Question 2 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 labelled diagram, draw Matt’s indifference map, putting Butter on the x-axis and Sour Cream on the y-axis. Make sure to indicate the direction in which the indiffference curves increase. (b) In a well labelled diagram, draw Matt’s budget set indicating the intercepts with the axes and the slope of the budget line. (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? (d) Obtain Matt’s optimal bundle when: – β > 3/2 – β < 3/2 – β = 3/2 (e) Now, suppose that the price of butter changes, whereas the price of sour cream and Matt’s income remain the same. The new price of Butter is P ′ B = βPB. What is Matt’s new optimal bundle? Does it depend on the value of β?
Marginal Rate of Technical Substitution
MRTS reaches a manufacturer when a part of the product is lowered to sustain the manufacturing level when the other part is extended. It is the level of the quantity that is lowered when one extra volume is used, and the output is unchanged.
Preferences and Utility Analysis
Before understanding what is preference and utility analysis, it is very important to understand the terms preference and utility separately.
Question 2 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 labelled diagram, draw Matt’s indifference map, putting Butter on the x-axis and Sour Cream on the y-axis. Make sure to indicate the direction in which the indiffference
(b) In a well labelled diagram, draw Matt’s budget set indicating the intercepts with the axes and the slope of the budget line.
(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?
(d) Obtain Matt’s optimal bundle when:
– β > 3/2
– β < 3/2
– β = 3/2
(e) Now, suppose that the price of butter changes, whereas the price of sour cream and Matt’s income remain the same. The new price of Butter is P ′ B = βPB. What is Matt’s new optimal bundle? Does it depend on the value of β?
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