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?

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.

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)).

Collin likes milkshakes (m) and sushi (s). His preferenes over these two goods are representedby the following utility functionU (m, s) = 2√m + s.Collin’s income is $100 and the price of sushi is $10.(a) Suppose the price of milkshakes is initially $2. Find Collin’s optimal consumption bundle.(b) Draw a graph (with m on the horizontal axis and s on the vertical axis) to show Collin’sbudget line, his indifference curve, and his optimal bundle.(c) Suppose the price of milkshakes increases to $5. How many units of milkshake and sushiare in Collin’s new optimal consumption bundle?(d) Draw a new graph for the new optimal bundle (or add it to the graph you have drawnabove in part (b)).(e) What are the substitution and income effects that result from the increase in the price ofmilkshake? Calculate these effects algebraically and illustrate them on a new graph.(f) What is the amount of additional income needed for Collin to achieve the initial level ofutility? What is the amount of additional income needed for Collin to purchase the initialbundle? What is the ideal cost of living index

Fill in the spaces:a. Along an indifference curve ____________ is constant.b. The rate at which a consumer is willing to substitute one good for another, holding utilityconstant, is given by the ____________ of an indifference curve. This rate is called the_________________________________.c. If at a given combination of X and Y, a consumer’s marginal rate of substitution is 4, thismeans that the consumer is willing to give up ______ units of Y for another X or ______units of X for another Y.d. If a consumer is choosing the levels of goods X and Y in order to maximize utility with agiven budget the _________ equals the ____________ ratio of the goods.e. The rate at which a consumer can substitute one good for another in the market is given bythe ______ of the budget line and is equal to the __________ratio of the two goods

The figure depicts indifference curves for consumption today and consumption later for Abraham and Sarah. These indifference curves are unusual as they are straight lines. Which of the following statements is correct?Select one correct answer  Group of answer choicesAbraham is more likely to want to smooth his consumption than Sarah.Abraham is more impatient than SarahSarah is more willing to give up more units of future consumption for the same amount of current consumption.Sarah’s indifference curve exhibits a higher degree of diminishing marginal returns to consumption than Abraham’s