Q2: A consumer receives utility from consuming good X and good Y as given by the following utility function: U(x,y) = 101n(x) + 2y where x denotes quantity of good X and y denotes quantity of good Y. The price of good X is Px rupees per kg. The price of good Y is P, rupees per kg. The consumer's total budget for these two goods is denoted by I rupees per time period. (a) Write the consumer's utility maximization problem. Define the Lagrangian function for this utility maximization problem. Write the first order necessary conditions. (b) Suppose Pr = 25 rupees per kg, P, = 25 rupee per kg, and I = 200 rupees. Compute the optimal choice of good X and good Y that maximizes the consumer's utility function subject to the budget constraint. (c) Suppose Pr = 25 rupees per kg, Py = 25 rupee per kg, and I = 100 rupees. Compute the optimal choice of good X and good Y that maximizes the consumer's utility function subject to the budget constraint. (d) Find the Marshallian demand function for each good. (e) Find the indirect utility function. (f) For part (b) and part (c), show the solution graphically. Note: First draw the budget line. Next, compute the utility level (U*) at the optimal choice of x' and y'; then compute different values of values x and y for that utility level (U*), and finally draw the indifference curve. Make a proper graph with actual values of intercepts and quantities in this problem. (g) Check the second order condition to ensure that utility is maximized