Lucy consumes only scoops of ice-cream (x) and cones (y). Moreover, she insists on consuming these two goods in the combination of α1 scoops of ice-cream and α2 cones, where α1 and α2 are real numbers greater than 1. If there are more scoops of ice-cream than cones, she throws the extra ice-cream away. If there are more cones than scoops of ice-cream, she throws the extra cones away. (a) (4 marks) Draw a couple of Lucy’s indifference curves when: (i) α1 = α2; (ii) α1 > α2; and (iii) α1 < α2. Put ice-cream on the horizontal axis. (b) (8 marks) Suppose each scoop of ice-cream costs α2, and each cone costs α1. Lucy has an income of (α1 2 + α2 2 ) dollars. Obtain Lucy’s utility maximising consumption bundle for general α1, α2 (i.e., without making any of the assumptions about α1 and α2 in (a)).

Lucy consumes only scoops of ice-cream (x) and cones (y). Moreover, she insists on consuming these two goods in the combination of 1 scoop of ice-cream and 1 cone. If there are more scoops of ice-cream than cones, she throws the extra ice-cream away. If there are more cones than scoops of ice-cream, she throws the extra cones away. Her utility function for ice-cream and cones is given by U(x, y) = min {x, y} . (The function min {x, y} returns the smaller number between x and y. In other words, if x < y, min {x, y} = x; if x > y, min {x, y} = y; and if x = y, min {x, y} = x = y.) (a) Draw a couple of indifference curves for Lucy. Put ice-cream on the horizontal axis. (Hint: Draw the 45◦ line. Choose a point on the line. If you increase the amount of x but not y from that point, how would Lucy’s utility change? If you increase the amount of y but not x from that point, how would Lucy’s utility change?) (b) Suppose each scoop of ice-cream costs $2, and each cone costs $1. Lucy has an income of $6. Draw her budget line in the diagram you have drawn in part (a). (c) Using the diagram you have drawn, find Lucy’s utility maximising consumption bundle. Lucy’s sister, Mary, also insists on a particular combination of ice-cream and cones. Unlike Lucy, however, Mary must have 2 scoops of ice-cream with every cone. Mary’s utility function is given by U(x, y) = min  x 2 , y . (d) In a separate diagram, draw a couple indifference curves for Mary. (Hint: Instead of drawing the 45◦ line, draw the line y = x/2. Then follow the procedures as in part (a).) (e) Mary faces the same prices as Lucy, but has an income of $10 instead. Using the diagram you have drawn in part (d), find Mary’s utility maximising consumption bundle

Suppose there are only two goods in the economy: Yo-yos and Marbles. Bob only cares about his consumption of Yo-yos; the more Yo-yos he has the happier he is, regardless of his consumption of Marbles. In contrast, Lucy only cares about his consumption of Marbles; the more Marbles she has the happier she is, regardless of her consumption of Yo-yos. (a) Draw Bob’s indifference curves, putting Yo-yos in the x-axis and Marbles in the y-axis. (b) Draw Lucy’s indifference curves, putting Yo-yos in the x-axis and Marbles in the y-axis. (c) Do Bob’s and Lucy’s preferences comply with the property of diminishing marginal rate of substitution? (d) Are Bob’s and Lucy’s preferences transitive?

Lucy’s sister, Mary, also insists on a particular combination of ice-cream and cones. Unlike Lucy, however, Mary must consume these two goods in the com￾bination of α2 scoops of ice-cream and α1 cones. Mary is envious of Lucy and wants to achieve the same utility level that Lucy gets when she is consuming her optimal bundle in (b). What is the minimum income that Lucy’s and Mary’s parents must give to Mary so that she can achieve the utility level of Lucy at the current prices? Is this income greater or lower than the income of Lucy in (b)

Title11) Refer to Figure 6.15. The slope of the indifference curve is the ratio of the A) marginal...Description 11) Refer to Figure 6.15. The slope of the indifference curve is the ratio of theA) marginal utility of ice cream cones to the marginal utility of ice cream sandwiches.B) marginal utility of ice cream sandwiches to the marginal utility of ice cream cones.C) total utility of ice cream cones to the total utility of ice cream sandwiches.D) total utility of ice cream sandwiches to the total utility of ice cream cones.12) Refer to Figure 6.15. At point A, the slope of the indifference curve isA) -0.67.B) -1.5.C) -3.0.D) indeterminate because the marginal utilities are unknown.13) Refer to Figure 6.15. If the price of an ice cream cone is $2, the price of ice cream sandwiches isA) $2.B) $3.C) $50.D) $100.14) Refer to Figure 6.16. If the price of a hot dog is $2, Jason's income isA) $25.B) $200.C) $300.D) indeterminate because the price of sandwiches is not given.15) Refer to Figure 6.16. Why was Jason NOT maximizing his utility at point C?A) He is not spending his entire budget.B) His marginal utility per dollar spent on the last sandwich is greater than his marginal utility per dollar spent on his last hot dog.C) His marginal utility per dollar spent on the last sandwich is less than his marginal utility per dollar spent on his last hot dog.D) He is maximizing his utility at point C.16) Refer to Figure 6.16. The highest indifference curve depicted is the one on which point D lies. Why is Jason NOT maximizing his utility at point D?A) He cannot afford point D.B) His marginal utility per dollar spent on the last sandwich is greater than his marginal utility per dollar spent on his last hot dog.C) His marginal utility per dollar spent on the last sandwich is less than his marginal utility per dollar spent on his last hot dog.D) He is maximizing his utility at point C.17) We derive the demand curve for X from indifference curves and a budget constraint by changing theA) level of income.B) price of X.C) price of Y.D) consumers? preferences.18) Assuming the properties of normal indifference curves, a consumer will maximize his utility where his indifference curve is just tangent to his budget constraint.19) An indifference curve is a set of points, each point representing a combination of two goods, all of which represent the same total utility.

Consider an individual with preferences defined over two goods, X1 and X2. This consumer has preferences such that she must have 1/3 of a unit of X1 with every 1/2 unit of X2. In addition, let P1 = 1, P2 = 1, and suppose this individual has an income of $45,000. (a) Draw indifference curves with X1 on the horizontal axis to depict this consumer’s 1 preferences. Comment.