2. Explain how applying the axioms of completeness, transitivity and strict monotonicity to consumer preferences ensures that indifference curves never intersect. You are encouraged to make use of an illustration to support your answer. 3. Suppose that the utility functions u(x, y) and v(x, y) are related by v(x, y) = f(u(x, y)). In each case below, check iff is a positive monotonic transformation' of u. (a) f(u) = 3.141592u b) f(u) = 5000 – 23u -

2. Explain how applying the axioms of completeness, transitivity and strict monotonicity to consumer preferences ensures that indifference curves never intersect. You are encouraged to make use of an illustration to support your answer. 3. Suppose that the utility functions u(x, y) and v(x, y) are related by v(x, y) = f(u(x, y)). In each case below, check iff is a positive monotonic transformation' of u. (a) f(u) = 3.141592u b) f(u) = 5000 – 23u -

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

See similar textbooks

Similar questions

4B. Which one(s) of the following functions v(x, y) = 2x°y – 100, w(x, y) = 3(x + y) + 120, t(x, y) = xy - 150 is an ordinal utility function for a preference relation which admits u(x, y) = 3x/2y1/2 + 120 as an utility function? (a) w only (b) v and w (c) v and t (d) v, w and t (e) none of the previous four statements is correct. %3D %3!
B.3 Marie has preferences over two goods, cake q₁ and bread q2. She chooses quantities to consume so as to best satisfy these preferences subject to the budget constraint p1q1 + P292 y where p₁ and P2 are prices and y is total budget. Suppose that Marie's preferences are represented by utility function u(q1, 92) = 91 + In (bq1 +92) where b≥ 0 is a preference parameter. Assume that p1/bp2 ≥ y/ (P1 - bp2) ≥ 1. (a) Show that Marie's indifference curves are downward sloping and that her weakly preferred sets are convex for all possible values of b. (b) Show that her Marshallian demand for cake gi is Y fi (y, P1, P2) 1 P1-bp2 and find her Marshallian demand for bread, f2 (y, P1, P2). Discuss the shape of Engel curves for the two goods. (c) Explain why Marshallian demand curves for normal goods slope down. Are there any values of b for which either cake or bread could be a Giffen good for Marie? Discuss. (d) Find the form of the indirect utility function and expenditure function and hence…
5. Suppose a preference relation is represented by a utility function u(x₁, x₂) = x₁ + x₂. Explain why the function -u(x₁, x₂) = −x₁ - x₂ does not represent the same preference relation. It is enough to explain using two appropriate bundles.
Suppose that one of your friends does not care if she consumes spaghetti (S) or noodle (N). She wants toconsume either two-dish spaghetti or two-dish noodle or any combination of both which adds up to twodishes.(i) Write the utility function of your friend to represent his preferences.(ii) Draw couple of indifference curves of your friend on graph with appropriate labels.(iii) Denote prices as Pn, Ps; income as M. If Pn < Ps, then determine the demand function of your friend foreach product as a function of prices and income.
Question 4: Consider a general utility function U(x₁, x₂). Let's now solve for the optimal bundle generally using the Lagrangian Method. 1. Write down the objective function and constraint in math. 2. Set up the Lagrangian Equation. 3. Fnd the first derivatives. 4. Find the first order conditions. What's the interpretation for >? 5. Rearrange them to get the tangency condition.
2 Indifference curves Suppose an individual who derives utility u(x, y) from consuming a units of good X and y units of good Y. Derive the indifference curve for a level of utility U for each of the following utility functions. Draw them in the graph below for a utility level U = 18. (A) u(x, y) = 2x + 3y (B) u(x, y) = min{3x, y} (C) u(x, y) = xy
Consider a consumer with M = $120 to spend (income) and faces prices PX = $15 and PY =$5 for goods X and Y. Her utility function is U(X, Y) = X1/2 + Y1/2.a Carefully. express the consumer’s choice problem, using the given information (this is whereyou write out the max operator, the choice variables, the objective function, and the budget constraint). b. Compute the absolute value of the consumer’s marginal rate of substitution, and inspect it todetermine the shape of the consumer’s indifference curves: C-shaped, linear, )-shaped, or some other shape.To show your work, neatly use the arrow argument, increasing X (↑) and decreasing Y (↓) to see whether|MRS(X, Y)| is diminishing along an indifference curve. c. If the indifference curves are C-shaped write out the budget line and the equal slopes conditionthat characterize an interior solution to the consumer’s choice problem. Use the particulars for the givenconsumer. Solve these conditions to find the interior solution. On the other…
Suppose the utility function for a consumer is given by U = X + Y, where X and Y are a consumer's consumption of goods X and Y. Which of the following bundles does this consumer find indifferent between 10 units of X and 5 units of Y? You Answered a. 4 units of X, 10 units of Y b. 2 units of X, 13 units of Y c. 5 units of X, 7 units of Y d. 8 units of X, 8 units of Y
Suppose you have a $20 gift card and want to buy Blue and Red yarn. The utility function from yards of blue (B) and red (R) yarn can be expressed as follows: U(B,R) = 3B+R Red yarn costs $4 per yard. blue yarn costs $4 per yard. A) Graph the budget constraint and the indifference curves that can be reached. How many yards of each type of yarn will he purchase at these prices with his gift card?