suppose you are at a bundle, such that MRS>MRT, how should you change your consumption so...
suppose you are at a bundle, such that MRS>MRT, how should you change your consumption so as to maximize utility subject to your budget constraint?
Homework Answers
Utility is maximized when MRS = MRT. MRS is the slope of the budget line and MRT is the slope of the budget constraint. If MRS > MRT then indifference curve is steeper than the budget line so to maximize utility, more of good X and less of good Y should be consumed so that MRS decreases and becomes equal to MRT. This will cause indifference curve to become flatter and become tangent to the budget line thus maximizing utility.
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suppose you are at a bundle, such that MRS>MRT, how should
you change your consumption so...
Your utility function over the goods X and Z takes the following form: You want to...
Your utility function over the goods X and Z takes the following form: You want to maximize your utility subject to your budget constraint. Assume that the price of X is $3 per unit and the price of Z is $6 per unit, and that the total income you have to spend on X and Z is $720. The consumption bundle that will maximize your utility subject to your budget constraint is X 240 and Z 0 (enter only numbers...
Question 5 4 pts Your utility function over the goods X and Z takes the following...
Question 5 4 pts Your utility function over the goods X and Z takes the following form: You want to maximize your utility subject to your budget constraint. Assume that the price of X is $3 per unit and the price of Z is $6 per unit, and that the total income you have to spend on X and Z is $720 The consumption bundle that will maximize your utility subject to your budget constraint is X- 240 and Z-0...
how did they get MRS= -x2/x1? Consider the utility function u ( 2 2) = Inc. +Inc. Suppose that the initial situation...
how
did they get MRS= -x2/x1?
Consider the utility function u ( 2 2) = Inc. +Inc. Suppose that the initial situation s given by Pi = 1, P2 = 2 and m = 100. Note that MU = 1 and MU2 = a) Find the consumer's optimal consumption bundle (0,2) and his utility at this consumption bundle. Solution: The budget line is 2.02 = 100 - 21 (1) Since the optimal bundle is an interior point, the tangency condition...
D Question 6 4 pts As in question 5, your utility function over the goods X...
D Question 6 4 pts As in question 5, your utility function over the goods X and Z takes the following form: You want to maximize your utility subject to your budget constraint. Assume again that the price of X is $3 per unit and the price of Z is $6 per unit, but that owing to a new government welfare program, the total income you have to spend on X and Z is $900 instead of $720. The consumption...
1. (24 total points) Suppose a consumer’s utility function is given by U(X,Y) = X1/2*Y1/2. Also,...
1. (24 total points) Suppose a consumer’s utility function is given by U(X,Y) = X1/2*Y1/2. Also, the consumer has $72 to spend, and the price of Good X, PX = $4. Let Good Y be a composite good whose price is PY = $1. So on the Y-axis, we are graphing the amount of money that the consumer has available to spend on all other goods for any given value of X. a) (2 points) How much X and Y...
As in the previous two questions, your utility function over the goods X and Z takes...
As in the previous two questions, your utility function over the goods X and Z takes the following Suppose now that the government wants to discourage consumption of X. It places a tax on X such that the price consumers now face is $4 per unit instead of $3 per unit. Assume that the price of Z remains at $6 per unit and that your income is $900. The consumption bundle that will now maximize your utility subject to your...
Each individual consumer takes the prices as given and chooses her consumption bundle, (r, 2) R, by maximizing...
Each individual consumer takes the prices as given and chooses her consumption bundle, (r, 2) R, by maximizing the utility function U (r1, T)= In(xr2), subject to the budget constraint pi 1 + p2 2 900 (a) (3 points) Write out the Lagrangian function for the consumer's problem (b) (6 points) Write out the system of first-order conditions for the consumer's problem (e) (6 points) Solve the system of first-order conditions to find the optimal values of r and r2....
Please show all steps so I can fully understand how to solve. Thank you 3. Utility...
Please show all steps so I can fully understand how to
solve. Thank you
3. Utility maximization under constraint, substitution and income effect, CV and EV (20 points) Josh gets utility (satisfaction) from two goods, A and B, according to the utility function U(A,B) = 5A/B/. While Luke would like to consume as much as possible he is limited by his income. a. Maximize Josh's utility subject to the budget constraint using the Lagrangean method. b. Suppose PA increase. Show...
