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

Suppose Miles’ utility function is such that u(A)=40 and u(B)=50, while Janis’ utility function is such that u(A)=40 and u(B)=42. Based on this information, which one of the following statements is correct?Group of answer choicesMiles and Janis have different tastes over bundles A and BMiles and Janis have the same tastes over bundles A and BMiles likes bundle B more than Janis doesMiles likes bundle B less than Janis doesNone of the above

If a consumer is consuming both goods and the price of one of the goods rises, the consumer will experienceGroup of answer choicesa desire to consume a different bundle.a decrease in utility.a southwesterly movement on the indifference map.All of the above.

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?

Which of the following statements described preference theory?

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?