N1

In a two-good economy, let x and y denote quantities of the first and second goods, respectively. Let px> 0 and py> 0 denote prices per unit of the first and second goods, respectively. Let I > 0 be a consumer's income. Let the consumer's preferences be represented by the utility function u(x,y) = 2x + 2y. (a) Carefully write down the utility maximization problem. (b) Find the Marshallian demand functions. (c) Show that the demand functions you found in (b) are indeed the solutions of the utility maximization problem. (d) Derive the indirect utility function of the consumer. (e) Derive the expenditure function of the consumer. Hint: Use the duality between the utility maximization and expenditure minimization problems.