Suppose there are 100 workers in the economy, indexed by

Suppose there are 100 workers in the economy, indexed by i 1, 2, ..., 100. preferences given by Ui w avr Worker i has where w is the wage, x is the proportion of the firm's air that is composed of toxic pollutants, and ai is a preference parameter. Suppose that preferences are heterogeneous, such that (11 1, 100. Suppose there are only two types of jobs in the economy: clean jobs (x O) a2 , (1100 and dirty jobs (x 1). Let wo be the wage paid by the clean job and WI be the wage paid for doing the dirty job. (A) (10 points) What is the reservation price for each worker i? Make a graph of the labor supply curve in the market for dirty jobs, with employment on the horizontal axis and the wage differential (WI wo) on the vertical axis. (B) (10 points) Suppose that there are only 30 available jobs in the dirty sector. Assume that labor demand is fully inelastic. If the clean job pays $10 per hour, then what is the equilib- rium compensating wage differential? Who is the "marginal worker" here? Show that the 'marginal worker" gets the same utility irrespective of whether he accepts a clean or a dirty job. (C) (10 points) Make a graph that depicts the workers' total welfare surplus from accepting dirty jobs. How large is it, and how do you interpret it in words?