Assignment
1. Suppose a factory manager is deciding whether to implement a slower production process in which q = 1.6E or a faster production process in which q = 2E, where q is units of output and E is the level of employment in each production process. The slower production process is safer than the faster one. Given the equilibrium compensating differential between safe and risky jobs in the labor market, this manager knows that he will have to pay an additional $4 per hour to his workers if he implements the faster, less safe production process. The factory manager also knows that his output sells at an equilibrium price of $5 per unit. Which production process should this manger implement? Justify your answer.
2. Suppose all workers have the same preferences represented by
U = √w - x
where U is utility, w is the wage rate, and x is whether or not the firm's air contains toxic pollutants. There are only two types of companies: one that provides a clean work environment with no toxic chemicals in the air (x = 0), and one that provides an unsafe work environment with toxic chemicals in the air (x = 1).
(a) If the clean job pays $16 per hour in equilibrium wages, what must be the wage rate paid by companies that have toxic air? What is the compensating differential between these jobs?
(b) Assume all workers at both types of companies spend 1,645 hours working each year. Given the hourly compensating differential found in part (a), calculate the annual difference in salary paid to a worker at the unclean job relative to the clean job.
(c) Suppose breathing clean air leads to zero probability of death, while breathing toxic air for 1,645 hours per year (a full year of work) increases the probability of death to 0.0015. Calculate the statistical value of life implied by these risk probabilies and the workers' utility function above.
3. Consider the issue of incentive pay.
(a) What is the principle-agent problem between employers and employees in a labor market?
(b) Suppose you are consulting for a CFO who is deciding whether to implement piece-rate pay or an annual salary with equity compensation in order to solve the principle-agent problem.
(i) Provide 2 key characteristics of the firm and/or production process under which piecerate pay would be the better choice. Briefly explain your answer.
(ii) Provide 2 key characteristics of the firm and/or production process under which annual pay with equity compensation would be the better choice. Briefly explain your answer.
4. Suppose labor supply and labor demand are described by the following equations, where E represents employee-hours and w represents the hourly wage.
Labor Supply: Es = 50w - 100
Labor Demand: Ed = -50w + 500
(a) Calculate the equilibrium quantity of employment and wage rate in this labor market.
(b) Suppose the government decides to mandate that all employers provide health insurance coverage to their workers. Workers' value of insurance coverage scaled to an hourly rate is $2 per employee-hour, and the cost of insurance coverage scaled to an hourly rate is $4 per employee-hour. With the mandated benefit, the labor supply and labor demand curves are now represented by the following equations:
Labor Supply: Es = 50(w + 2) - 100
Labor Demand: Ed = -50(w + 4) + 500
Calculate the total cost (wage plus cost of benefit) of an employee-hour to firms, the total compensation (wage plus value of benefit) received by workers per employee-hour, and the equilibrium quantity of employee-hours with the mandated benefit in place.
(c) Calculate the deadweight loss created by the mandated benefit.
(d) What size subsidy per employee-hour would the government need to provide firms to prevent this mandated health insurance benefit from causing a decrease in equilibrium employment relative to the equilibrium quantity from part (a)?