4. (3 points) Assume that Firm A earns a predetermined sales revenue of $100 when it employs one worker. The firm can provide the worker varying degrees of safety at a cost of $10 per unit of safety. Therefore, the firm's total cost can be expressed as TC = W + 10S where W is the wage of the worker and S is the amount of safety provided. For simplicity, assume that Firm A hires only one worker.

a) (1 point) Draw the isoprofit schedule for this firm, for level of profits =0, and profits =50. Make sure to denote which isoprofit schedule corresponds to which profit level. Is the isoprofit schedule for profits = 0 below or above that for profits = 50?

b) (1 point) Suppose there is another firm, Firm B, with a predetermined level of sales revenue equal to 75 when using one worker. The total cost for this firm is TC = W + 5S. Assume that both firms earn zero profits and hire only one worker. Graph the employer's offer curve.

c) (1 point) Suppose David is a worker and has preferences over wages and safety such that his utility function is U(W,S)=WS. Would David be matched with Firm A or Firm B? Also, solve for the optimal (W* ,S* ).