Microeconomic Theory
12th Edition
ISBN: 9781337517942
Author: NICHOLSON
Publisher: Cengage
expand_more
expand_more
format_list_bulleted
Question
Chapter 3, Problem 3.14P
a
To determine
To prove:Whether the preference is continous, transitive and complete.
b)
To determine
Whether the preference is continous, transitive and complete.
c)
To determine
Whether the preference is continous, transitive and complete.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
1. Let k = one plus the last digit of your student number. For example, if your student number is 1234567 then k=8. Suppose an individual as preferences over goods x and y that can be represented by the utility function:
U(x,y) = 120 / 1+ |x-ky|
where |x-ky| is the absolute value of x - ky (that's k times y)
a. Draw the indifference curve of the bundles (x,y) that are indifferent to bundle (x,y) = (11,2). It doesn't have to be drawn to scale (hand drawn is fine), but make sure to label any intercepts .
b. Are these preferences monotonic? Explain?
c. Are these preferences convex? Explain intuitively with a diagram.
Lionel eats ham (x) and cheese (y). The utility function U(x,y)=0.25x + 2y^0.5 represents his preferences.a) What is Lionel’s MRS? Holding y constant, how does his MRS change as ham (x) is increased?b) What does your answer in (a) imply about his indifference curves as you hold y constant and increase x? In (c) and (d) you are asked about the Marshallian and Hicksian Demands for cheese (y). Do NOT calculate the demand functions to answer these questions. Use your answers to (a) and (b) to explain your answer. c) Holding prices constant, what is the effect of an increase in income on his Marshallian demand for cheese (y)? Briefly explain your answer.d) Holding prices constant, what is the effect of an increase in utility on his Hicksian demand for cheese (y)? Briefly explain your answer.
Consider the following utility functions:
(1) u(x₁, x₂) = x₁ + 2x2.
(2) u(x1, 1₂) = 2125 12.75
(3) u(x₁,1₂)=-1²-1₂.
(4) u(x1, 1₂) min{x1, 2x2).
For utility functions (1) to (3), give the equations of the indifference curves correspond-
ing to utility level k, where 22 is expressed as a function of 2₁ and k.
For utility functions (1) to (4), draw two indifference curves for each function. That
is, draw four graphs (one for each utility function) and two indifference curves on each
graph.
Knowledge Booster
Similar questions
- Suppose an individual has a utility function u (x1, x2) = 2*2. Present your mathmatical expressions below in the simplest form you can. a) Derive an expression for the marginal utility of good 1, and for the marginal utility of good 2. b) Using these, solve for an expression describing the slope of an indifference curve: MRS (11, 12). c) Sketch indifference curves for this consumer corresponding to u = 0,10,20. (Hint: z rı = k solves for m} = 11 (21) . Solve this expression and approximate it on a graph for the three values of k.)arrow_forwardKreese derives utility from two types of goods: cigars (good 1) and sleeveless shirts (good 2). consumption bundle is a pair (r1, x2), where r, > 0 is the quantity of cigars and r2 20 is the quantity of sleeveless shirts (for simplicity, assume these goods can be measured in arbitrary-not just integer-quantities). (a) Suppose Kreese's preferences are monotone (more is better) and that he is willing to give up one sleeveless shirt in exchange for three cigars. Find a utility function representing his preferences. (b) Through trial and error, Kreese has discovered that there are no benefits to smoking more than 10 cigars per day. When smoking less than 10 cigars he is still willing to exchange one shirt for three cigars, but if he smokes more than ten cigars, there is no additional benefit and he only gains by owning more shirts. Find a utility function describing these preferences.arrow_forwardWhich form of utility is expressed on ranking the bundles According to preferencesarrow_forward
- Given a utility function that represents preference over bundles which consists of two goods. Can we find some information of the relative cardinal value between two bundles? Explain your answer.arrow_forward1. For each of the following scaling functions for a von Neumann-Morgenstern utility func- tion, determine the Marginal Rate of Substitution between X1 and X2 and the equation for an indifference curve through the consumption bundle (100,100) (solve for X2 on the left hand side of the equation). State 1 is the bad outcome that occurs with probability 0.2 and State 2 the good outcome that occurs with probability 0.8. Graph these indif- ference curves and comment on what you see. Is a consumer with these preferences risk averse, risk neutral, or risk loving? (a) V(X) = InX (b) V(X)= VX (c) V(X)= X (d) V(X)= X²arrow_forwardFind the optimal bundle using the following utility functions and budget constraints. 1. U(x,y)=lnx+yand2x+y=10 2. U(x,y)=3x+2yand3x+2y=24 3. U(a,z)=3a+2zand3a+6z=24 4. U(a,z)=a2z2 and4a+2z=485. U(x,z)=a2z3 and3a+2z=36arrow_forward
- QUESTION 8 If the ulitity function is: U=41x₁ + 11x2 and considering the following bundles: A=(73,52) B=(31,61) C=(9,59) D=(5,46) E=(81,45) How much utility does the consumer get from bundle C?arrow_forwardFor each of the following utility functions draw the indifference curve that passes through (1,1). Label at least three points on each curve and indicate the direction of increased preference: a) u(x1, x2 ) = 3x1 b) u(x1, x2 ) = x1 + 2x2 c) u(x1, x2 ) = x1+ logx2 d) u(x1, x2 ) = min (2x1, x2) e) u(x1, х2) %3D max (1, x2)arrow_forwardDerive the relationship between the quantity of X demanded and the price of X if the consumer’s indifference map vis-à-vis X and Y has curves concave to the origin. Let X be games of golf per annum and Y all other goods. Draw the indifference map and budget constraint of: (a) an amateur who pays to play golf; (b) a professional who is paid to play golf. May we conclude that golfers turn professional because they dislike the game?arrow_forward
- Consider the utility function U(x,y)=3x +6y. An agent with a budget constraint of 15x + 5y = 30 will choose which of the following bundles in order to maximize his/her utility? 2 units of x and 0 units of y 2/3 units of x and 4 units of y 1 unit of x and 3 units of y 0 units of x and 6 unit of y 1/2 unit of x and 1 unit of yarrow_forwardConsider the following utility functions. G(x,y) = x² + 3y² H(x,y) = (x+1)¹/2 + y + 1 L(x,y) = xey U(x,y) = In(x) + y² W(x,y) = 100 x - 4x² + 3 y Z(x,y) = (x)¹/² + y Which function or functions have strictly convex indifference curves (at every point where x>0 and y>0)?arrow_forwardConsider a consumer with utility function u(x1, x2) = min{4 min{x1, x2}, x1 + x2} (a) Draw indifference curves passing through points (2, 2), (1, 2) and (4, 2). Make sure you correctly determine kink points. What properties of the preferences can you deduce from the shape of indifference curves? (b) When X = R 2 +, does UMP have a solution when p1 = p2 = 0? What property of the preference relation did you use to get your answer? (c) Assume that prices are such that p1, p2 > 0 and that p > 0 for some `e {1, 2} (i.e. the price of at least one good is positive). Derive Walrasian demand. What are the prices for which Walrasian demand is single-valued?arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Economics (MindTap Course List)EconomicsISBN:9781337617383Author:Roger A. ArnoldPublisher:Cengage Learning
Economics (MindTap Course List)
Economics
ISBN:9781337617383
Author:Roger A. Arnold
Publisher:Cengage Learning