# Homework: Hedonic Theory Assume that there is a baseline risk of death on the job of q0 percent annually. Firms can invest to reduce this risk, so that actual risk at a job is q(i)=q0 – i*ß. Here i is amount invested into reducing the risk a given employee faces. Of course mortality is bounded below by 0, so the maximum productive amount that can be invested in reducing mortality risk is iMax = q0/ß . All firms produce the same good c and this good has a price equal to 1. All workers are equally productive and produce an output of H of the consumption good. Question 1 Derive an expression of wages w(q) in this economy that has to be satisfied by wage – risk combinations that competitive firms would be willing to offer to workers in equilibrium. Question 2 Consider now individuals that have preferences over consumption and risk of death given by U c s ( , ), where 0 s ? q ? q is “job safety” relative to base-line risk 0 q . Write down the maximization problem that workers face and illustrate the choice problem in a graph in a two-dimensional graph with c and s on the axes. Assume that the parameter values are such that the solution is in the interior (ie 0 s q ? ) Question 3 Say consumers preferences are such that a both c and s are normal goods. Assume furthermore that individuals differ in the human capital H (but still everybody has 0 s q ? ). Consider two individuals of whom one has a higher level of H than the other. Who will earn higher wages and who will face greater risk? Will the two individuals differ in their Value of a Statistical Life (VSL)? Question 4 Use your answer to question 3 to explain why it might be difficult to empirically measure the VSL using the relation between wages and risk. SHORT, PRECISE, CLEAR, AND CORRECT ANSWERS RECEIVE FULL POINTS.

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