Problem 1: Alice’s utility function is ?(?, ?) = √?√? where ? is her consumption of...
Problem 1: Alice’s utility function is ?(?, ?) = √?√? where ? is her consumption of good 1 and ? is her consumption of good 2. Denote Alice’s income by ?, and denote the prices of good 1 and 2 by ?? and ?? respectively.
A) Derive the formula for Alice’s marginal rate of substitution.
B) Write down the two equations necessary to solve for Alice’s optimal values of ? and ?.
C) Using the equations from part B, solve for Alice’s demand functions (that is, the optimal values of ? and ? such that the formula for ? does not depend on ?, and the formula for ? does not depend on ?).
D) Let ? = 100, ?1 = 2, and ?2 = 5. What are the optimal values of ? and y
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Problem 1: Alice’s utility function is ?(?, ?) = √?√? where ? is
her consumption of...
Alice’s utility function is ?(?, ?) = √?√? where ? is her consumption of good 1...
Alice’s utility function is ?(?, ?) = √?√? where ? is her consumption of good 1 and ? is her consumption of good 2. Denote Alice’s income by ?, and denote the prices of good 1 and 2 by ?1 and ?2 respectively. 1. What is the formula for Alice's marginal rate of substitution? 2. Write down the two equations necessary to solve for Alice's optimal values of x and y.
2. Consider the Cobb-Douglas utility function u(x,y) = x2y2. Let the budget 1, where pr, py...
2. Consider the Cobb-Douglas utility function u(x,y) = x2y2. Let the budget 1, where pr, py are the prices and I denotes the constraint be prx + pyy income. (a) Write the Lagrangian for this utility maximization problem. (b) Solve the first-order conditions to find the demand functions for both good a and good y. [Hint: Your results should only depend on the pa- rameters pa, Py, I.] (c) In the optimal consumption bundle, how much money is spend on...
Suppose an individual’s utility function is u=x11/2, x21/2. Let p1=4, p2=5, and income equal $200. With...
Suppose an individual’s utility function is u=x11/2, x21/2. Let p1=4, p2=5, and income equal $200. With a general equation and general prices, derive the equal marginal principle. Graphically illustrate equilibrium and disequilibrium conditions and how consumers can reallocate their consumption to maximize utility. What is the optimal amount of x1 consumed? What is the optimal amount of x2 consumed? What is the marginal rate of substitution at the optimal amounts of x1 and x2? As functions of p1, p2, and...
Question Kayla's utility depends on her consumption of good 1(Q1) and good 2 (Q2), and it...
Question Kayla's utility depends on her consumption of good 1(Q1) and good 2 (Q2), and it is described by the following utility function: U(Q), Q2 ) = 27 Q7'3 Q3 Deriving Demand functions 1. What are her uncompensated demand functions (Marshallian demand function) for Q1 and Q2? 2. What are her compensated demand functions (Hicksian demand function) for Q1 and Q2? Effects of a price increase (substitution, income, and total effects) Her income is currently $360. Consider that the price...
I NEED ANSWER FOR 5-6-7-8-9 Question Kayla's utility depends on her consumption of good 1(Q1) and...
I NEED ANSWER FOR 5-6-7-8-9
Question Kayla's utility depends on her consumption of good 1(Q1) and good 2 (Q2), and it is described by the following utility function: U(Q), Q2 ) = 27 Q7'3 Q3 Deriving Demand functions 1. What are her uncompensated demand functions (Marshallian demand function) for Q1 and Q2? 2. What are her compensated demand functions (Hicksian demand function) for Q1 and Q2? Effects of a price increase (substitution, income, and total effects) Her income is currently...
QUESTION; Given Biwei’s utility function U=4XY, where X is consumption of beer and Y is consumption...
QUESTION; Given Biwei’s utility function U=4XY, where X is consumption of beer and Y is consumption of pizza. For this utility function, the marginal utility of X is MUx = 4Y; the marginal utility of Y is MUY = 4X. 1) Suppose Y = 3. Calculate Biwei’s utility for X = 2, 3, 10, and 11. For a given level of Y, does good X display diminishing marginal utility? 2) Suppose X = 3. Calculate Biwei’s utility for Y =...
Anna spends all her income on wine (good 1) and cheese (good 2). Her utility function...
