textbook: Pindyck and Rubinfeld, Microeconomics, 9ed. microeconomic question from Sejong University student

7. Suppose a consumer would like to buy food and clothing optimally in order to maximize his utility. Prices of food and clothing are 2 and 3, respectively. Her income is 30.

(a) (4 points) Draw her budget line. Clearly indicate its slope and vertical and horizontal intercepts.

(b) (4 points) Indicate his utility-maximizing market basket and draw an indifference curve that contains the chosen basket. Demand for food and clothing must be larger than 0, and the marginal rate of substitution is strictly positive and finite. Now her income changes to 60. The income elasticity of demand for food is assumed to be zero.

(c) (10 points) Draw her new budget line, his utility-maximizing market basket, and a corresponding indifference curve. Again, clearly indicate its slope, as well as vertical and horizontal intercepts.

(d) (8 points) Does the demand for food increase? Does it imply the demand curve is downward-sloping?

(e) (8 points) Can the income elasticity for clothing be negative?