Question

In: Economics

The utility that Jane receives by consuming good X and good Y is given by u(X,Y)...

The utility that Jane receives by consuming good X and good Y is given by u(X,Y) = XY.

5.1) Draw the indifference curve associated with a utility level of 12 and the indifference curve associated with the utility level of 36.

5.2) Suppose that X costs $1 per unit and Y $3 per unit. Jane has $12 to spend on X and Y. Graph the budget line that she faces.

5.3) Derive Jane’s demand functions. What is the utility-maximizing choice of X and Y (solve the problem both mathematically and graphically).

5.4) What is the marginal rate of substitution of X for Y when utility is maximized? Give a concise explanation of the meaning of the marginal rate of substitution.

5.5) Suppose Jane buys 3 units of X and 3 units of Y with her $12 budget. What is her MRS of X for Y? What is she willing to do to have her MRS equal to the price ratio?

5.6) Suppose the price of X increases to $2, X=3 and Y=3. How much extra income does the agent need to compensate her for the price rise, so that the original bundle is affordable?

Solutions

Expert Solution


Related Solutions

The utility that James receives by consuming good X and good Y is given by u(X,Y)...
The utility that James receives by consuming good X and good Y is given by u(X,Y) = XY. 5.1) Draw the indifference curve associated with a utility level of 12 and the indifference curve associated with the utility level of 36. 5.2) Suppose that X costs $1 per unit and Y $3 per unit. James has $12 to spend on X and Y. Graph the budget line that he faces. 5.3) Derive James' demand functions. What is the utility-maximizing choice...
Assume that Roberts’s utility from consuming good X and good Y is given by the following...
Assume that Roberts’s utility from consuming good X and good Y is given by the following function: U = 5X0.2Y0.8 Where X is the quantity of good X while Y is the quantity of good Y. Assume the price of X (PX) is £5, the price of Y (PY) is £8 and he has a budget of £100 to spend on the two goods. Using the Lagrangian multiplier, calculate the quantities of good X and good Y Robert should purchase...
Suppose a consumer's utility function is given by U ( X , Y ) = X...
Suppose a consumer's utility function is given by U ( X , Y ) = X 1 2 Y 1 2. The price of X is PX=8 and the price of Y is PY=5. The consumer has M=80 to spend. You may find that it helps to draw a graph to organize the information in this question. You may draw in the blank area on the front page of the assignment, but this graph will not be graded. a) (2...
Given the utility function U ( X , Y ) = X 1 3 Y 2...
Given the utility function U ( X , Y ) = X 1 3 Y 2 3, find the absolute value of the MRS when X=10 and Y=24. Round your answer to 4 decimal places.
Assume diminishing marginal utility in good X and Y. Leigh is currently consuming 4 units of...
Assume diminishing marginal utility in good X and Y. Leigh is currently consuming 4 units of X and 4 units of Y. At these levels of consumption, the marginal utility of a unit of X is 10 utils and the marginal utility of a unit of Y is 10 utils. The price of good X is $1 and the price of good Y is $2. According to our consumer equilibrium condition, which of the following is true? Question 3 options:...
A consumes two goods, x and y. A ’s utility function is given by u(x, y)...
A consumes two goods, x and y. A ’s utility function is given by u(x, y) = x 1/2y 1/2 The price of x is p and the price of y is 1. A has an income of M. (a) Derive A ’s demand functions for x and y. (b) Suppose M = 72 and p falls from 9 to 4. Calculate the income and substitution effects of the price change. (c) Calculate the compensating variation of the price change....
Suppose a consumer has a utility function given by u(x, y) = x + y, so...
Suppose a consumer has a utility function given by u(x, y) = x + y, so that the two goods are perfect substitutes. Use the Lagrangian method to fully characterize the solution to max(x,y) u(x, y) s.t. x + py ≤ m, x ≥ 0, y ≥ 0, where m > 0 and p < 1. Evaluate and interpret each of the multipliers in this case. What happens to your solution when p > 1? What about when p =...
Suppose Anne’s utility function for food (X) and clothing (Y) is given by U (X,Y) =...
Suppose Anne’s utility function for food (X) and clothing (Y) is given by U (X,Y) = 4X1/2 + Y and Anne had budget constraint I = PxX + PyY. a. Find Anne’s optimal bundle if Px = 4 and Py = 4 and Anne has I = 60. b. Discuss how the demand for X depends on her income. c. Suppose now that the price of X increases to 8. Find the SE and IE of the price change.
Chepa’s utility function is given by U (x, y) = ln x + 4 ln y....
Chepa’s utility function is given by U (x, y) = ln x + 4 ln y. Assume that Chepa has endowments (10, 10) and that Py = 10 throughout the problem. (h) This part of the question is to investigate Chepa’s welfare under different prices. We will do it step by step. (i) By substituting out the M with the expression of Chepa’s endowment income (see part (g)), obtain Chepa’s gross demands as functions of Px. (ii) Plug your answer...
Jim’s utility function is U(x, y) = xy. Jerry’s utility function is U(x, y) = 1,000xy...
Jim’s utility function is U(x, y) = xy. Jerry’s utility function is U(x, y) = 1,000xy + 2,000. Tammy’s utility function is U(x, y) = xy(1 - xy). Oral’s utility function is -1/(10 + xy. Billy’s utility function is U(x, y) = x/y. Pat’s utility function is U(x, y) = -xy. a. No two of these people have the same preferences. b. They all have the same preferences except for Billy. c. Jim, Jerry, and Pat all have the same...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT