Suppose you run a shop that produces sweatshirts. You are considering switching from paying your worker a weekly wage of $500 (which you chosen in order to keep the worker indifferent between their payoff from working for you and instead choosing their next best alternative) to a system in which you pay a smaller weekly wage plus a piece rate per shirt. Suppose that: I) the worker has a cost of effort function: cle) = je? – 2e + 10
II) the worker's utility function is U = w - cle) where w is the worker's total wages.
III) total shirt production is given by 6e per week.
IV) You can sell each shirt for $10 - your only cost is labor costs.
(a) 6 points How much effort is the employee putting in under the current system (a weekly wage of $500)?
(b) 6 points What are your profits under the current system?
(c) 6 points Consider the alternative of paying the worker a weekly wage of $400 and a piece rate of $2 per shirt produced. Again, how much effort will the employee put in and what are your profits?
(d) 8 points If you continue paying the workers a piece rate of $2 per shirt, but change the fixed component, what is the lowest that the fixed component of the wage can be in order to keep the worker indifferent between this and the workers outside option? What is the highest fixed weekly wage the firm is willing to offer while still paying $2 piece rate?