1. Consider Consumers A, B, and C with the following preferences over two goods. UA (x1,x2)...

1. Consider Consumers A, B, and C with the following preferences over two goods.

U_A (x₁,x₂) = x₁²x₂³

U_B (x₁,x₂) = 2x₁+3x₂

U_C (x₁,x₂) = min{2x₁,3x₂)

The prices given are p1, p2 and income for each consumer is m.

Solve for the Engel curves for each consumer.

please be very detailed, thank you!

Expert Solution

Rahul Sunny answered 3 hours ago

Consider an individual with preferences defined over two goods, X1 and X2. This individual has preferences...

Consider an individual with preferences defined over two goods, X1 and X2. This individual has preferences that can be represented by the following utility function: u(X1, X2) = X1 + X 0.5 2 Let P1 = 4 and P2 = 2. In addition, suppose this individual has an income of $120. (a) Write down the expression for this consumer’s marginal rate of substitution of X1 for X2 (MRS12). Identify the distinguishing feature of this particular MRS12. (b) Calculate the optimal...

Consider a consumer with textbook preferences defined over two goods x1 and x2. Why is the...

Consider a consumer with textbook preferences defined over two goods x1 and x2. Why is the condition MRS = p1/p2 necessary for utility maximization? Is this condition alone sufficient?

Consider a consumer with textbook preferences defined over two goods X1 and Y2. Why is the...

Consider a consumer with textbook preferences defined over two goods X1 and Y2. Why is the condition MRS = p1/p2 necessary for utility maximization? Is this condition alone also sufficient?

Nigella has the following utility function over two goods (x1, x2): U(x1, x2) = min {0.5x1,...

Nigella has the following utility function over two goods (x1, x2): U(x1, x2) = min {0.5x1, 3x2} a.What is the Nigella’s utility level if x1= 20 andx2= 3? b.Suppose P1= 1 andP2= 3(where P1is the price x1andP2is theprice of x2) and Nigella has an income of 18. What is Nigella’s budget constraint? Illustrate it in a graph c.Solve for the Nigella’s utility maximizing bundle of x1andx2.

An MRS & Elasticity of substitution question. Consider the following utility function : Ua(x1, x2) =...

An MRS & Elasticity of substitution question. Consider the following utility function : Ua(x1, x2) = x12 x22 (a) Calculate MRS(x1, x2) (b) Find the Elasticity of Substitution (c) Is the preference homothetic? Is the preference quasilinear? (d) Sketch the indifference curve with x1 on the horizontal and x2 on the vertical axis

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's preferences over consuming two goods that are represented by the following utility function:...

Consider a consumer's preferences over consuming two goods that are represented by the following utility function: U（x1，x2）= x1^a x2^1-α 0 < α < 1 x1，x2 ≥ 0 (a) Do her preferences satisfy monotonicity? (4 mark) (b) Do her preferences exhibit diminishing marginal utility? (c) Are her preferences convex? In other words, do her preferences exhibit diminishing marginal rate of substitution? (Hint: Find MRS and its rate of changes with respect to the good on the horizontal axis.) (d) Use a...

1. Consider the preferences of an individual over two goods, x and y, with prices px...

1. Consider the preferences of an individual over two goods, x and y, with prices px and py and income I. (a) If the individual's preferences can be represented by the utility function u(x,y) =2x1/2 + y, what is the marginal rate of substitution? What does this MRS imply about how this consumer would trade y for x? Are the underlying preferences homothetic (explain)? Graphically illustrate a typical indifference curve and explain how you know the shape. (b) If the...

1.) Individual A and B have the following preferences: uA = (x1A) · (x2A)3 and uB...

1.) Individual A and B have the following preferences: uA = (x1A) · (x2A)3 and uB = (x1B ) · (x2B ). Their endowments are given by ωA = (3, 0) and ωB = (0, 3). Solve for (and graph) competitive equilibrium and the contract curve. 2.) Individual A and B have the following preferences: uA = ln(x1A) + ln(x2A) and uB = ln(x1B ) + ln(x2B ). Their endowments are given by ωA = (2, 6) and ωB =...

Let’s assume that there are two goods x1= cat food, x2 = money. Consider a retirement...

Let’s assume that there are two goods x1= cat food, x2 = money. Consider a retirement home with two inmates, Mrs M and a grumpy old man, Mr Q. Mrs. M has the following endowment: W1=0, W2=30 , while Mr.Q has: W1=30, W2=0 . They have the following utility functions: U(x1,x2) = x1x2 (a) Illustrate the available resources and the initial allocation (=endowment) in an Edgeworth box. (b) Set the price of money equal to one, and define p as...

Question