Quantitative Problems

How might the hedonic theory be reconciled with the following statement?
The really exhausting and repulsive labours, instead of being better paid than others, are almost invariably paid the worst of all, because they are performed by those who have no choice.
John Stuart Mill (1848)
Let $w denote the wage and z the level of an undesirable job attribute. Consider a competitive industry in which each firm's profits (per worker) are $Π = zw.

(a) Sketch the isoprofit schedules of each firm in a figure that has $w on the vertical axis, and z on the horizontal one. Which one is relevant in a competitive market?

Dave's utility is given by . (N.b., exp [x] is just a more elegant way of writing .)

(b) Sketch Dave's indifference curves in the same graph, and sketch his optimal choice of $w* and $z*.

(c) Determine his optimal choice (algebraically).

Now suppose that Rambo decides to work in the industry. His utility is ], where δ > ρ.

(d) Show that Rambo picks a less desirable job (his choice of z is higher) but is rewarded for his troubles (his wage is higher). (Hint: Given ], it can be shown the slope of an indifference curve with respect to z (the MRS) is simply δw.)
The facts are as follows. A total of L = 20,000 homogenous workers are employed in a given industry. Every year, 50 of them die because of injuries sustained on the job. If the government imposes some regulation X it can save 5 lives per year. Each worker places of value of $200 on the passage of regulation X. What is the VSL? What of the range of costs, $C of regulation X for which implementation is worthwhile?
Recently, and with much fanfare, several states passed no smoking bans in bars and restaurants to protect employees from secondhand smoke. Discuss the merits, or otherwise, of this policy.
According to a recent New York Times report ( December 10, 2006), a researcher found that when he wore a bike helmet, motorists passed by 3.35 inches closer than when his head was bare; wearing a helmet increased his risk of an accident! What factors might account for this?
Under what circumstances might workplace safety regulations improve overall well-being?

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