Select the function that represents the marginal utility of X for the utility function: U-X0.5 Y0.25...
Select the function that represents the marginal utility of X for the utility function: U-X2Y4 Select one: a. 4X2y3 b. 0.5x2y4 c. 2XY4 d. 2X2y4 e. 4X-2y4
Suppose the following equations represent an individual’s utility maximization problem: U(X,Y) = X0.5 + Y0.5 And the budget constraint is: I = PxX + PyY (a) Set up the individual’s maximization problem using the Lagrange technique. (b) Find the individual’s demand function for X and Y (Derive from first order condition). (c) Find the indirect utility function. (d) Find the expenditure function. (e) Find the share of X and Y on expenditure. (f) Find the marginal utility of income.
Find the demand curves for U(x,z) if the utility function is a.) U(x,z)=(x0.5+z0.5)2 b.) U(x,z)= 10x0.5+z Please show all algebra work, the algebra is confusing me as I work through these two problems!! :)
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...
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?
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 the function u(x) = x0.5 , where x is consumption, represents your preference over gambles using an expected utility function. You have a probability 0.1 of getting consumption xB (bad state) and a probability 0.9 of getting xG (good state). An insurance company allows you to choose an insurance contract (b, p), where b is the insurance benefit the company pays you if the bad state occurs and p is the insurance premium you pay the company regardless of...
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)
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...
Suppose the function u(x) = x0.5 , where x is consumption, represents your preference over gambles using an expected utility function. You have a probability 0.1 of getting consumption xB (bad state) and a probability 0.9 of getting xG (good state). An insurance company allows you to choose an insurance contract (b, p), where b is the insurance benefit the company pays you if the bad state occurs and p is the insurance premium you pay the company regardless of...