2) Chimichanga Fest Your utility function is given by U-X,X, where xi s your consumption of Chimichangas and x, is your consumption of all the other goods in the economy. Yes, you spend 60% of...
2) Chimichanga Fest Your utility function is given by U-X,X, where xi s your consumption of Chimichangas and x, is your consumption of all the other goods in the economy. Yes, you spend 60% of your budget on Chimichangas, which is totally reasonable after the Dumpling House tragedy. a) Solve the utility maximization problem, finding the uncompensated demand for x, & x, and the indirect utility function in terms of p,, p, and Y. b) Solve the expenditure minimization problem,...
1. Suppose that the price of oranges is $1 per unit and the price of pencils...
1. Suppose that the price of oranges is $1 per unit and the price of pencils is $70 per unit. In addition, suppose that your income is $1900. If you spend all your money on oranges, how many oranges can you buy? 1900 oranges 2. The table below shows total utility for two products. Suppose that the price for product A is $5 and the price for product B is $5. Number of product A Total Utility for A Number...
Your utility function over the goods X and Z takes the following form: You want to maximize your utility subject to your budget constraint. Assume that the price of X is $3 per unit and the price of Z is $6 per unit, and that the total income you have to spend on X and Z is $720. The consumption bundle that will maximize your utility subject to your budget constraint is X 240 and Z 0 (enter only numbers...
Question 5 4 pts Your utility function over the goods X and Z takes the following form: You want to maximize your utility subject to your budget constraint. Assume that the price of X is $3 per unit and the price of Z is $6 per unit, and that the total income you have to spend on X and Z is $720 The consumption bundle that will maximize your utility subject to your budget constraint is X- 240 and Z-0...
how
did they get MRS= -x2/x1?
Consider the utility function u ( 2 2) = Inc. +Inc. Suppose that the initial situation s given by Pi = 1, P2 = 2 and m = 100. Note that MU = 1 and MU2 = a) Find the consumer's optimal consumption bundle (0,2) and his utility at this consumption bundle. Solution: The budget line is 2.02 = 100 - 21 (1) Since the optimal bundle is an interior point, the tangency condition...
D Question 6 4 pts As in question 5, your utility function over the goods X and Z takes the following form: You want to maximize your utility subject to your budget constraint. Assume again that the price of X is $3 per unit and the price of Z is $6 per unit, but that owing to a new government welfare program, the total income you have to spend on X and Z is $900 instead of $720. The consumption...
As in the previous two questions, your utility function over the goods X and Z takes the following Suppose now that the government wants to discourage consumption of X. It places a tax on X such that the price consumers now face is $4 per unit instead of $3 per unit. Assume that the price of Z remains at $6 per unit and that your income is $900. The consumption bundle that will now maximize your utility subject to your...
Each individual consumer takes the prices as given and chooses her consumption bundle, (r, 2) R, by maximizing the utility function U (r1, T)= In(xr2), subject to the budget constraint pi 1 + p2 2 900 (a) (3 points) Write out the Lagrangian function for the consumer's problem (b) (6 points) Write out the system of first-order conditions for the consumer's problem (e) (6 points) Solve the system of first-order conditions to find the optimal values of r and r2....
Please show all steps so I can fully understand how to
solve. Thank you
3. Utility maximization under constraint, substitution and income effect, CV and EV (20 points) Josh gets utility (satisfaction) from two goods, A and B, according to the utility function U(A,B) = 5A/B/. While Luke would like to consume as much as possible he is limited by his income. a. Maximize Josh's utility subject to the budget constraint using the Lagrangean method. b. Suppose PA increase. Show...
2) Chimichanga Fest Your utility function is given by U-X,X, where xi s your consumption of Chimichangas and x, is your consumption of all the other goods in the economy. Yes, you spend 60% of your budget on Chimichangas, which is totally reasonable after the Dumpling House tragedy. a) Solve the utility maximization problem, finding the uncompensated demand for x, & x, and the indirect utility function in terms of p,, p, and Y. b) Solve the expenditure minimization problem,...
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