Suppose x represents weekly meat consumption and y represents
weekly vegetables consumption. Their prices are px and py. Paul’s
utility function is U1(x,y) = x2y3 and
Peter’s utility function is U2(x,y) = 2x + 3y. Please
a. Derive the MRS for both at the bundle (1,1) respectively.
(4pts)
b. Are their MRS the same at (1,1)? Explain the economic
interpretation of this MRS value at (1,1).
Suppose x represents weekly meat consumption and y represents weekly vegetables consumption. Their prices are px...
Consider a consumer whose income is 100 and his preference is given by U-10x04yo6. If PX-Py-1, what is the optimal consumption bundle by the consumer? (Please write out the constraint utility maximization problem completely, including the budget function.) Derive the demand of Good X and Y by this consumer. (The result should be a function giving you the amount of X he will buy at every given price level Px, and a function for good Y as well.) a. 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*.
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...
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...
Sally consumes two goods, X and Y. Her preferences over consumption bundles are repre- sented by the utility function r, y)- .5,2 where denotes the quantity of good X and y denotes the quantity of good Y. The current market price for X is px 10 while the market price for Y is Pr = $5. Sally's current income is $500. (a) Write the expression for Sally's budget constraint. (1 point) (b) Find the optimal consumption bundle that Sally will...
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*.
Dafna’s utility function for weekly consumption of apples (X) and bananas (Y) is given by U = 3XY. a. Derive equations for Dafna’s demand functions for X and Y. b. Draw a diagram of Dafna’s demand curve for apples (X) when PY = 2.5 and M = 100. c. Dafna always spends the same fraction of her budget on apples, no matter what the prices. What fraction is that? Explain. (Hint: Use the demand functions from part a.)
can someone explain this step
by step? especially don't understand how they got m/px? why we
can't use the lagrange. and not sure how they drew the graph for
this question. SOMEONE PLEASE HELP MIDTERM SOON AND WILL GIVE BIG
THUMBS UP!!!! confused where 4x20+5x0 is coming from
Problem 4 Eric's preferences for goods x and y are represented by the following utility function: U(X,Y) = 4X +5Y. The price of good X is px = 2 and the price...
Suppose an individual’s utility function for two goods X and Y is givenby U(X,Y) = X^(3/4)Y^(1/4) Denote the price of good X by Px, price of good Y by Py and the income of the consumer by I. a) (2 points) Write down the budget constraint for the individual. b) (4 points) Derive the marginal utilities of X and Y. c) (3 points) Derive the expression for the marginal rate of substitution of X for Y. Write down the tangency...
U = (x – x0)^α ⋅ (y – y0)^β, where x0, y0 are constants, best interpreted as minimum consumption quantities, and α + β = 1. Goods prices are given by px and py. Derive the demand functions for x and y. Derive the indirect utility function V(px,py,I). Derive the expenditure function E(px,py,U).