Consider the following indirect utility functions for the states “alive” (A) and “dead” (D), where m is non-labor income and w is the wage:

Let ρ denote the person’s risk of a job-related fatality, and assume there is no other source of risk.

(a) Derive an expression for the marginal willingness to pay for a change in the fatality risk.

(b) Derive the comparative statics of the marginal willingness to pay with respect to ρ, m, and w. Interpret the signs.

(c) Suppose that you have data on hours of work h, as well as wage w and non-wage income m for a sample of people. In addition, suppose that ρ is measured in fatalities per 100,000 workers.
Describe how you would estimate the marginal willingness to pay and present a formula for the VSL based on your estimates (you can derive the labor supply function from the indirect utility function).

Transcribed Image Text:

VA V = -exp(-um) exp(a+B) -exp(-um) +