1.2 (10 mks each). In parts a) and b) below, assume px = $1, py =...
(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 =...
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.
Consumer Theory 13 Ordinary Goods 1. Let U(x, y) = x2/3743, MU2 = 173 MUY = 2 x 5 Pa = 6, Py = 3, and M = 30. 2. Let U(x, y) = x2/3y1/3, MUX 17, MUY Px = 6, Py = 3, and M - 30. 3. Let U(x, y) = 2x1/3y2/3, MU, = 2 21/a, Px = 6, Py = 3, and M = 30. 4. Let U(x, y) = 2x4 3y1/3, MUx = * * 78,...
1. (5 pts.) If U X13y23, M 120, Px-2, and Py-10, find the utility-maximizing combination of X and Y using the Lagrangian multiplier. Also find the MRS and the ratio of the prices at the utility-maximizing combination. Show your work on a separate page. a. Units of X b. Units of Y c. MRS d. Px/Py
py = $1 ACE Problem 1 (25 marks) BI LET A consumer buys two goods, good X and a composite good Y. The utility function is given as ELLE DEMO U(X,Y) = XY + X. 1=$10 Px = $0.5 Where I is income level, Px is the price of good X EL ele 1) Find the optimal basket that maximizes utility and calculate its corresponding utility level.(5 marks) 2) Show your answer for Questions (1) on a graph. ( 5...
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*.
3. If the utility is given by U(X,Y)= X +4Y and px = 1, the indirect utility is given by PY I (a) 4py I (b) py 41 (c) рү 21 (d) py
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?
Derive indirect utility function when facing Px, Py and I; from the below (direct) utility from consumption of x and y: U(x,y)=x^0.5+y^0.5 Why do we bother calculating the indirect utility function? Briefly explain.
u(x,y)= x+3y,INCOME=12;px =1,py =2;p′x =1,p′y =4 initial prices px,py and final prices p′x,p′y. For THE problem, you are to find: (a) the optimal choice at the initial prices (b) the optimal choice at the final prices (c) the change = optimal choice at final prices - optimal choice at initial prices (d) the income effect and the substitution effect