3. (36 points) Consider the utility function u(21,*2) = @1 27 . Let the prices of good 1 and good 2 be p, and p2, and let the consumer's income be m. a. State the consumer's maximization problem and use this problem to derive his demand functions for the two goods. (8 points) b. Is good 1 ordinary or Giffen? Is good 1 normal or inferior? Is good 1 luxury or necessary? Justify your answers. (6 points) c. Suppose the prices per unit for the two goods are p1 = p2 = $2 and the consumer's income is m = $100. Calculate his optimal consump- tion bundle. (6 points) d. Now suppose the price of good 1 increases to p1 = $4 per unit. What is his new optimal consumption bundle? (6 points) e. Calculate the substitution effect and the income effect of the price change in demand of good 1. Illustrate them on a graph. (10 points)