[30 marks]. Kevin is a risk-neutral person who owns a construction firm with production function Q = 2L1/2, where L is the number of workers employed. The price of output is set at p = 1. He can only get workers from an employment agency called Belkoni Ltd. Belkoni charges w > 0 per worker. It either sends exactly the number of workers requested by Kevin with probability, , or sends no workers with probability (1 ), where 0 < < 1. Kevin has to place a request for workers and pay the total cost before the workers are sent to his firm and if Belkoni fails to send the workers, it does not compensate Kevin (e.g., it is prohibitively costly to legally get Belkoni to honor its obligation). Kevin can buy insurance against this risky event but he can only buy full insurance. For each dollar of insurance coverage, the premium is dollars, where 0 < < 1. So if the total cost of workers requested by Kevin is $X, he pays an insurance premium of $X and is paid $X if Belkoni fails to send the workers.

(a) Assuming that Kevin buys insurance, derive his optimal worker request, L*.

(b) Determine the effect of an increase in on Kevin's optimal worker request, L*.

(c) In part (a), you found his optimal worker request, L*, assuming that he bought insurance. But will he buy insurance at all? Determine whether this assumption is valid.