Robinson's technology for producing coconuts (x) is represented by x = l^2/3, where l is labor in hours per day. His preferences for coconuts and labor are given by the utility function

u(l, x) = x - l/2 . Assume Robinson is the only consumer of coconuts, and the owner of the only firm which produces coconuts. Suppose the price of coconuts is set at 1.

a. Calculate the Pareto efficient allocation.

b. Derive the competitive equilibrium of this economy. Find Robinson's consumption of coconuts, his labor supply, the market wage rate, and the firm's profits.