Answer Happy

Question 3 (20 marks) Carla consumes two goods, x and y. Her utility function is given by: = u(x, y) = 3x + 4y. The price pa of one unit of x is 12 dollars, and Carla's income is w = 60 dollars. = (a) Suppose that the price Py of one unit of y is 10 dollars. y (1) (1.5 marks) For each consumption bundle, compare the marginal utility per dollar spent on x to the marginal utility per dollar spent on y. Is there a consumption bundle at which bang-for-buck equalization holds? (2) (1 mark) Determine and write down Carla's optimal consumption bundle. Briefly explain your answer. (3) (2.5 marks) In a figure with x on the horizontal axis draw and label Carla's bud- get line, her optimal consumption bundle and Carla's indifference curve which contains her optimal consumption bundle. (b) Now suppose that py increases to 20 dollars. (1) (2 marks) Add and label Carla's new budget line and new optimal bundle to your figure from (a). (2) (8 marks) For each of the goods x and y, compute a numerical value for each of the total effect TE, the income effect IE and the substitution effect SE associ- ated with this price increase. Illustrate each of these effects in your figure from part (a). Also add into this figure a “hypothetical” budget line that is analogous to those that we discussed in the lectures and that aids you in determining the income and substitution effects. (3) (2 marks) Compute the compensating variation in dollars that leaves Carla as happy after the price increase as she was before the price increase. Explain your answer.
(c) (3 marks) Suppose again that py 10. Does there exist an increase in Py for which for each good the total effect equals the income effect? If so, give an example of such a price increase. Explain your answer in detail.