i need hlp with the folllowing question

1. (54 pts) Tom's utility function is given by U(21, 12) = 0.25 Inc, + 0.75 Inc2, where r] and zz are the two goods he consumes. The price of good r is p1. The price of good T2 is p2. His income is m. (a) Write his maximization problem, calculate his MRS between the two goods and find 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, = $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 effect of the price change on his demand for c2? (14 pts) (d) Calculate the substitution effect and the income effect of the price change on his demand for 12. (10 pts) (e) How would the demand functions for the two goods found in part (a) change if Tom's utility function were given by V(11, 12) = 401 12 259.757 Explain. (5 pts)