please show ALL work/steps 15. Clara’s utility function is U(x, y) = (x + 2)(y +...
please show ALL work/steps
15. Clara’s utility function is U(x, y) = (x + 2)(y + 1). If Clara’s marginal rate of substitution is −4 and she is consuming 10 units of good x, how many units of good y is she consuming?
|
a. |
48 |
|
b. |
14 |
|
c. |
4 |
|
d. |
47 |
|
e. |
9 |
Homework Answers
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please show ALL work/steps
15. Clara’s utility function is U(x, y) = (x + 2)(y +...
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?
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 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...
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 =...
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 an individual had a utility function given by: U=X^4*Y^1. Calculate this individual's Marginal Rate of...
Suppose an individual had a utility function given by: U=X^4*Y^1. Calculate this individual's Marginal Rate of Substitution (MRSxy) when they have a bundle with 5 units of Good X and 0.25 units of Good Y. (Round to the nearest decimal place if necessary.)
Ex. 1: Imagine there are two goods, X and Y. The utility function is: U =...
Ex. 1: Imagine there are two goods, X and Y. The utility function is: U = XY. The price of X is $2 and the price of Y is $4. The budget is $20. What is the optimal quantity of X and Y to consume? Ex. 2: Imagine there are two goods: books and coffees. Your utility function is U = BC, where B is the number of books you consume and C is the number of coffees you consume....
5. Consider the utility function U(x, y) = 2/x + y. 1) Is the assumption that...
5. Consider the utility function U(x, y) = 2/x + y. 1) Is the assumption that "more is better” satisfied for both goods? 2) What is MRS, for this utility function? 3) Is the marginal rate of substitution diminishing, constant, or increasing in x as the consumer substitutes x for y along an indifference curve? 4) Will the indifference curve corresponding to this utility function be convex to the origin, concave to the origin, or straight lines? Explain.
10. For this question, use the utility function U(X,Y)= In(X) + 3 In(Y). (a) (2 Points)...
10. For this question, use the utility function U(X,Y)= In(X) + 3 In(Y). (a) (2 Points) What is the marginal utility of X? (b) (2 Points) What is the marginal utility of Y? (c) (2 Points) What is the marginal rate of substitution of X for Y? (d) (2 Points) What is the equation for the slope of the indifference curves?
Income and substitution, Compensating Variation: Show your work in the steps below. Consider the utility function...
Income and substitution, Compensating Variation: Show your work in the steps below. Consider the utility function u(x,y)-x"y a. Derive an expression for the Marshallian Demand functions. b. Demonstrate that the income elasticity of demand for either good is unitary 1. Explain how this relates to the fact that individuals with Cobb-Douglas preferences will always spend constant fraction α of their income on good x. Derive the indirect utility function v(pxPod) by substituting the Marshallian demands into the utility function C....
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?
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?
5. Consider the utility function U(x, y) = 2/x + y. 1) Is the assumption that "more is better” satisfied for both goods? 2) What is MRS, for this utility function? 3) Is the marginal rate of substitution diminishing, constant, or increasing in x as the consumer substitutes x for y along an indifference curve? 4) Will the indifference curve corresponding to this utility function be convex to the origin, concave to the origin, or straight lines? Explain.
10. For this question, use the utility function U(X,Y)= In(X) + 3 In(Y). (a) (2 Points) What is the marginal utility of X? (b) (2 Points) What is the marginal utility of Y? (c) (2 Points) What is the marginal rate of substitution of X for Y? (d) (2 Points) What is the equation for the slope of the indifference curves?
Income and substitution, Compensating Variation: Show your work in the steps below. Consider the utility function u(x,y)-x"y a. Derive an expression for the Marshallian Demand functions. b. Demonstrate that the income elasticity of demand for either good is unitary 1. Explain how this relates to the fact that individuals with Cobb-Douglas preferences will always spend constant fraction α of their income on good x. Derive the indirect utility function v(pxPod) by substituting the Marshallian demands into the utility function C....
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