Utility function is given as
Given the utility functionDetermine the value of marginal utilities 1at the point (25,8). Hence (a) estimate the change in utility when both x1 and x2 increase by 1 unit (b) find MRCS at this point.
4. Anne's utility function is given by u(xi,x2) Michael's utility function is given by u(xı, x2)' = x1x2. She has two friends, Michael and Peter 1 and Peter's is given by u(x1, X2) = = 1042 1 Τ) -x12. Who has the same preferences as Anne? And who has indifference curves with similar shape as Anne's indifference curves? Explain. 4. Anne's utility function is given by u(xi,x2) Michael's utility function is given by u(xı, x2)' = x1x2. She has two...
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...
(10 Question 1: marks) Given is the Total Utility Function along with Budget Constraint: Utility Function: U (X, Y) = X°.270.3 Budget Constraint: I = XP, + YP, a. What is the consumer's marginal utility for X and for Y? b. Suppose the price of X is equal to 4 and the price of Y equal to 6. What is the utility maximizing proportion of X and Y in his consumption? {construct the budget constraint) c. If the total amount...
8. Problems 3.8 k1/6 Suppose indifference curves for a utility function U are given by z --kısx-usy-As. The utility function U k associated with these indifference curves is Suppose indifference curves for a utility function U are given by y 0.51/x2 - 4 (x2-k) -0.5x The utility function U k associated with these indifference curves is Suppose indifference curves for a utility function U are given by z-- 2x The utility function U k associated with these indifference curves is
2) Assume that utility is given by Utility-U(X,Y)-X03yo7 a) Calculate the ordinary demand functions, indirect utility function, and expenditure function. b) Use the expenditure function calculated in part (a) together with Shephard's lemma to compute the compensated demand function for good X. Use the results from part (b) together with the ordinary demand function for good X to show that the Slutsky equation holds for this case. c) d) Prove that the expenditure function calculated in part (a) is homogeneous...
* * 5. A consumer's preferences are given by the utility function U = x;'°*". The price of good 1 is 3 and the price of 2 is 6, while her income is 36. The utility maximising bundle for the consumer is a. X* = 4, x* = 4 b. x1 = 4, x = 3 C. x1 = 2, x = 6 d. x1 = 8, x* = 2 e. None of the above * * N * *...
Question 6 (Utility). Suppose a consumer's utility function is given by U(x, x)=x7x2 Draw an indifference curve with a value of 10 and an indifference curve with a value of 16. Label two points on each indifference curve as well as the axes. a) b) What is the marginal utility with respect to xi? What is the marginal utility with respect to x? What is the
Suppose a person has a utility function given by U = [xρ + yρ]1/ρ where r is a number between −∞ and 1. This is called a constant elasticity of substitution (CES) utility function. You will encounter CES functions in Chapter 6, where the concept of elasticity of substitution will be explained. The marginal utilities for this utility function are given by MUx=[xρ+yρ]1ρ−1xρ−1 MUy=[xρ+yρ]1ρ−1yρ−1 Does this utility function exhibit the property of diminishing MRSx,y?
1.Suppose a consumer had a utility function given by: U= 9X + 2Y. If the price of Good X (Px) is $8 and the price of Good Y is $4then what is the utility maximizing quantity of Good X the consumer will purchase with a budget of $32? 2. Suppose an individual had a utility function given by: U=X^4Y^0.6 Calculate this individual's Marginal Rate of Substitution (MRSxy) when they have a bundle with 3 units of Good X and 1.8...