Consider a firm with production function F(L)=max(0, 13L-L^2) This firm is a price taker at output market and sells its output at $2 per unit. The firm is the only employer at considered city. Suppose that there are two groups of workers that are looking for a job in this city with the following labour supply functions: L¹(w)=2w and L²(w)=w, where w is the per hour nominal wage rate. Assume that the firm owner can easily differentiate between the two groups.

a) Suppose that the firm can discriminate between the groups but non-linear pricing is not allowed. Find the profit- maximizing wage rates and explain the result.

b) Suppose that the firm owner decided to modify the payment scheme. Under new scheme every worker is offered a contract. This contract specifies a fixed payment that this worker should pay for the possibility to get a job and a per hour wage rate that the worker will get. Each worker either accepts the contract or rejects the contract. Assuming that the firm owner can offer different contracts to the native workers and immigrants find the profit maximizing contracts.

c) Suppose that the new payment scheme described in (b) should be approved by the regulator that cares about social welfare measured by the total surplus. Should the regulator approve the new scheme? (no graphs or calculations needed)

d) Reconsider part (b) assuming that the firm owner is not allowed to offer different contracts to the two groups.