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3. Given a utility function U(x, y) -rys, (a) Show that the marginal rate of substitution,...
3. The following utility function is known as CES (constant elasticity of substi- tution) function where...
3. The following utility function is known as CES (constant elasticity of substi- tution) function where α > 0 β > 0 (a) Is this function homothetic? (b) How does the MRS,y depend on the ratio x/y? Specifically, show that the MRSy is strictly decreasing in the ratio x/y for all values δ < 1, increasing in the ratio x/y for all values δ > 1 and constant for δ 1. (c) Show that if x = y, the MRS...
Suppose you have following utility function :U(x,y)=(x + yaja where x >0, y>0 and a 70, a <1 The price of comm...
Suppose you have following utility function :U(x,y)=(x + yaja where x >0, y>0 and a 70, a <1 The price of commodity x is P >0 and the price of good y is P, > 0. Let us denote income by M, with M>0 a) Compute the marginal utilities of X and Y. b) Write down the utility maximization problem and corresponding Lagrangian function. c) Solve for optimal bundle, X* and y* as a function of Px, Py, and M.
QUESTION; Given Biwei’s utility function U=4XY, where X is consumption of beer and Y is consumption...
QUESTION; Given Biwei’s utility function U=4XY, where X is consumption of beer and Y is consumption of pizza. For this utility function, the marginal utility of X is MUx = 4Y; the marginal utility of Y is MUY = 4X. 1) Suppose Y = 3. Calculate Biwei’s utility for X = 2, 3, 10, and 11. For a given level of Y, does good X display diminishing marginal utility? 2) Suppose X = 3. Calculate Biwei’s utility for Y =...
4. Consider the utility function U(x,y) -Iny (a) Find the marginal rate of substitution, MRS of...
4. Consider the utility function U(x,y) -Iny (a) Find the marginal rate of substitution, MRS of this function. Interpret the result (b) Find the equation of the indifference curve for this function (c) Compare the marginal utility of x and y. How do you interpret these functions? How might a consumer choose between z and y as she tries to increase utility by, for example, consuming more when their income increases?
Suppose that a consumer's utility function is u(x, y) = x, defined for all bundles such...
Suppose that a consumer's utility function is u(x, y) = x, defined for all bundles such that x > 0 and y > 0. For any given positive level of utility, the corresponding indifference curve is O strictly convex. a vertical line. O a horizontal line. a line that is neither horizontal nor vertical.
Joe has a utility function given by u(x, y) = x^ 2 + 2xy + y^...
Joe has a utility function given by u(x, y) = x^ 2 + 2xy + y^ 2 a. Compute Joes marginal rate of substitution, MRS(x, y). b. Joe’s cousin, Alex, has a utility function v(x, y) = x+y. Compute Alex’s marginal rate of substitution, MRS(x, y). c. Do u(x, y) and v(x, y) represent the same preferences?
Suppose utility is given by the following function: u(x, y) = xy3 Use this utility function...
Suppose utility is given by the following function: u(x, y) = xy3 Use this utility function to answer the following questions: (d) What is the marginal rate of substitution implied by this utility function? What does this mean in words? (e) How much of each good would this individual need to have to be willing to trade 1 unit of good x for 1 unit of good y (i.e. for the MRS to be equal to 1)? (f) Suppose we...
4. Consider the utility function U(x, y) = x + ln y. (a) Find the marginal...
4. Consider the utility function U(x, y) = x + ln y. (a) Find the marginal rate of substitution, MRS of this function. Interpret the result (b) Find the equation of the indifference curve for this function (c) Compare the marginal utility of x and y. How do you interpret these functions? How might a consumer choose between x and y as she tries to increase utility by, for example, consuming more when their income increases?
Consider a utility function u(x,y) = Xayb, where 0くaく1 and 0 < b 〈 1. Also...
Consider a utility function u(x,y) = Xayb, where 0くaく1 and 0 < b 〈 1. Also assume that x,y>0 7.1. Derive the marginal utility of x and the marginal utility of y and state whether or not the assumption that more is better is satisfied for both goods. 7.2. Does the marginal utility of x diminish, remain constant, or increase as the consumer buys more x?What does it mean in words? 7.3. What is MRS.y? 7.4. Suppose a, b- Wht...
Use the following table to indicate whether the marginal rate of substitution (MRS) of each utility...
Use the following table to indicate whether the marginal rate of substitution (MRS) of each utility function increases, decreases, or is constant as x increases. MRS Increases with Utility Function Ux,y)- 3x y U(x,y) = MRS Decreases with x Constant MRS MRS Increases withx x-y U(x,y) = For a utility function for two goods, U xy to have a strictly diminishing MRS ie, to be strictly quasi concave), the following condition must hold: Use the following table to indicate whether...
3. The following utility function is known as CES (constant elasticity of substi- tution) function where α > 0 β > 0 (a) Is this function homothetic? (b) How does the MRS,y depend on the ratio x/y? Specifically, show that the MRSy is strictly decreasing in the ratio x/y for all values δ < 1, increasing in the ratio x/y for all values δ > 1 and constant for δ 1. (c) Show that if x = y, the MRS...
Suppose you have following utility function :U(x,y)=(x + yaja where x >0, y>0 and a 70, a <1 The price of commodity x is P >0 and the price of good y is P, > 0. Let us denote income by M, with M>0 a) Compute the marginal utilities of X and Y. b) Write down the utility maximization problem and corresponding Lagrangian function. c) Solve for optimal bundle, X* and y* as a function of Px, Py, and M.
4. Consider the utility function U(x,y) -Iny (a) Find the marginal rate of substitution, MRS of this function. Interpret the result (b) Find the equation of the indifference curve for this function (c) Compare the marginal utility of x and y. How do you interpret these functions? How might a consumer choose between z and y as she tries to increase utility by, for example, consuming more when their income increases?
Suppose that a consumer's utility function is u(x, y) = x, defined for all bundles such that x > 0 and y > 0. For any given positive level of utility, the corresponding indifference curve is O strictly convex. a vertical line. O a horizontal line. a line that is neither horizontal nor vertical.
4. Consider the utility function U(x, y) = x + ln y. (a) Find the marginal rate of substitution, MRS of this function. Interpret the result (b) Find the equation of the indifference curve for this function (c) Compare the marginal utility of x and y. How do you interpret these functions? How might a consumer choose between x and y as she tries to increase utility by, for example, consuming more when their income increases?
Consider a utility function u(x,y) = Xayb, where 0くaく1 and 0 < b 〈 1. Also assume that x,y>0 7.1. Derive the marginal utility of x and the marginal utility of y and state whether or not the assumption that more is better is satisfied for both goods. 7.2. Does the marginal utility of x diminish, remain constant, or increase as the consumer buys more x?What does it mean in words? 7.3. What is MRS.y? 7.4. Suppose a, b- Wht...
Use the following table to indicate whether the marginal rate of substitution (MRS) of each utility function increases, decreases, or is constant as x increases. MRS Increases with Utility Function Ux,y)- 3x y U(x,y) = MRS Decreases with x Constant MRS MRS Increases withx x-y U(x,y) = For a utility function for two goods, U xy to have a strictly diminishing MRS ie, to be strictly quasi concave), the following condition must hold: Use the following table to indicate whether...
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