Q2. Suppose a consumer seeks to maximize the utility function U(x,y)=(x+2)(y+1), where x and y represent the quantities of the two goods consumed. The prices of the two goods and the consumer's income are px,py, and I. (a) (5) Write out the consumer's budget constraint and the Lagrangian function for the problem. (b) (10) State the first-order conditions for utility maximization. Find the consumer's demand functions, x and y. (c) (10) Show the bordered Hessian matrix, H for this problem. What does the second order condition require for this problem? Show if it is satisfied. (d) (10 Extra points) Find the consumer's indirect utility function. Q2. Suppose a consumer seeks to maximize the utility function U(x,y)=(x+2)(y+1), where x and y represent the quantities of the two goods consumed. The prices of the two goods and the consumer's income are px,py, and I. (a) (5) Write out the consumer's budget constraint and the Lagrangian function for the problem. (b) (10) State the first-order conditions for utility maximization. Find the consumer's demand functions, x and y. (c) (10) Show the bordered Hessian matrix, H for this problem. What does the second order condition require for this problem? Show if it is satisfied. (d) (10 Extra points) Find the consumer's indirect utility function