2. Consider the following utility function defined over two goods: 1 and 2: U(x1, x2) = x/3x/3. The prices of goods 1 and 2 are p and p2 respectively. (a) Does the law of diminishing marginal utility hold for good 2? Find the MRS of good 1 for good 2. [15] (b) Write the equation representing the budget constraint, assuming the consumer's income is M. [3] (c) Using the method of Lagrange, maximize the utility subject to the budget constraint. What are the demand functions for x and x2. Assuming p = 2, p2 = 1 and M = 100, find the quantities of x1 and x2 that maximizes utility. [25] (d) Check the SOC for the Lagrangian method. [12]