(54 pts) Toms utility function is given by U(x1; x2) = 0:25 ln x1 + 0:75 ln x2, where x1 and x2 are the two goods he consumes. The price of good x1 is p1. The price of good x2 is p2. His income is m. (a) Write his maximization problem, calculate his MRS between the two goods and nd his demand functions for the two goods. (15 pts) (b) Determine whether the two goods are normal or inferior. What fraction of his income does he spend on each good? (10 pts) (c) Suppose that initially p1 = $1, p2 = $1 and m = $100. Then, p2 suddenly increases to p 0 2 = $2. Calculate his optimal consumption bundle before and after the price change. Write his budget constraint before and after the price change. What is the total eect of the price change on his demand for x2? (14 pts) (d) Calculate the substitution eect and the income eect of the price change on his demand for x2. (10 pts) (e) How would the demand functions for the two goods found in part (a) change if Toms utility function were given by V (x1; x2) = 4x 0:25 1 x 0:75 2 ? Explain. (5 pts)