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23) Solve the following consumption choice between xi and X2, for an individual who has Thayler's...
22) Consider the following consumption choice between x1 and 2 for an individual who has a classical utility functi...
22) Consider the following consumption choice between x1 and 2 for an individual who has a classical utility function (eg, no Thayler's utility). Only consider they are looking for an interior solution. (10pts) U(X, X) = 6x} +8xź MU( x ) = 12x MU(X) = 16X2 Subject to the budget constraint: 1000 = 5.X1 +4. X2 a. Find the optimal consumption bundle. (4 pts) b. Find the utility at this point. (1 pt) C. Show work (5 pts)
The following questions are worth 6 points each. 21) Solve the following utility function to be...
The following questions are worth 6 points each. 21) Solve the following utility function to be optimized. Only consider they are looking for an interior solution: (10pts) U(X1,x2) = 1 ln(x) + 2 In(x2) MU(x)= 1/ MU(X) = 2/2 Subject to the budget constraint: 500 = 2 + xy +4.X2 a. Find the optimal consumption bundle. (4 pts) b. Find the utility at this point. (1 pt) C. Show work (5 pts) u (x,x) = 1 in (X.) + 2...
Lorelai's choice behavior can be represented by the utility function 11(xi, X2) = 0.91n(xi) + 0.1x2...
Lorelai's choice behavior can be represented by the utility function 11(xi, X2) = 0.91n(xi) + 0.1x2 The prices of both x and x2 are $5 and she has an income of $40. 1. What preference does this utility function represent? (Hint: the utility is function is not linear, but at least linear in good x2.) 2. Drawinwg indifference curves: you can copy down the graph on your paper using econgraphs. Set the preferences and parameters accordingly as given in the...
Luke's choice behavior can be represented by the utility function u(x1,x2)= x1 + x2
Luke's choice behavior can be represented by the utility function u(x1,x2)= x1 + x2.The prices of x1 and x2 are denoted as p1 and p2, and his income is m. 1. Draw at least three indifference curves and find its slope (i.e. MRS). Is the MRS changing depending on the points of (x1, x2) at which it is evaluated, or constant? 2. Draw a budget constraint assuming that p1 < P2. Find the optimal bundle (x1*,x2*) as a function of income and prices. 3....
3. There are two goods, Xi and X2 with prices pı > 0 and P2 =...
3. There are two goods, Xi and X2 with prices pı > 0 and P2 = 1. Assume that a consumer has income I> 0 that she will allocate for the bundle (X1, X2), and has preferences represented by the utility function u(X1, X2) = a ln x1 + x2, for some a > 0. (a.) Derive the marginal utilities and bang-for-bucks for each good. (b.) Find the optimal bundle assuming an interior solution, i.e. x > 0 and x...
Cursue a consumer with preferences described by (x1, x2) = x1 + x2 Suppose she faces...
Cursue a consumer with preferences described by (x1, x2) = x1 + x2 Suppose she faces prices pi 1 and P2 = 1/2 and that she has an income of I = 2. For your reference, the marginal utilities at a bundle (x1, x2) in this setting are given by MU (x1, x2) = 1 MU?(x), x2) = 2V x2 3(a) Write down the two equations which characterize the consumer's utility-maximizing bundle (X1.3) in this situation. In other words, write...
Lorelai's choice behavior can be represented by the utility function u(x1, 2) 0.9n(x)0.1x2. The prices of...
Lorelai's choice behavior can be represented by the utility function u(x1, 2) 0.9n(x)0.1x2. The prices of both xi and x2 are $5 and she has an income of $40. 1. What preference does this utility function represent? (Hint: the utility is function is not linear, but at least linear in good x2) 2. Drawinwg indifference curves: you can copy down the graph on your paper using econgraphs. Set the preferences and parameters accordingly as given in the question. Click on...
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...
The utility function of the consumer is u(x1,x2) = (10x1 + x2). a) Plot all the...
