ECON104A: INTERMEDIATE MICROECONOMIC THEORY HOMEWORK 5 INSTRUCTION

ECON104A: INTERMEDIATE MICROECONOMIC THEORY HOMEWORK 5 INSTRUCTION. Submit your answer on iLearn before the due date. Due: Friday May 7th, 11:59:00PM. PROBLEM I. Consider a consumer who consumes good 1 and good 2. A consumption bundle where the consumer consumes x1 units of good 1 and x2 units of good 2 is written as (x1 , x2 ). The price of good 1 is p1 , the price of good 2 is p2 , and the consumer’s income is m. Q1. Suppose that the consumer’s utility function is given by U (x1 , x2 ) = x21 x2 . When the price of good 1 is 2, the price of good 2 is 3, and the consumer’s income is 18, what is the consumer’s optimal consumption bundle? (a) (3, 2) (b) (3, 4) (c) (6, 9) (d) (4, 8) (e) (6, 2) Q2. Suppose that the consumer’s utility function is given by U (x1 , x2 ) = x21 x2 . When the price of good 1 is 2 and the price of good 2 is 3, (a) the income offer curve is a line with slope 2. (b) the Engel curve of good 2 is a line with slope 1/3. (c) the Engel curve of good 1 is a line with slope 3. (d) the income offer curve is a line with slope 1. (e) the income offer curve coincides with the horizontal axis. Q3. Suppose that the consumer’s utility function is given by U (x1 , x2 ) = x1 + 3x2 . When the price of good 1 is 2, the price of good 2 is 3, and the consumer’s income is 24, what is the consumer’s optimal consumption bundle? (a) (0, 8) 1 (b) (6, 4) (c) (3, 6) (d) (9, 2) (e) (12, 0) Q4. Suppose that the consumer’s utility function is given by U (x1 , x2 ) = x1 + 3x2 . When the price of good 1 is 2 and the price of good 2 is 3, (a) the income offer curve coincides with the vertical axis. (b) the income offer curve is a line with slope 3. (c) the Engel curve of good 2 is a line with slope 2. (d) the income offer curve is a line with slope 1/3. (e) the income offer curve coincides with the horizontal axis. Q5. Suppose that the consumer’s utility function is given by U (x1 , x2 ) = min{2x1 , x2 }. When the price of good 1 is 2, the price of good 2 is 3, and the consumer’s income is 16, what is the consumer’s optimal consumption bundle? (a) (3, 3) (b) (2, 4) (c) (0, 6) (d) (8, 0) (e) (5, 2) Q6. Suppose that the consumer’s utility function is given by U (x1 , x2 ) = min{2x1 , x2 }. When the price of good 1 is 2 and the price of good 2 is 3, (a) the income offer curve is a line with slope 4. (b) the income offer curve coincides with the horizontal axis. (c) the income offer curve is a line with slope 8. (d) the Engel curve of good 1 is a line with slope 8. (e) the income offer curve coincides with the vertical axis. Q7. Suppose that the consumer’s demand function for good 1 is given by m . x1 (p1 , p2 , m) = 4p1 + p2 Choose a correct statement from below. 2 (a) Good 1 is an inferior, ordinary good and a complement to good 2. (b) Good 1 is a normal, ordinary good and a complement to good 2. (c) Good 1 is a normal, Giffen good and a complement to good 2. (d) Good 1 is a normal, ordinary good and a substitute to good 2. (e) Good 1 is an inferior, ordinary good and a substitute to good 2. Q8. Suppose that the consumer’s demand function for good 1 is given by x1 (p1 , p2 , m) = m p1 −4 . p1 p2 Choose a correct statement from below. (a) Good 1 is a normal, ordinary good and a substitute to good 2. (b) Good 1 is a normal, ordinary good and a complement to good 2. (c) Good 1 is an inferior, ordinary good and a substitute to good 2. (d) Good 1 is a normal, Giffen good and a complement to good 2. (e) Good 1 is an inferior, ordinary good and a complement to good 2. 3