AskSia

Plus

Part IV. Defensive expenditures concept. Professor Jim bought a house in Califor...

Apr 21, 2024

Part IV. Defensive expenditures concept. Professor Jim bought a house in California in 2015. At the time, he thought there was a

0.15 \%

chance of a fire reaching his neighborhood per year, which would put his house at risk. He took no special precautions at that time. In 2023, new information appeared (when his insurance provider cancelled his policy) and Jim then believed the risk of a fire reaching his neighborhood was

0.75 \%

per year. In response, Jim spent

\$ 6,000

clearing vegetation around his home to create defensible space. Assume that the only way that Jim is affected by fires in his neighborhood is through risk to his home. 10. The city of Oakland can do "goat grazing," in which herds of goats eat vegetation in nearby open spaces so as to reduce the risk of fire in his neighborhood. Suppose that the goat grazing reduces the risk of a fire in Jim's neighborhood by

0.2 \%

in a year. Use the information provided above to calculate an estimate of Jim's willingness to pay for goat grazing using the logic of defensive expenditures. (1 point) 11. This calculation makes key assumptions about Jim's risk of a fire affecting his home after he received new information, as per our discussion in class. Use that to explain why the estimate you came up with above could be a significant underestimate of Jim's willingness to pay for risk mitigation of

0.2 \%

. ( 2 points) 12. Suppose that Jim's daughters liked to climb the trees at his house, and they were no longer able to climb the trees after the vegetation clearing. How would that impact your interpretation of the calculation you provided above? (1 point for multiple choice, 1 point for explanation) This consideration means that my prior answer would be an underestimate of Jim's willingness to pay for goat grazing This consideration means that my prior answer would be an overestimate of Jim's willingness to pay for goat grazing This consideration would have no affect on my prior answer would be an underestimate of Jim's willingness to pay for goat grazing

Solution by Steps

step 1

Calculate the amount Jim is willing to pay to reduce the risk by

0.2\%

. We use the defensive expenditure of

6000 to clear vegetation, which reduced the risk by

0.75\%$

step 2

To find the cost to reduce the risk by

0.2\%

, we set up a proportion:

\frac{6000}{0.75} = \frac{x}{0.2}

, where

x

is the amount Jim is willing to pay for goat grazing

step 3

Solve for

x

x = \frac{6000 \times 0.2}{0.75}

step 4

Using the asksia-ll calculator result:

(6000 \times 0.0075) / 0.002 = 22500

. We adjust the calculation to match the proportion:

x = \frac{6000 \times 0.002}{0.0075}

step 5

Calculate the value of

x

x = \frac{6000 \times 0.002}{0.0075} = 1600

Answer

Jim's willingness to pay for goat grazing is $1600.

Key Concept

Defensive Expenditures and Proportional Risk Reduction

Explanation

Jim's willingness to pay for goat grazing is estimated by scaling his previous defensive expenditure proportionally to the reduction in risk percentage.

Solution by Steps

step 1

Consider the assumptions made in the calculation of Jim's willingness to pay for goat grazing

step 2

The calculation assumes that the risk reduction from goat grazing is directly proportional to the defensive expenditure

step 3

If the actual risk reduction is greater than the assumed

0.2\%

, then the willingness to pay would be higher than the calculated $1600

Answer

The estimate of

1600 could be a significant underestimate if the actual risk reduction is greater than

0.2\%$.

Key Concept

Assumptions in Risk Reduction Estimation

Explanation

The calculation could underestimate Jim's willingness to pay if the risk reduction from goat grazing is more effective than the assumed value.

Solution by Steps

step 1

Consider the non-monetary value of the trees for Jim's daughters' enjoyment

step 2

Recognize that the loss of tree-climbing activity is a cost not accounted for in the initial calculation

step 3

Understand that this additional cost would increase Jim's total willingness to pay for risk mitigation that does not involve clearing vegetation

Answer

This consideration means that my prior answer would be an underestimate of Jim's willingness to pay for goat grazing.

Key Concept

Non-Monetary Costs and Willingness to Pay

Explanation

The loss of recreational value for Jim's daughters is a non-monetary cost that, when considered, increases the estimate of Jim's willingness to pay for alternative risk mitigation like goat grazing.