1. (5 pts.) If U X13y23, M 120, Px-2, and Py-10, find the utility-maximizing combination of...
Given a utility function U=(x+2)(y+1) and Px = 4, Py = 6, and budget B = 130: a) Write the Lagrangian function; b) Find the optimal levels of purchases x* and y*; c) Is the second-order sufficient condition for maximum satisfied?
U(X,Y) = 10X^2 Y, Px =$25, Py=$5 Income= 1500 what combination of X and Y will maximize utility
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*.
Your friend has the following utility unction: U(X,Y) = 10 X + 40 Y – X2- 3Y2 Where X is her consumption of Redbox movies, with price Px = $1, and Y is her consumption of iTunes, with Py = $2. Income is 48 dollars. a. Using the Lagrangian approach, derive your friend’s demand equations for Redbox movies and iTunes. That is, find X and Y. (Hint: Substitute the budget constraint in the Lagrangian problem using the given prices and...
Name 1. (3 pts.) Draw the budget lines representing the following information. In each case identify the numerical value of the intercepts of the budget line and the slope. a. Initially assume: M-150, P 3, Py-5.Redraw the budget line on the same graph assuming l 90, P 3, Py 5 b. Initially assume: M- 150, Px 3, Py 5. Redraw the budget line assuming Px rose to $6 c. Initially assume: M : 150, Px-3, P,-5, Redraw the budget line...
Complete parts a-e.
1. Consider the following (Cobb-Douglas) utility function: U = xayB And budget constraint: MZ PeX+PY *Treat Px, P, M, a, and B as positive constants. Note, a + B < 1. Using these equations, please answer the following questions: a. Formally state this consumer's utility maximization problem and write down the relevant Lagrangian. (6 pts) b. Using your work from part "a.", derive demand curves for X and Y. Show all work. (6 pts) C. Show that...
1.2 (10 mks each). In parts a) and b) below, assume px = $1, py = $5, I = income = $21. Solve the U-max problem for each of the following two utility functions: (a) U = xy?, x, y = 0; (b) U=x1/3y2/3, x, y 2 0; (c) now, let px = p, Py = $5, 1 = $21, find the u-max solution for U = xy?, x, y = 0; (d) let px = 1, Py = p,...
(a) 1.2 (10 mks each). In parts a) and b) below, assume px = $1, Py = $5, I = income = $21. Solve the U-max problem for each of the following two utility functions: U= xy?, x, y 2 0; (b) U = x1/3y2/3, x, y = 0; now, let px = P, Py = $5, I = $21, find the u-max solution for U = xy?, x, y 2 0; let px = 1, Py =p, I =...
4. Let the household utility function be given by U(x,y) = Vxy. a. Find the marginal utilities of X and Y and write the expression for the marginal rate of substitution between X and Y. b. Let I = $100, Px = $10 and Ry = $10 be the set of prices and income. Find the utility maximizing combination of X and Y given the prices and income. c. What is the level of utility of the chosen bundle of...
Suppose you have the following utility function U(X.,Y)-min{2X,Y} Let's assume you have $80 to spend between goods X and Y and the prices are Px 2 and Py -4 Find the utility maximizing consumption level of X and Y. Please show all your work and provide explanations.