Consider preferences over x and y given U(x,y) = min(x,2y) and suppose that income is 60....
Consider preferences over x and y given U(x,y) = min(x,2y) and suppose that income is 60. Let the initial prices be px=1 and py=2.
1. What is the initial optimal consumption?
2. Suppose px increases to px=2. Find the total change in the consumption of x and y.
3. Decompose the total effect into its substitution effect and its income effect.
Please do each step of every question for a complete understanding of the reasoning behind the steps.
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Consider preferences over x and y given U(x,y) = min(x,2y) and
suppose that income is 60....
4. Andy's utility is represented by the function U(X,Y) - XY. His marginal utility of X...
4. Andy's utility is represented by the function U(X,Y) - XY. His marginal utility of X is MUx = Y. His marginal utility of Y is MUY = . He has income $12. When the prices are Px - 1 and Py -1, Andy's optimal consumption bundle is X* -6 and Y' = 6. When the prices are Px = 1 and P, = 4, Andy's optimal consumption bundle is X** = 6 and Y* 1.5. Suppose the price of...
Consider an individual making choices over two goods, x and y with initial prices px=5 and...
Consider an individual making choices over two goods, x and y with initial prices px=5 and py= 2, with income I= 100: a) If the individual's preferences can be represented by the utility function u = 4x+ 2y; find the income, substitution and total effects of a decrease in the price of x to px= 3. b) If the individual's preferences can be represented by the utility function u = min(4x,2y); find the income, substitution and total effects of a...
Consider an individual making choices over two goods,x and y with initial prices px= 5 and...
Consider an individual making choices over two goods,x and y with initial prices px= 5 and py= 2, with incomeI=100: A) If the individual's preferences can be represented by the utility function u= 4x+ 2y; find the income, substitution and total effects of a decrease in the price of x to px= 3. B) If the individual's preferences can be represented by the utility function u= min(4x,2y); find the income, substitution and total effects of a decrease in the price...
In Problems 5 - 7, you are given the utility function u(x, y), income I and...
In Problems 5 - 7, you are given the utility function u(x, y), income I and two sets of prices: initial prices px,py and final prices p,%-For each problem, you are to find: (a) the optimal choice at the initial prices (b) the optimal choice at the final prices (c) the change- optimal choice at final prices - optimal choice at initial prices (d) the income effect and the substitution effect 5) u(x, y)-min(x, 3y), 1-14, p.-1, p,-2. p,-2, p,-2
2. Consider a utility function that represents preferences: u(x,y)= min{80x,40y} Find the optimal values of x...
2. Consider a utility function that represents preferences: u(x,y)= min{80x,40y} Find the optimal values of x and y as a function of the prices px and py with an income level m. (5)
Question 7 In Problems 5 - 7, you are given the utility function u(x, y), income...
Question 7
In Problems 5 - 7, you are given the utility function u(x, y), income I and two sets of prices: initial prices px,py and final prices p,%-For each problem, you are to find: (a) the optimal choice at the initial prices (b) the optimal choice at the final prices (c) the change- optimal choice at final prices - optimal choice at initial prices (d) the income effect and the substitution effect 5) u(x, y)-min(x, 3y), 1-14, p.-1, p,-2....
u(x,y)= x+3y,INCOME=12;px =1,py =2;p′x =1,p′y =4 initial prices px,py and final prices p′x,p′y. For THE problem,...
u(x,y)= x+3y,INCOME=12;px =1,py =2;p′x =1,p′y =4 initial prices px,py and final prices p′x,p′y. For THE problem, you are to find: (a) the optimal choice at the initial prices (b) the optimal choice at the final prices (c) the change = optimal choice at final prices - optimal choice at initial prices (d) the income effect and the substitution effect
You have preferences described by u(x,y)=2x+7y. Your income is I and prices are px =1, py...
You have preferences described by u(x,y)=2x+7y. Your income is I and prices are px =1, py =4. a) Decompose the effect of a change in the price of px from 1 to 3 into an Income and Substitution Effect for x and y. Note: Unless specified otherwise, you can assume that the price of the other good remains unchanged, i.e. here the price of y remains unchanged at 4. b) Suppose the government gives you enough income so that you...
Suppose the preferences of an individual are represented by a quasilinear utility function: U (x, y)...
Suppose the preferences of an individual are represented by a quasilinear utility function: U (x, y) = ln(x) + y (a)Suppose px =1, py =5 and I = 20. The price of x increases to 2 (px = 2). Calculate the changes in the demand for x. What can you say about the substitution and income effects for small changes in the price of x? What happens to the demand for y? Is y a gross substitute? (b)Now suppose px...
Question 6 6 In Problems 5 - 7, you are given the utility function u(x, y),...
Question 6
6
In Problems 5 - 7, you are given the utility function u(x, y), income I and two sets of prices: initial prices px,py and final prices p,%-For each problem, you are to find: (a) the optimal choice at the initial prices (b) the optimal choice at the final prices (c) the change- optimal choice at final prices - optimal choice at initial prices (d) the income effect and the substitution effect 5) u(x, y)-min(x, 3y), 1-14, p.-1,...
4. Andy's utility is represented by the function U(X,Y) - XY. His marginal utility of X is MUx = Y. His marginal utility of Y is MUY = . He has income $12. When the prices are Px - 1 and Py -1, Andy's optimal consumption bundle is X* -6 and Y' = 6. When the prices are Px = 1 and P, = 4, Andy's optimal consumption bundle is X** = 6 and Y* 1.5. Suppose the price of...
In Problems 5 - 7, you are given the utility function u(x, y), income I and two sets of prices: initial prices px,py and final prices p,%-For each problem, you are to find: (a) the optimal choice at the initial prices (b) the optimal choice at the final prices (c) the change- optimal choice at final prices - optimal choice at initial prices (d) the income effect and the substitution effect 5) u(x, y)-min(x, 3y), 1-14, p.-1, p,-2. p,-2, p,-2
2. Consider a utility function that represents preferences: u(x,y)= min{80x,40y} Find the optimal values of x and y as a function of the prices px and py with an income level m. (5)
Question 7
In Problems 5 - 7, you are given the utility function u(x, y), income I and two sets of prices: initial prices px,py and final prices p,%-For each problem, you are to find: (a) the optimal choice at the initial prices (b) the optimal choice at the final prices (c) the change- optimal choice at final prices - optimal choice at initial prices (d) the income effect and the substitution effect 5) u(x, y)-min(x, 3y), 1-14, p.-1, p,-2....
Question 6
6
In Problems 5 - 7, you are given the utility function u(x, y), income I and two sets of prices: initial prices px,py and final prices p,%-For each problem, you are to find: (a) the optimal choice at the initial prices (b) the optimal choice at the final prices (c) the change- optimal choice at final prices - optimal choice at initial prices (d) the income effect and the substitution effect 5) u(x, y)-min(x, 3y), 1-14, p.-1,...
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