Are the following transformations valid for transforming a
utility function. Explain about each one, how
you know:
U^T = Ln(U(x,y))
U^T = 1/ (U(x,y))
Are the following transformations valid for transforming a utility function. Explain about each one, how you...
State (and explain) whether these are monotonic transformations or not for the utility function u = (x,y). f(u) = 3.14u f(u) = 5000-23u f(u) = 1/u2
7. State (and explain) whether these are monotonic transformations or not for the utility function u = (x,y). f(u) = 3.14u f(u) = 5000-23u f(u) = 1/u2
question #5
(b) Suggest two distinct utility functions that represent such preterences. (Hint: Think about monotonic transformations.) (c) Find MRS analytically. How does MRS depend on the values of (1, 72). Intuitively explain why (d) She spends her total income of $100 paying pi $2 for each Red Delicious and p2 $1 for each Gala. Find her optimal demand and show it on the graph. (e) Describe Kate's optimal choice(s) when p $1. Consumer Demand 5. For each of the...
8.1. Consider a transformation of the utility function in Question 7 using In(u). In other words the new utility function u' = In(u) = In(xay!) = x In(x) + b × ln(y). What is MRSr.y of this new utility function? Is it the same as or different from MRS,y you found in Q7.3? Explain. 8.2.Will the MRS be still the same for each of the following transformation? Explain without directly solving for MRS. a), u, = u2 b). 1/ =...
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 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?
Problem 1 (10pts) Jim's utility function is U (x, y) = xy. Jerry's utility function is U (x,y) = 1,000xy +2,000. Tammy's utility function is U2, y) = xy(1 - xy). Bob's utility function is U(x,y) = -1/(10+ 2xy). Mark's utility function is U (2,y) = x(y + 1,000). Pat's utility function is U (2,y) = 0.5cy - 10,000. Billy's utility function is U (x,y) = x/y. Francis' utility function is U (x,y) = -ry. a. Who has the same...
The following questions are worth 6 points each. 21) Solve the following utility function to be optimized. Only consider they are looking for an interior solution: (10pts) U(X1,x2) = 1 ln(x) + 2 In(x2) MU(x)= 1/ MU(X) = 2/2 Subject to the budget constraint: 500 = 2 + xy +4.X2 a. Find the optimal consumption bundle. (4 pts) b. Find the utility at this point. (1 pt) C. Show work (5 pts) u (x,x) = 1 in (X.) + 2...
There are three consumers A, B and C. A's utility function is u^ = x; xz, B's utility function is u = 3xx, and C's utility function is u = ln x; + ln x, -100. Your friend argues that A, B and C have an identical Marshall demand function for good 1. Do you agree with this argument? Give the reason for your answer.
how to find indirect utility function here?
Jeanette has the following utility function: U-ain(x) + b*In(y), where a+b=1 a) For a given amount of income I, and prices Px, Py, find Jeanette's Marshallian demand functions for X and Y and her indirect utility function. (6 points)