Matt considers Butter (B) and Sour Cream (S) as substitutes. His utility function has the form u(B, S) = βB + S, where β > 0. Suppose the price of Butter is PB = 3, the price of Sour Cream is PS = 2, and Matt has an income of M = 100 dollars to spend between Butter and Sour Cream.  (a) In a well-labeled diagram, draw Matt's indifference map, putting Butter in the x-axis and Sour Cream in the y-axis. Make sure to indicate the direction in which the indifference curves increase.

e) Now, suppose that the price of butter changes, whereas the price of the sour cream and Matt's income remain the same. The new price of Butter is P ′ B = βPB. What is the new Matt's optimal bundle? Does it depend on the value of β?

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

(c) Obtain the Marginal Rate of Substitution between Butter and Sour Cream. What would happen to the MRS if Matt doubles his consumption of Butter and Sour Cream?

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?

Assume that a consumer's indifference curve is bowed inward and negatively sloped. As the consumer moves from left to right along the horizontal axis, the consumer's marginal rate of substitutionGroup of answer choicesincreases.decreases.increases, then decreases.remains constant.