Consider two firms, Firm A and B. Suppose a job only has two attributes: wages (W) and safety (S). Assume that Firm A earns a predetermined sales revenue of $500 when it employs one worker and it costs the firm $50 per unit of safety. Therefore, the firm's total cost can be expressed as TC = W + 50S. Firm B's predetermined sales revenue is $300 when employing one worker and the firm's cost of providing one unit of safety is $20. Firm B's total cost can be expressed as TC=W+20S. For simplicity, assume that each firm hires only one worker.

a) (1.5 points) Draw the isoprofit schedule for both Firm A and B when both firms earn zero profits. Make sure to draw the two isoprofit schedules on the same graph (place W on the vertical axis and S on the horizontal axis). Graphically illustrate the employer's offer curve.

b) (3 points) Suppose there are three workers, David, Kate, and John with different preferences over wages and safety. Assume that their utility functions can be expressed as follows:

David: U(W,S)=WS

Kate: U(W,S) = min{W,20S}

John: U(W,S) = W+ 30S

For each worker, do the following:

1) Solve for the optimal (W*, S*).

2) Explain which firm the worker would prefer to work at.

3) Graphically illustrate how the optimum is found.

c) (1 point) Suppose the government implements a new policy such that all firms must provide a minimum of 6 units of safety to hire a worker. Graphically illustrate how the isoprofit schedules of the two firms and the employer's offer curve change.

d) (1.5 points) Assume that David, Kate, and John have the same utility function as in part b). Given the new policy described in part c), which firm will they work for? Also, solve for the optimal (W*,S*) for each individual.