Suppose Amjad’s preferences for pants and shirts are represented by: U(x1,x2 )=x1^2 x2^3, and he faces...

Suppose Amjad’s preferences for pants and shirts are represented by: U(x1,x2 )=x1^2 x2^3, and he faces a linear

budget constraint, 2x1+ x2=50. Given that the price of good 1 increases to 4, what are (1) the compensating and (2)

equivalent variations? You must set up the Lagrangian and derive the demand functions for this question. Be sure

to clearly identify which prices, old or new, are used to derive the values for EV vs. CV, and which utility, old or new,

is used to derive EV vs. CV.

Expert Solution

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Rahul Sunny answered 7 months ago

Suppose an agent has preferences represented by the utility function: U(x1, x2) =1/5 ln (x1) +...

Suppose an agent has preferences represented by the utility function: U(x1, x2) =1/5 ln (x1) + 4/5 ln (x2) The price of x1 is 6 and the price of x2 is 12, and income is 100. a) What is the consumer’s optimal consumption bundle? b) Suppose the price of x2 is now 4, what is the consumer’s new best feasible bundle?

Suppose an agent has preferences represented by the following utility function: u(x1, x2) = 1/4 ln(x1)...

Suppose an agent has preferences represented by the following utility function: u(x1, x2) = 1/4 ln(x1) + 3/4 ln(x2) The price of good x1 is 2, the price of good x2 is 6, and income is 40. a) What is the consumers best feasible bundle (ie, his optimal consumption bundle)? b) Interpret the consumer’s marginal rate of substitution at the best feasible bundle found in part a).

1/Laura's preferences over commodities x1 and x2 can be represented by U(x1,x2)=min{3x1, x2}. She maximizes her...

1/Laura's preferences over commodities x1 and x2 can be represented by U(x1,x2)=min{3x1, x2}. She maximizes her utility subject to her budget constraint. Suppose there is an increase in p1. There is an income effect but not a substitution effect of this price change. There are both income and substitution effects of this price change. There is a substitution effect but not an income effect of this price change. It is unclear whether the consumer will buy more or less x1...

Consider a consumer with preferences represented by the utility function: u(x, y) = x1/4y1/2 Suppose the...

Consider a consumer with preferences represented by the utility function: u(x, y) = x1/4y1/2 Suppose the consumer has income M = 10 and the prices are px=1 and Py = 2. (a) Are goods x and y both desirable? (b) Are there implications for the utility maximization problem for the consumer from your finding in 1a? If so, explain in detail. (c) Derive the utility maximizing bundle.

Consider a consumer with preferences represented by the utility function: u(x; y) = x1/4y1/2 Suppose the...

Consider a consumer with preferences represented by the utility function: u(x; y) = x1/4y1/2 Suppose the consumer has income M = 10 and the prices are px = 1 and py = 2. (a) Are goods x and y both desirable? (b) Are there implications for the utility maximization problem for the consumer from your finding in a? If so, explain in detail.

Slutsky Equation: Exercise 12: Assume preferences can be represented by the following utility function: u(x1, x2)...

Slutsky Equation: Exercise 12: Assume preferences can be represented by the following utility function: u(x1, x2) = x1 x22 a. Are preferences monotonic? Justify. b. Set up the consumer’s utility maximization problem for prices p1, p2 and income m (the general case) c. Solve the problem. You will obtain demand functions x∗1 (p1 , p2 , m) and x∗2 (p1, p2, m) in terms of the parameters (p1, p2, m) . Obtain price elasticity of demand for good one. Obtain...

Exercise 14: Assume preferences can be represented by the following utility function: u(x1,x2)=−x12 +100x1 +20x2 a....

Exercise 14: Assume preferences can be represented by the following utility function: u(x1,x2)=−x12 +100x1 +20x2 a. Is the utility function monotonic? Justify. b. Set up the consumer’s utility maximization problem for prices p1, p2 and income m (the general case) c. Solve the problem. You will obtain demand functions x∗1 (p1 , p2 , m) and x∗2 (p1, p2, m) in terms of the parameters (p1, p2, m) . d. Graph the demand function for good 1 when the price...

1. Suppose that Lexi preferences are given by the utility function u(x1; x2) = x12x2, where...

1. Suppose that Lexi preferences are given by the utility function u(x1; x2) = x12x2, where x1 denotes bottles of juice, and x2 denotes the number of meat plates. A meat dish costs $15 on average, and bottle of juice is $3. You are told that at these prices Lexi can afford 10 meat plates and 40 bottles of juice per month. i) Derive Lexi optimal consumption bundle. ii) Which of the following two options would Lexi prefer? Show work....

1. Suppose the consumer has Cobb-Douglas preferences U(x1, x2)=X1aX2b Find out Ordinary Demands 2. Suppose the...

1. Suppose the consumer has Cobb-Douglas preferences U(x1, x2)=X1aX2b Find out Ordinary Demands 2. Suppose the consumer has a perfect complement preferences U(X1,X2)=min{aX1, X2} Find out Ordinary Demands

u(x1, x2) = min {x1/2, x2/3} if the price of good 1 is $7/unit, the price...

u(x1, x2) = min {x1/2, x2/3} if the price of good 1 is $7/unit, the price of good 2 is $4/unit and income is 114.. What is this person's optimal consumption level for good 2?

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