Consider the economy of production with Robinson as both consumer and producer. As a producer, Crusoe, Inc has a production function with labor L as input and consumption good y as output given by y = 4L. Assume the price of the consumer good is 1 and the labor wage is w.

4.a) Solve the company's problem and specify labor demand L* (w), output y* (w) and show that the company's profit is given by (w) = 1 w .