2 A Robinson Crusoe economy Robinson Crusoe is shipwrecked on an island, where coconuts are the only available food. Crusoe enjoys both leisure and eating coconuts, and his utility function over the two activities is u (C, L) = C2/5 13/5, where C is the number of coconuts Crusoe eats and L is the fraction of the day he spends at leisure. Crusoe can work to gather coconuts, which cuts into leisure time. His foraging technology has production function f(H) = 8H1/2, where H = 1 - L is the fraction of the day Crusoe spends working rather than loafing. Crusoe begins every day endowed with L = 1 day of leisure and C = 0 coconuts. Coconuts are perishable and cannot be stored for future consumption. Crusoe decides to incorporate a firm to manage the gathering of coconuts. Crusoe is the sole shareholder of the firm. Each day Crusoe-the-marketmaker wakes up and posts fixed prices (in shells, the island currency) for coconuts and labor, which Agent Crusoe and Crusoe, Inc. must respect. Agent Crusoe sells labor and buys coconuts with his wage income and his share dividends. Crusoe, Inc. buys labor and produces coconuts using Crusoe's foraging technology. Suppose Crusoe-the-marketmaker sets prices so that the markets for labor and coconuts clear. If the wage for a day of labor is normalized to 1 shell, what will be the price of coconuts, how many coconuts are produced, and how much of Crusoe's day does he spend working