U= X2 Y4
MUX = Partial derivative of U with respect to X
MUX= 2XY4
Hence, option(C) is correct.
Select the function that represents the marginal utility of X for the utility function: U-X2Y4 Select...
Select the function that represents the marginal utility of X for the utility function: U-X0.5 Y0.25 Select one: a. 0.25X-0.5 y0.25 b. 0.5X-0.5 y0.25 c. 0.5x0.5 y0.25 d. 0.25X 0.5 v-0.25 e. 2X-0.5 y025
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?
3. For each of the utility functions below, compute expressions for the marginal utility with respect to good X, QU(X,Y)/OX, and the marginal utility with respect to good Y, CU(X,Y)/CY a. U(X,Y)= XY b. U(X,Y)= 4x + 3Y c. U(X,Y)= XY2 + 3X d. U(X,Y)= X + Y5 e U(X,Y)=(2X+2Y)
3. Suppose the utility function for two goods, x and y, is: U = U(x,y) = xłyż. a. Graph the indifference curve for U = 10. b. If x = 5, what must y equal to be on the U = 10 indifference curve? What is the MRS at this point? c. Derive a general expression for the MRS for this utility function. Show how it can be interpreted as the ratio of the marginal utilities. d. Does this individual...
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) -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?
4. Let the household utility function be given by U(x,y) = Vxy. a. Find the marginal utilities of X and Y and write the expression for the marginal rate of substitution between X and Y. b. Let I = $100, Px = $10 and Ry = $10 be the set of prices and income. Find the utility maximizing combination of X and Y given the prices and income. c. What is the level of utility of the chosen bundle of...
Question 2 2 pts Consider the utility function u(x1, x2)= x x Calculate the marginal utility of good 2. 7xx? O 7xx? 7x x 8xx
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?
Find the Marginal Utility of X; the Marginal Utility of Y; the ratio MUx / MUy for each of the following: a. U(x,y) = 15x.2y.3 b. U(x,y)=.5xy c. U(x,y)=6x.4y.5 d. U(x,y)=3x.5y.8