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2. Consider the Robinson Crusoe model with the utility function given by u(x, y) = ln x + 2 ln y and the production function given by f(l) = ?l. As in the lecture notes, suppose that leisure and labor are measured in hours and there are 24 hours in a day. (a) Write down the budget constraint for Robinson Crusoe as a consumer, where denotes the price of the good, denotes the hourly wage, and \Pi denotes the profit. (b) Derive the demand function for the good and the labor supply function by solving the utility maximization problem given the budget constraint and using the MRS=relative prices formula. (c) Derive the supply function of the good and the demand function for labor by solving the profit maximization problem. (d) Find the competitive equilibrium such that the wage rate is set to . u(x, y) = ln x + 2 ln y f(l) = l p w \Pi w = 1