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2. (20 marks) Consider a consumer planning their consumption over two years. They have income m1 during the rst year and H12 during the second year. In each year, there are two goods to consume. In year 1, the prices are p1 and Q1, and the corresponding quantities are an and 321. In year 2, we similarly have p2, qz and x2, y2. (NOTE that g refers to price as does p.) The utility function is: u : (11 ln(x1) + B1 ann) + (12 ln(x2) + B1 111022). Utility is to be maximized subject to the two budget constraints for each year. Solve this problem and nd the multipliers X1 and kg for the two constraints. Examine how they depend on money income and other parameters of the problem. How much of year2 income will the consumer require if they give up dml of year1 income? In other words, what is the rate of retum needed to induce the consumer to save a little? You would expect borrowing and lending institutions to arise in an economy populated by such consumers. What governs who will borrow and who will lend