There are two firms, namely a coal mine and a pillow manufacturer, in a certain town and its 20K inhabitants all work for exactly one of the two firms. Given that the coal mine poses a higher risk to the worker than the pillow firm (assume the risk in the coal mine is p= .006 but only .005 in the pillow firm), the workers ask for compensation in terms of a higher wage when working in the mine. Workers differ by their risk preferences and the reservation prices of workers are uniformly distributed on the interval [0,10]. Demand for labor in the coal mine is described by the following inverse labor demand function w = 20-0.002E while the one of the pillow manufacturer equals w = 20.5-0.0004E (w denotes hourly wage and E is labor demand).

a) Derive the equilibrium wage differential.

b) From the information provided and part a), infer the value of a statistical life assuming workers work 2000 hours a year. (Recall that denotes the percentage of fatal accidents in a given year).

c) (Assume the value of a statistical life is $2.58 million. The government during a pandemic has to make the following difficult choice. It could either i) mandate a mask mandate or ii) a full lockdown of four weeks. It is projected that under policy i) 5,000 additional people will die while ii) causes Economic damage of $15 billion. Derive which action the government needs to take