Suppose there are only two goods: Beer and Milk. Tom’s preference over bundles of beer and milk is as follows: For any two bundles A = (bA, mA) and B = (bB, mB) (where b and m denotes the amount of beer and milk, respectively), A ≿ B (i.e., “A is at least as good as B”) if and only if: Either bA > bB; Or bA = bB and mA ≥ mB. In other words, Tom cares, first and foremost, about the amount of beer, but if the two bundles contain the same amount of beer, then he prefers having more milk to less. • Is Tom’s preference complete? If yes, show why; if no, give an example of two bundles which Tom cannot compare. • Is Tom’s preference monotone? Strongly monotone? • Does Tom’s preference comply with the property of diminishing marginal rate of substitution?

Suppose the tastes of a consumer are described by the utility function . Consider bundles A=(1,16) and B=(16,1). Which of the following statements best describes the consumer’s preferences over bundles A and B?Group of answer choicesThe consumer strictly prefers A to BThe consumer strictly prefers B to AThe consumer is indifferent between A and BFor the consumer, A is at least as good as BFor the consumer, B is at least as good as A

Consider a consumer whose preferences are defined over bundles of non-negative consumption quantities for each of two commodities: Widgets anda composite consumption commodity known as “All Other Goods”. Thisconsumer’s preferences are both rational and locally non-satiated. Denote2the price of Widgets by p1, the consumption of Widgets by q1, the price of“All Other Goods” by p2, the consumption of “All Other Goods” by q2, andthe consumer’s income by y. Use the composite consumption commodity(that is, “All Other Goods”) as the numeraire throughout this question. (Inother words, assume that p2 = $1 throughout this question. Note that thisassumption allows you to interpret the amount of “All Other Goods” con-sumption as expenditure on “All Other Goods”, because q2 = 1q2 = p2q2.)Suppose that this consumer’s uncompensated demand function for Wid-gets is given byq1 (p1, y; p2 = 1) = (0.02) y − (2) p1.(Uncompensated demands are also known as Marshallian demands, or Wal-rasian demands, or ordinary demands.) Initially, this consumer has an in-come of $6, 500 and faces a Widget price of $50 per Widget. Following aneconomic shock, the Widget price rises to $60 per widget. This economicshock has no impact whatsoever on either this consumer’s income or the“All Other Goods” price.1. Illustrate the total impact of the economic shock on this consumer’soptimal consumption decision using an “indifference curve / budgetline” diagram. (Assume that the consumer’s indifference curves havethe conventional “downward sloping and bowed-in towards the ori-gin” shape.) Make sure that you indicate the various numerical valuesof the intercepts of the budget lines with the axes, along with the nu-merical values of the pre-shock and post-shock optimal consumptionbundles.2. Illustrate the revealed preference approximation of the Slutsky de-composition of the total effect of the economic shock on this con-sumer in an “indifference curve / budget line” diagram, using the“pre-shock consumption bundle, post-shock prices” approach to thisdecomposition. (Assume that the consumer’s indifference curves havethe conventional “downward sloping and bowed-in towards the origin”shape.) Be sure to identify the numerical values of each commodityin all of the relevant consumption bundles for this decomposition, themovement between bundles that constitutes the substitution effect,the movement between bundles that constitutes the income effect, thesize (including both magnitude and sign) of the substitution effect interms of widgets, and the size (including both magnitude and sign)of the income effect in terms of widgets.3. Does the revealed preference approximation to the substitution effectthat you found in part 3 of this question overstate, exactly equal, or3understate the true (or Hicksian) substitution effect that it is approx-imating? Does the revealed preference approximation to the incomeeffect that you found in part 3 of this question overstate, exactlyequal, or understate the true (or Hicksian) income effect that it isapproximating? Justify your answers.

A consumer’s preferences are Cobb-Douglass. In the initial optimal bundle the consumer buys 4 and 9 units of x1 and x2 respectively. If income doubles from its initial level of $100 to $200, in the consumer's new optimal bundle they consumer units of good 1 and and of good 2.

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?

Question 1Joe’s preferences are described by the following utility functionU (x, y) = xαyβwith α > 0 and β > 0.(a) Let I denote Joe’s income, and px and py denote the prices of good x and y, respectively.Find Joe’s optimal consumption bundle.(b) Now, suppose α = 6, β = 2, px = 2, py = 3 and I = 24. Evaluate Joe’s optimal choice.(c) Suppose px increases by 50%. What is Joe’s new optimal consumption bundle? Calculateboth the Income Effect and the Substitution Effect.Question 2Collin 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?