Suppose a consumer has income of $120 per period and faces prices pX = 2 and...
Suppose a consumer has income of $120 per period and faces prices pX = 2 and pZ = 3. Her goal is to maximize her utility, described by the function U = 10X0.5Z0.5. Calculate the utility maximizing bundle (X* , Z* )
Homework Answers
![] C-10x² z ² + x[120-2x-32 6 Px=2 P2=3 I = 120 ah - Llox 1 1 2 -2 = 1) 24 = 1.10x625 - 34 = 0 -- 26 - 120 = 2X +32 . ☺ . 24 D](http://img.homeworklib.com/questions/49fb5f00-2f67-11ea-8955-192d14e4f3fa.png?x-oss-process=image/resize,w_560)
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Suppose a consumer has income of $120 per period and faces prices pX = 2 and...
4. Suppose Dora has an income of $720 per period and faces prices Px-2 and Pz-...
4. Suppose Dora has an income of $720 per period and faces prices Px-2 and Pz- 3. Her goal is to maximize her utility, described by the function U 10X025 Z075. Calculate the utility maximizing bundle (X*, Z*) using the Lagrangian method. Derive the result and show all your work.
Suppose that a consumer has a utility function given by u(x1, x2) = 2x1 + x2. Initially the consumer faces prices (2, 2) and has income 24. i. Graph the budget constraint and indifference curves. Find...
Suppose that a consumer has a utility function given by u(x1, x2) = 2x1 + x2. Initially the consumer faces prices (2, 2) and has income 24. i. Graph the budget constraint and indifference curves. Find the initial optimal bundle. ii. If the prices change to (6, 2), find the new optimal bundle. Show this in your graph in (i). iii. How much of the change in demand for x1 is due to the substitution effect? How much due to...
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...
Question: Consider a consumer with utility function4, income Z, and who faces market prices of p,...
Question: Consider a consumer with utility function4, income Z, and who faces market prices of p, and py (a) Use our optimality condition of MRSy MRTay to find the relationship between x and y which must always be satisfied by a bundle that maximizes the consumer's utility (b) After incorporating the consumer's budget to the problem, calculate the consumer's de- mand for x and y which we will call x(P Z) and y(Py, Z), respectively, because it empha- sizes the...
Suppose a consumer had a utlity function given by U- X04Y02. If the price of Good...
Suppose a consumer had a utlity function given by U- X04Y02. If the price of Good X (Px) is $8 and the price of Good Y is $16 then what is the utility maximizing quantity of Good X the consumer will purchase with a budget of $84? Round to the nearest decimal place if necessary) Answer Suppose an individual had a utility function given by U XY? Suppose that Bundle A contains 5 units of Good X and 5 units...
1.Suppose a consumer had a utility function given by: U= 9X + 2Y. If the price...
1.Suppose a consumer had a utility function given by: U= 9X + 2Y. If the price of Good X (Px) is $8 and the price of Good Y is $4then what is the utility maximizing quantity of Good X the consumer will purchase with a budget of $32? 2. Suppose an individual had a utility function given by: U=X^4Y^0.6 Calculate this individual's Marginal Rate of Substitution (MRSxy) when they have a bundle with 3 units of Good X and 1.8...
Suppose a consumer’s utility function is given by U(X,Y) = X*Y. Also, the consumer has $180...
Suppose a consumer’s utility function is given by U(X,Y) = X*Y. Also, the consumer has $180 to spend, and the price of X, PX = 4.50, and the price of Y, PY = 2 a. How much X and Y should the consumer purchase in order to maximize her utility? b. How much total utility does the consumer receive? c. Now suppose PX decreases to 2. What is the new bundle of X and Y that the consumer will demand?...
2. (24 points) Suppose a consumer has preferences represented by the utility function U(X,Y)- X2Y Suppose...
2. (24 points) Suppose a consumer has preferences represented by the utility function U(X,Y)- X2Y Suppose Py, and the consumer has $300 to spend. Draw the Price-Consumption Curve for this consumer for income values Px-1, Px 2, and Px- 5. Your graph should accurately draw the budget constraints for each income level and specifically label the bundles that the consumer chooses for each income level. Also, for each bundle that the consumer chooses, draw the indifference curve that goes through...
Diogo has a utility function: U = 100X0.8Z0.2 The price of X is Px = $10,...
Diogo has a utility function:
U = 100X0.8Z0.2
The price of X is Px = $10, the price of Z is Pz = $2, and his income is $800.
What is Diogo's optimal bundle? (roundyour answer to one decimal place)
Xo = units
Zo = units
Vasco's utility function is: U = 10x²z The price of X is px = $2, the...
Vasco's utility function is: U = 10x²z The price of X is px = $2, the price of Z is pz = $4, and his income is $60. What is his optimal bundle? (round your answer to two decimal places) X= Z. = units units
4. Suppose Dora has an income of $720 per period and faces prices Px-2 and Pz- 3. Her goal is to maximize her utility, described by the function U 10X025 Z075. Calculate the utility maximizing bundle (X*, Z*) using the Lagrangian method. Derive the result and show all your work.
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...
Question: Consider a consumer with utility function4, income Z, and who faces market prices of p, and py (a) Use our optimality condition of MRSy MRTay to find the relationship between x and y which must always be satisfied by a bundle that maximizes the consumer's utility (b) After incorporating the consumer's budget to the problem, calculate the consumer's de- mand for x and y which we will call x(P Z) and y(Py, Z), respectively, because it empha- sizes the...
Suppose a consumer had a utlity function given by U- X04Y02. If the price of Good X (Px) is $8 and the price of Good Y is $16 then what is the utility maximizing quantity of Good X the consumer will purchase with a budget of $84? Round to the nearest decimal place if necessary) Answer Suppose an individual had a utility function given by U XY? Suppose that Bundle A contains 5 units of Good X and 5 units...
2. (24 points) Suppose a consumer has preferences represented by the utility function U(X,Y)- X2Y Suppose Py, and the consumer has $300 to spend. Draw the Price-Consumption Curve for this consumer for income values Px-1, Px 2, and Px- 5. Your graph should accurately draw the budget constraints for each income level and specifically label the bundles that the consumer chooses for each income level. Also, for each bundle that the consumer chooses, draw the indifference curve that goes through...
Diogo has a utility function:
U = 100X0.8Z0.2
The price of X is Px = $10, the price of Z is Pz = $2, and his income is $800.
What is Diogo's optimal bundle? (roundyour answer to one decimal place)
Xo = units
Zo = units
Vasco's utility function is: U = 10x²z The price of X is px = $2, the price of Z is pz = $4, and his income is $60. What is his optimal bundle? (round your answer to two decimal places) X= Z. = units units
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