The utility function of the consumer is u(x1,x2) = (10x1 + x2). a) Plot all the consumption bundles that gives the consumer utility 100. (3 points) b) Plot all the consumption bundles that gives the consumer utility 144. (3 points) c) Plot the budget constraint when p. = 10,P2 = 10 and m = 100 (3 points) d) Plot the budget constraint when P1 = 20, P2 = 5 and m = 60 (3 points) e) What is the optimal...
My utility is given by u(x1, X2)-240.4X21.2 + 1n(%) + [min{x, xjf + 2x2 + x11.1...
My utility is given by u(x1, X2)-240.4X21.2 + 1n(%) + [min{x, xjf + 2x2 + x11.1 True, False, or Cannot Be Determined: When P1 $2,P2-$4, and I-$100, my optimal consumption bundle is (xi,xż) (25, 15)
22) Consider the following consumption choice between x1 and 2 for an individual who has a classical utility function (eg, no Thayler's utility). Only consider they are looking for an interior solution. (10pts) U(X, X) = 6x} +8xź MU( x ) = 12x MU(X) = 16X2 Subject to the budget constraint: 1000 = 5.X1 +4. X2 a. Find the optimal consumption bundle. (4 pts) b. Find the utility at this point. (1 pt) C. Show work (5 pts)
The following questions are worth 6 points each. 21) Solve the following utility function to be optimized. Only consider they are looking for an interior solution: (10pts) U(X1,x2) = 1 ln(x) + 2 In(x2) MU(x)= 1/ MU(X) = 2/2 Subject to the budget constraint: 500 = 2 + xy +4.X2 a. Find the optimal consumption bundle. (4 pts) b. Find the utility at this point. (1 pt) C. Show work (5 pts) u (x,x) = 1 in (X.) + 2...
Lorelai's choice behavior can be represented by the utility function 11(xi, X2) = 0.91n(xi) + 0.1x2 The prices of both x and x2 are $5 and she has an income of $40. 1. What preference does this utility function represent? (Hint: the utility is function is not linear, but at least linear in good x2.) 2. Drawinwg indifference curves: you can copy down the graph on your paper using econgraphs. Set the preferences and parameters accordingly as given in the...
3. There are two goods, Xi and X2 with prices pı > 0 and P2 = 1. Assume that a consumer has income I> 0 that she will allocate for the bundle (X1, X2), and has preferences represented by the utility function u(X1, X2) = a ln x1 + x2, for some a > 0. (a.) Derive the marginal utilities and bang-for-bucks for each good. (b.) Find the optimal bundle assuming an interior solution, i.e. x > 0 and x...
Cursue a consumer with preferences described by (x1, x2) = x1 + x2 Suppose she faces prices pi 1 and P2 = 1/2 and that she has an income of I = 2. For your reference, the marginal utilities at a bundle (x1, x2) in this setting are given by MU (x1, x2) = 1 MU?(x), x2) = 2V x2 3(a) Write down the two equations which characterize the consumer's utility-maximizing bundle (X1.3) in this situation. In other words, write...
Lorelai's choice behavior can be represented by the utility function u(x1, 2) 0.9n(x)0.1x2. The prices of both xi and x2 are $5 and she has an income of $40. 1. What preference does this utility function represent? (Hint: the utility is function is not linear, but at least linear in good x2) 2. Drawinwg indifference curves: you can copy down the graph on your paper using econgraphs. Set the preferences and parameters accordingly as given in the question. Click on...
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...
The utility function of the consumer is u(x1,x2) = (10x1 + x2). a) Plot all the consumption bundles that gives the consumer utility 100. (3 points) b) Plot all the consumption bundles that gives the consumer utility 144. (3 points) c) Plot the budget constraint when p. = 10,P2 = 10 and m = 100 (3 points) d) Plot the budget constraint when P1 = 20, P2 = 5 and m = 60 (3 points) e) What is the optimal...
My utility is given by u(x1, X2)-240.4X21.2 + 1n(%) + [min{x, xjf + 2x2 + x11.1 True, False, or Cannot Be Determined: When P1 $2,P2-$4, and I-$100, my optimal consumption bundle is (xi,xż) (25, 15)
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