What is and MRS for this utility maximization u1(q, r, x, y) = min{qr, xy} where w=12, py=2, Pric...

Question

Question

what is and MRS for this utility maximization u1(q, r, x, y) = min{qr, xy} where w=12, py=2, Price of q=1 price of x=2 and price of r =1

Answer 1

Answer #1

MRS is defined as the slope of the untility function, hence the production function should be differentiable to find the MRS .

Thus when utility function is of Leontieff type, so it is not differentiable, hence MRS doesn't exist for this utility function

Answer 2

Similar Homework Help Questions

What is the utility maximization for u1(q, r, x, y) = min{qr, xy} where w=12, py=2, Price of q=1 ...

what is the utility maximization for u1(q, r, x, y) = min{qr, xy} where w=12, py=2, Price of q=1 price of x=2 and price of r =1
Utility maximization with more than two goods Suppose that there four goods Q, R, X and Y , avail...

Utility maximization with more than two goods Suppose that there four goods Q, R, X and Y , available in arbitrary non-negative quantities (so the the consumption set is R 4 +). A typical consumption bundle is therefore a vector (q, r, x, y), where q ≥ 0 is the quantity of good Q, r ≥ 0 is the quantity of good R, x ≥ 0 is the quantity of good X, and y ≥ 0 is the quantity of...
A) Suppose U = min[X, 3Y] and I=12, Px=1 and Py=5. Find X* and Y*. B) Draw an indifference curve and a normal linear budget constraint such that there is a tangency point (where MRS= price ratio) that...

A) Suppose U = min[X, 3Y] and I=12, Px=1 and Py=5. Find X* and Y*. B) Draw an indifference curve and a normal linear budget constraint such that there is a tangency point (where MRS= price ratio) that is not the optimal bundle. C) Suppose U=X∙Y5. Find X* and Y*. D) Suppose U = 5∙X + 2∙Y and I=12, Px=2 and Py=1. Find X* and Y*.

1. U = XY where MRS = Y/X; I = 1500, Px = Py = 15,...

1. U = XY where MRS = Y/X; I = 1500, Px = Py = 15, A. Derive optimal consumption bundle. B. If Px increases to be $30, derive the new optimal consumption bundle C. Using the results from A and B, derive the individual demand for good X assuming the demand is linear. 2. Assuming the market has two consumers for a very special GPU and their individual demands are given below Consumer A: P = 450 – 4...
A) Suppose U = min[X, 3Y] and I=12, Px=1 and Py=5. Find X* and Y*. B)...

A) Suppose U = min[X, 3Y] and I=12, Px=1 and Py=5. Find X* and Y*. B) Draw an indifference curve and a normal linear budget constraint such that there is a tangency point (where MRS= price ratio) that is not the optimal bundle. C) Suppose U=X∙Y5. Find X* and Y*. D) Suppose U = 5∙X + 2∙Y and I=12, Px=2 and Py=1. Find 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...

A) Let utility over 2 goods be defined as U(x,y)=x+xy+y. Find the MRS by implicitly solving...

A) Let utility over 2 goods be defined as U(x,y)=x+xy+y. Find the MRS by implicitly solving for y (hint: set U=k) and calculate -dy/dx. B) Now find the MRS by using MRS =Ux/Uy.
Anna's utility function is given by U (r.y) = (r + 3) (y + 2), where...

Anna's utility function is given by U (r.y) = (r + 3) (y + 2), where I and y are the two goods she consumes. The price of good r is p ,. The price of good y is Py. Her income is m. (a) Write her maximization problem and find her demand functions for the two goods. Is it always possible to have an interior solution? Justify your answer. (b) Are the two goods ordinary or giffen? Are the...
Utility Maximization with Substitutes Carol needs to decide how to spend her wealth on fish and...

Utility Maximization with Substitutes Carol needs to decide how to spend her wealth on fish and chicken. For Carol, 1 lb of fish is equivalent to 2 lb of chicken. Her preferences can be represented by the utility function u(x, y) = 2x +y where x is the quantity of fish (in lbs) and y is the quantity of chicken (in lbs). The consumption set is R 2 +. (a) Draw two typical indifference curves for Carol, one corresponding to...

Given a utility function U(x,y) = xy. The price of x is Px, while the price of y is Py. The income is I. Suppose at period 0, Px = Py = $1 and income = $8. At period 1, price of x (Px) is changed to $4. Compute the price effect, substitution effect, and

Given a utility function U(x,y) = xy. The price of x is Px, while the price of y is Py. The income is I. Suppose at period 0, Px = Py = $1 and income = $8. At period 1, price of x (Px) is changed to $4. Compute the price effect, substitution effect, and income effect for good x from the price change.