Problem
Suppose there are 100 workers in the labor market who differ in their innate productivity. Worker I has a value of marginal product equal to $1 per hour; worker 2 has a value of marginal product equal to $2, and so on. One firm decides to pay its workers a time rate of $35 per hour; the other firm decides to pay its workers a piece rate. How will the workers sort themselves across firms? Suppose that a decrease in demand for the firm's output cuts the price of the output by half. How do the workers now sort themselves between the piece-rate and the time-rate firm?