Anna spends all her income on wine (good 1) and cheese (good 2). Her utility function is u(x1; x2) = x1x2. Her income is m = $200. The prices for the two goods are p1 = $20 and p2 = $10 respectively. Find Annaís optimal consumption bundle. Show the complete calculations, and illustrate your answer graphically (draw the indi§erence curve and the budget constraint). How would your answer change to part (a) if Annaís utility function were given by v(x1;...
h. U(1, 2 For the utility function above, find the consumer's optimal consumption bundle when prices...
h. U(1, 2 For the utility function above, find the consumer's optimal consumption bundle when prices of goods 1 and 2 are pl and p2, and the consumer has an income m. 1. 2. For the utility function above, find the consumer's optimal consumption bundle when prices of goods 1 and 2 are pl and p2, and the consumer has an endowment (el, e2) of the two goods. For each of your answers in question 2, write down the consumer...
Joyce's utility function is as follows: U= 10X2Y3 Where, X, is the quantity of good X...
Joyce's utility function is as follows: U= 10X2Y3 Where, X, is the quantity of good X consumed, Y, is the quantity of good Y consumed and, U, is Joyce's utility function. The general budget constraint for the two goods is a follow: B=PxX + PYY A. Derive Joyce's Marshallian demand equation for good X. Also compute her demand for good X when B= 500, and the price of good X is 1 and 2. Also draw the Marshallian demand curve...
Question 1. (Consumption-Saving Problem): Suppose that a consumer lives for two periods. The utility function of...
Question 1. (Consumption-Saving Problem): Suppose that a consumer lives for two periods. The utility function of the consumer is given by with u> 0 where c and c2 are consumption in period 1 and period 2 respectively. Sup- pose that consumer has income y in the first period, but has no income in the second period. Consumer has to save in the first period in order to consume in the second period. Let s be the savings in the first...
2. Consider the Cobb-Douglas utility function u(x,y) = x2y2. Let the budget 1, where pr, py are the prices and I denotes the constraint be prx + pyy income. (a) Write the Lagrangian for this utility maximization problem. (b) Solve the first-order conditions to find the demand functions for both good a and good y. [Hint: Your results should only depend on the pa- rameters pa, Py, I.] (c) In the optimal consumption bundle, how much money is spend on...
Question Kayla's utility depends on her consumption of good 1(Q1) and good 2 (Q2), and it is described by the following utility function: U(Q), Q2 ) = 27 Q7'3 Q3 Deriving Demand functions 1. What are her uncompensated demand functions (Marshallian demand function) for Q1 and Q2? 2. What are her compensated demand functions (Hicksian demand function) for Q1 and Q2? Effects of a price increase (substitution, income, and total effects) Her income is currently $360. Consider that the price...
I NEED ANSWER FOR 5-6-7-8-9
Question Kayla's utility depends on her consumption of good 1(Q1) and good 2 (Q2), and it is described by the following utility function: U(Q), Q2 ) = 27 Q7'3 Q3 Deriving Demand functions 1. What are her uncompensated demand functions (Marshallian demand function) for Q1 and Q2? 2. What are her compensated demand functions (Hicksian demand function) for Q1 and Q2? Effects of a price increase (substitution, income, and total effects) Her income is currently...
h. U(1, 2 For the utility function above, find the consumer's optimal consumption bundle when prices of goods 1 and 2 are pl and p2, and the consumer has an income m. 1. 2. For the utility function above, find the consumer's optimal consumption bundle when prices of goods 1 and 2 are pl and p2, and the consumer has an endowment (el, e2) of the two goods. For each of your answers in question 2, write down the consumer...
Joyce's utility function is as follows: U= 10X2Y3 Where, X, is the quantity of good X consumed, Y, is the quantity of good Y consumed and, U, is Joyce's utility function. The general budget constraint for the two goods is a follow: B=PxX + PYY A. Derive Joyce's Marshallian demand equation for good X. Also compute her demand for good X when B= 500, and the price of good X is 1 and 2. Also draw the Marshallian demand curve...
Question 1. (Consumption-Saving Problem): Suppose that a consumer lives for two periods. The utility function of the consumer is given by with u> 0 where c and c2 are consumption in period 1 and period 2 respectively. Sup- pose that consumer has income y in the first period, but has no income in the second period. Consumer has to save in the first period in order to consume in the second period. Let s be the savings in the first...
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