1. (35 points) A consumer has a utility function given by U(r1, 12) = 4 x1 + 12, where x1 and 12 are the two goods he consumes. His income is m and the prices for the goods are p1 and p2 per unit. (a) Find the consumer's demand functions for the two goods. Are the goods normal or inferior? Justify your answer. (b) If the prices are p1 = p2 = $1 and the income is m = $12, find the optimal consumption bundle and the level of utility obtained from this consumption bundle. Draw the Engel curve for good 2. (c) Now suppose that the government imposes a quantity tax of t = $1 per unit of good 1 consumed. Find the new optimal consumption bundle and the new level of utility. (d) Calculate the substitution effect and the income effect of the price change on the con- sumer's demand for good 1. (e) Calculate the compensating and equivalent variations of the price change