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Chapter 4. Consumer Behavior and Individual Demand
4.1. The Utility Function 4.1.1. Characteristics 4.1.2. Depicting the Utility Function: The Cobb-Douglas Illustration 4.2 Indifference Curves 4.3 Budget Constraints and Constrained Maximization 4.3.1. The
CHAPTER 2
THE MATHEMATICS OF OPTIMIZATION
The problems in this chapter are primarily mathematical. They are intended to give students some practice with taking derivatives and using the Lagrangian techniques, but the problems in themselves offer few econo
The problems in this chapter examine some variations on the apartment market described in the text. In most of the problems we work with the true demand curve constructed from the reservation prices of the consumers rather than the smoothed demand curve t
Solutions to Problem Set 2: Consumer Theory Compulsory Home Assignment. Deadline: 13 November 1. Consider the indirect utility function given by v (p1 , p2 , m) = m . p1 + p2
(a) What are the (Marshallian) demand functions? Solution: Use Roys Identity: x1
Some Old Prelim Questions 1. Mr. Green consumes two goods, X and Y . His utility function is U (x, y ) = ln (x + 2y y2 ) 2
where x is his consumption of X and y is his consumption of Y . Let Good X be the numeraire with a price of 1 and let p be the price
Midterm Exam, Econ 210A, Fall 2008 1) Elmer Kinks utility function is mincfw_x1 , 2x2 . Draw a few indierence curves for Elmer. These are L-shaped, with the corners lying on the line x1 = 2x2 . Find each of the following for Elmer: His Marshallian demand
Midterm Exam, Econ 210A, Fall 2008 1) Elmer Kinks utility function is mincfw_x1 , 2x2 . Draw a few indierence curves for Elmer. Find each of the following for Elmer: His Marshallian demand function for each good. His Indirect utility function. His Hicksia
Name Midterm Exam, Econ 210A, Fall 2010 Answer as many questions as you can. Put your answers on these sheets. Question 1. Let f (x1 , x2 ) = for all x1 0, x2 0. A) Is f a homogeneous function? If so, of what degree? Explain your answer. If not, show that
Midterm Exam, Econ 210, Fall 2009 Answer Question 1 and any 3 of the other questions. Question 1. Mary Granola consumes only two goods and her utility function is 2 U (x1 , x2 ) = (mincfw_2x1 + x2 , x1 + 2x2 ) . a) Draw some indierence curves for Mary. b)
2004 Spring 1. Homothetic Preferences (a) Homothetic utility function is a utility function u that satises u(x) u(y ) u(kx) u(ky ) for all k > 0
Under these preferences, the income expansion path will be a ray from the origin. To see this, let x be the M
Separable PreferencesTed Bergstrom, UCSB
When applied economists want to focus their attention on a single commodity or on one commodity group, they often nd it convenient to work with a twocommodity model, where the two commodities are the commodity that
0.1
0.1.1
Production functions with a single output
Homothetic and Homogeneous Production Functions
Homothetic production functions have the property that f (x) = f (y) implies f (x) = f (y). Homogeneous production functions have the property that f (x) =
CES Problems, November 2007 1) There are two factors and the production function is F (x1 , x2 ) = M incfw_ x1 x2 , a1 a2
A) Draw the unit isoquant in the x1 , x2 plane. B) Calculate x(w1 , w2 , 1) and c(w1 , w2 , 1) where x(w1 , w2 , 1) = (x1 (w1 , w2 ,
Graduate Microeconomics I Problem Set 3
Fall 2010 - ECARES
Prof. Georg Kirchsteiger T.A. Ester Manna
1. You are given the following information about a consumers purchases. He consumes only two goods: Year 1 Year 2
Quantity Price Quantity Price Good 1 Goo
14.04 - Problem Set 1 Due Sept 22nd in recitation 1) Start with an arbitrary utility function ux 1 , x 2 that is differentiable. Let vu be a monotonic transformation of u. a) Solve: max ux 1 , x 2 ST : p 1 x 1 p 2 x 2 m b) Solve: max vux 1 , x 2 ST : p 1
Lecture Notes on Production and Cost Functions Ted Bergstrom UCSB Econ 210A
A very general model of production possibilities can be described as follows: Suppose that there are m goods, some of which may be used as inputs in production, some of which may