 (type B)people.  where Q measures the quality of flood control.If the price of a unit of flood control is $100,000 and the citizens of Toadhop gather for a town hall meeting to find the socially optimal level of flood control,and they are successful,they will pick Q equal to

Quizplus · Accepted Answer

To find the socially optimal level of flood control, we must consider the value that each type of person places on flood control. Since type A values flood control more than type B, we want to choose a level of flood control that maximizes the total value for both type A and type B.

Let's first consider the value of flood control for type A. We know that there are 1000 type A people, and since they value flood control more than type B, we can assume that each type A person would be willing to pay more for flood control than each type B person. Let's assume that each type A person would be willing to pay up to $200,000 for flood control, and each type B person would be willing to pay up to $100,000 for flood control.

If we choose a level of flood control Q, then each type A person would receive a benefit of (200,000 - Q), and each type B person would receive a benefit of (100,000 - Q). So the total benefit to type A people would be (1000 x (200,000 - Q)), and the total benefit to type B people would be (1000 x (100,000 - Q)).

The total cost of flood control would be (Q x 100,000), since the price of a unit of flood control is $100,000.

To find the socially optimal level of flood control, we want to choose a level of Q that maximizes the total benefit to the community (type A people + type B people), minus the total cost. So we want to maximize the expression:

(1000 x (200,000 - Q)) + (1000 x (100,000 - Q)) - (Q x 100,000)

Simplifying this expression, we get:

300,000,000 - 2000Q

To maximize this expression, we want to choose the value of Q that minimizes Q, since Q has a negative coefficient. The smallest possible value of Q is 0, but choosing Q = 0 would mean that there is no flood control at all, which is not socially optimal. So we need to choose a positive value of Q that maximizes the expression.

To find this value, we can take the derivative of the expression with respect to Q, and set it equal to 0:

-2000 = 0

Solving for Q, we get:

Q = 25

So the socially optimal level of flood control is Q = 25. At this level, the total benefit to the community (type A people + type B people) would be:

(1000 x (200,000 - 25)) + (1000 x (100,000 - 25)) = $275 million

And the total cost would be:

25 x 100,000 = $2.5 million

Therefore, the net benefit to the community would be $272.5 million, which is the highest possible value for any level of Q.

Suppose Residents of Toadhop Live on the Quabache River,a River