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4. Suppose Dora has an income of $720 per period and faces prices Px-2 and Pz-...
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* )
Consider Anne from the previous question with the utility function U = X2Y2 and facing prices...
Consider Anne from the previous question with the utility function U = X2Y2 and facing prices Px and Py and income I. a. Write out the Lagrangian function used for deriving the compensated demand functions. b. Use the Lagrangian method to derive the compensated demand functions. Show your work.
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...
4. Suppose you have the following Cobb-Douglas Utility Function: And $200 to spend. a. Use the...
4. Suppose you have the following Cobb-Douglas Utility Function: And $200 to spend. a. Use the method of Lagrangian Multipliers, to maximize this consumer's utility and derive demand equations for both goods. Sketch their respective demand curves. Show all work. (5 pts) b. If Px = Py = $1, how much utility will the consumer enjoy? Show work/explain. (2.5 pts) c. Does this allocation satisfy the rule of equal marginal utility per dollar spent? Explain/show work. (2.5 pts)
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...
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
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.
1. Sally has preferences represented by the utility function UC, M) = 3 + 61rC M, where C is coffee and M is meals....
1. Sally has preferences represented by the utility function UC, M) = 3 + 61rC M, where C is coffee and M is meals. Her income is S100, and she pays $2 per coffee and S10 per meal a. Distinguish (the concepts of) diminishing marginal rate of substitution from diminishing marginal uty Your answer does not have to be specific to Sally's preferences. (4 points) Use the Lagrangian method to derive Sally's utility maximizing bundle given her budget constraint. Circle...
(Use this information to answer a, b, c below) Suppose Mary’s utility function for two goods...
(Use this information to answer a, b, c below) Suppose Mary’s utility function for two goods X and Y is given by: U(X,Y) = 3X1/2Y1/2 . Suppose consumption bundle A consists of 10 units of X and 30 units of Y, and consumption bundle B consists of 40 units of X and 20 units of Y. a. Consumption bundle A lies on a higher/lower/same indifference curve than consumption bundle B. Show computations. b. Compute Mary’s MRSxy at consumption bundle A....
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 that a fast-food junkie derives utility from three goods-soft drinks (x), hamburgers (y), and ice...
Suppose that a fast-food junkie derives utility from three goods-soft drinks (x), hamburgers (y), and ice cream sundaes (z)-according to the Cobb- Douglas utility function: Suppose also that the prices for these goods are given by Px-1,py-4, and pz-8 and this consumer's income is given by 1-8 If z-0, then the combination of x and y that optimize utility involve x*- utility U and y*- , These values of x* and y result in a level of If z- 1,...
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...
4. Suppose you have the following Cobb-Douglas Utility Function: And $200 to spend. a. Use the method of Lagrangian Multipliers, to maximize this consumer's utility and derive demand equations for both goods. Sketch their respective demand curves. Show all work. (5 pts) b. If Px = Py = $1, how much utility will the consumer enjoy? Show work/explain. (2.5 pts) c. Does this allocation satisfy the rule of equal marginal utility per dollar spent? Explain/show work. (2.5 pts)
1. Sally has preferences represented by the utility function UC, M) = 3 + 61rC M, where C is coffee and M is meals. Her income is S100, and she pays $2 per coffee and S10 per meal a. Distinguish (the concepts of) diminishing marginal rate of substitution from diminishing marginal uty Your answer does not have to be specific to Sally's preferences. (4 points) Use the Lagrangian method to derive Sally's utility maximizing bundle given her budget constraint. Circle...
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 that a fast-food junkie derives utility from three goods-soft drinks (x), hamburgers (y), and ice cream sundaes (z)-according to the Cobb- Douglas utility function: Suppose also that the prices for these goods are given by Px-1,py-4, and pz-8 and this consumer's income is given by 1-8 If z-0, then the combination of x and y that optimize utility involve x*- utility U and y*- , These values of x* and y result in a level of If z- 1,...
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