Q10) U(x1 , x2 , x3, x4) = x12x2 + x32x4
At (x1,x2,x3,x4) = (1,2,1,4) = 1*2 + 1*4 = 6
Q11)
U = x1*x2
MRS = Marginal Rate of Substituion = -MUx1/MUx2 = -(dU/dx1)/(dU/dx2) = -x2/x1
At (x1,x2) = (4,20)
MRS(4,20) = -20/4 = -5
Matt's utility over consumption of goods 1, 2, 3, and 4 is given by +(+1, 12,...
18. (20 points) Matt's utility is given by u(x,,x2) - minfx,, x2) + minfx3, x4 Which of the following four bundles (A, B, C, and D) will he most prefer? Bundles are written (x.x2,x3,x4) a. A b. B (2, 2, 2, 2) (6, 0, 0, 2) d. D (6,1,3, 1 af(x,y,z) 19. If f(x, y.z) 3x2 + 2xyz +8y*z + Vž, find o 692when x - 1. y 2, z 3 20. If u(x1, x2) -8x1 + 4x2, find the...
4. Suppose the utility function is given by U(z1,x2) - (x^"2)*. Calculate the optimal consumption bundle 2.5 4 if Ann's income equals 10 and both goods have a price of 1.
how did they get MRS= -x2/x1? Consider the utility function u ( 2 2) = Inc. +Inc. Suppose that the initial situation s given by Pi = 1, P2 = 2 and m = 100. Note that MU = 1 and MU2 = a) Find the consumer's optimal consumption bundle (0,2) and his utility at this consumption bundle. Solution: The budget line is 2.02 = 100 - 21 (1) Since the optimal bundle is an interior point, the tangency condition...
4. consider the following utility functions a) for each of these utility function what is the equation of an indifference curve ? c) for each utility function show weather the function exhibits the diminishing rate of substitution property d) do the above utility function represent the same preference ordering? why or why not? c) Suppose the price of beer doubles, but the price of pizza and Tom's income stay the same. How much beer is Tom consuming as a percentage...
19. If f(x, y, z) = 4x2 + 3xyz + 2y3z + Vz, find the value of °(3.) Y2) when x = 1, y=2, z= 3. дх 20. If u(x1, x2) = 18x1 + 3x2, find the value of MRS(8,13). (Don't forget to include a minus sign when entering your answer!) unit unit unit 21. Bryan consumes only goods 1, 2, and 3 (in quantities X1, X2, and xz respectively) and as preferences over (X1, X2, X3) bundles that are...
1) Eor each of the utility functions below, find the optimal consumption bundle if pi-3 and p2-2 and m-240 a. u(x)-2x2 b. u(x)-xix22 c. d, e. u(x)- 2x1+X2 u(x)-min(x1,2%) u(x)-x1-X22 y(x)-max(x1,x2) X(X1,X2 2) Suppose p1-2, p2-7 for the first 2 units and p2 4 for the rest. a) Ifm-54 and u(x) -X1+3x2, then what is the optimal consumption bundle? b) Ifm-22 and u(x) - min(3xı, 2x2), , thenwhat is the optimal consumption bundle? Erom Workouts: 5.3,5.6,5.7 3)
) A consumer's utility function is given by: U(x,y) = 10xy Currently, the prices of goods x and y are $3 and $5, respectively, and the consumer's income is $150 . a. Find the MRS for this consumer for any given bundle (x,y) . b. Find the optimal consumption bundle for this consumer. c. Suppose the price of good x doubles. How much income is required so that the Econ 201 Beomsoo Kim Spring 2018 consumer is able to purchase...
Is the answer to part (a) 2/3 or 1/2? 1. Alice enjoys consuming goods z and y. Where (x, y) is the consumption bundle and 0 < a < 1, Alice's utility is: u(z, y) -zy- (a) Originally, Alice has income m 16, and faces prices p Py1, and consumes a bundle at which her utility (subject to her budget) is maximised. Then, py rises to 4. Alice is sadder with the new bundle she chooses, and tells you that...
10. If u(x1,x2) = 44x{x}, what is the value of MRS(1, 6)? (Don't forget to include the minus sign when entering your answer!)
2) Chimichanga Fest Your utility function is given by U-X,X, where xi s your consumption of Chimichangas and x, is your consumption of all the other goods in the economy. Yes, you spend 60% of your budget on Chimichangas, which is totally reasonable after the Dumpling House tragedy. a) Solve the utility maximization problem, finding the uncompensated demand for x, & x, and the indirect utility function in terms of p,, p, and Y. b) Solve the expenditure minimization problem,...