Homework Answers
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
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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...
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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...
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...
19. If f(x, y, z) = 4x2 + 3xyz + 2y3z + Vz, find the value...
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1) Eor each of the utility functions below, find the optimal consumption bundle if pi-3 and...
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4. consider the following utility functions a) for each of these utility function what is the equation of an indifferenc...
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...
Is the answer to part (a) 2/3 or 1/2? 1. Alice enjoys consuming goods z and...
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...
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!)
Gloria likes watching movies (x1) and listen to her favorite songs(x2). Her utility function is given...
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(10 points) Wendy's utility over consumption bundles (x1, x2) is given by u(x1,x2) = VX1 +...
(10 points) Wendy's utility over consumption bundles (x1, x2) is given by u(x1,x2) = VX1 + 21X2. If the price of good 1 is $2/unit, the price of good 2 is $1/unit and income is $120, what is Wendy's optimal consumption of Good 2? (You can use the 5 step method to solve this problem). (10 points) When u(x1, x2) = min ), at prices and income P1, P2, and I, demand for good 1 is given by xi (P1,...
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...
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)
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...
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!)
(10 points) Wendy's utility over consumption bundles (x1, x2) is given by u(x1,x2) = VX1 + 21X2. If the price of good 1 is $2/unit, the price of good 2 is $1/unit and income is $120, what is Wendy's optimal consumption of Good 2? (You can use the 5 step method to solve this problem). (10 points) When u(x1, x2) = min ), at prices and income P1, P2, and I, demand for good 1 is given by xi (P1,...
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