Consider the following competitive labour market. There are many identical firms that can hire workers. Each firm produces the same output using a constant returns to scale technology and the price of output is 1. The market determines a wage level for labour. Let denote the number of units of output (equal to revenue) that a worker can produce. There is asymmetric information. Worker productivity levels are privately known, and are uniformly distributed between 5 and 35. Let () denote the reservation wage of an employee with productivity . More productive workers are more demanding, in the following sense. If < 15, then () = /2 , but if 15 then () = 3/5.

QUESTION 1) IN DETAIL, Derive the competitive equilibrium of this labour market.

QUESTION 2) Suppose that, instead of a continuum of types, the labour force is comprised of equal amounts of only four types: 5, 10, 20, and 35. Explain in detail, how would this change the results?