Imagine that preferences of a given individual are presented with U(X1 ,x 2 )=X 1 -e^ ? x 2....
Question:
Imagine that preferences of a given individual are presented with {eq}U(x_{1},x_{2})=x_1-e^{-x_2} {/eq}. Assume that the prices of the two goods consumed by this individual are given by {eq}p_1 {/eq} and {eq}p_2 {/eq}. Normalize the price of the first good to 1. Furthermore, assume that the individual earns income, {eq}I {/eq}.
(a) Derive the demand of the individual for the two goods
(b) Plot the indifference curves as a function of income.
Utility Maximization:
In economic theory it is assumed that the primary objective of the consumer is to maximize utility subject to a budget constraint. The allocation of an individuals income between goods depends on the consumers preferences. There are several methods to solve utility maximization problems including the Lagrangian method, dynamic programming and numerical methods.
Answer and Explanation: 1
Become a Study.com member to unlock this answer! Create your account
View this answer(a) Derive the demands of the individual for the two goods
Starting with the utility function we must first set-up the Lagrangian with the budget...
See full answer below.
Ask a question
Our experts can answer your tough homework and study questions.
Ask a question Ask a questionSearch Answers
Learn more about this topic:
Get access to this video and our entire Q&A library
Utility Maximization: Budget Constraints & Consumer Choice
from
Chapter 3 / Lesson 2
14K
Learn about utility maximization. Discover various types of utility, examine utility maximizing rules, and study examples of maximizing utilities in economics.
Related to this Question
- Suppose an individual has a preference represented by the utility function U(X_{1},X_{2} = X_{1} + lnX_{2}. The individual consumes two goods,X_{1} and X_{2} and faces the prices P_{1} and P_{2}. Con
- Suppose an individual has a preference represented by the utility function U(X1, X2) = X1 + lnX2. The individual ocnsumes two goods, X1 and X2 and faces the prizes P1 and P2. Consumption is constraine
- Assume that utility over two goods is given by U(x1,x2) = 0.3lnx1 +0.7lnx2. The price of good x1 is equal to p1 and the price of good x2 is p2. The total income of the individual is given by I. a Writ
- Consider three ways of allocating two goods in a two-person exchange economy. I. Both individuals take prices as given and equilibrium prices are established by an impartial auctioneer. II. One individual can act as a perfect price discriminator and force
- Suppose the utility function for an individual is given by u(x, y) = x + y, where x and y are two goods. The budget constraint of an individual is 2x + 5y = 10, where I = 10 is the income of an individual, P_x = 2 - the price of good x, and P_y = 5 - the
- Assume that a person's utility over two goods is given by U(x1, x2) = (x1 - 5)^{1/3}(x2 - 10)^{2/3} The price of good x1 is equal to p1 and the price of good x2 is p2. The total income of the individual is given by I. (a) Write down the budget constrai
- 1. Suppose David spends his income (I) on two goods, x and y, whose market prices are px and py, respectively. His preferences are represented by the utility function u(x, y) = ln x + 2 ln y (MUx = 1
- Consider a consumer who allocates her income m to the consumption of goods 1 and 2. Denote by pi the price of good i = 1, 2. The consumer's preferences are such that there exists a bundle x = (x1, x2)
- Question 1 A consumer has preferences represented by the utility function u(x1, x2) = \sqrt{ (x1x2)}. If she faces prices p1 = 1 and p2 = 5, and has income m = 10, what are her demands for goods 1 an
- Suppose that a person's preferences can be described by the utility function U = ? L n q 2 where 0 is less than ? is less than 1 . They have income Y and face prices of p1 and p2. a).What is the
- Preferences [{Blank}]. a. are influenced only by costs, b. are the same for everyone, c. are based on the individual.
- Assume that your preference is characterized by U(x, y) = x + ln y. Further, assume that I = 100 (income), Px = 1 (price of x), and Py = 1 (price of y). Obtain the optimal consumption bundle. If I increases, what happens to your consumption?
- Suppose that there are two goods. You observe that p_1 = 1, but you do not know p_2 and your income yet. Suppose that you can (exactly) afford 4 units of Good 1 and 6 units of Good 2 or 12 units of Go
- Agent i's preferences over goods x and y can be represented by the utility function Ui (x, y)=x1/2 y1/2. Let M denote i's income and px and py denote the prices of the respective goods. Use the Lagran
- Assume that there are 1,000 identical consumers in the market for good X, each with the same income and the same preferences. When the price of X is $50, the typical consumer 4 is willing and able to
- Priyesh's preferences for goods x and y is given by the utility function U = x2/3y1/3. His income is $192 and the price of good y is always $1. Suppose the price of x starts at $8 and then decrease
- A consumer has strictly monotonic preferences that can be represented by a utility function. She chooses bundle A under certain prices and income. Furthermore, bundle A is cheaper than bundle B under those prices. If prices change and bundle B becomes mor
- Assume that Jack has the preferences shown in the above table. Also assume that the price of a can of Pepsi is $3.00 and that the price of a slice of pizza is $1.00. If he has $16 available to spend, what combination of Pepsi and pizza will be his consume
- Which of the following is not an assumption of our Rational Consumer Choice Model? A) Consumers observe and set prices of goods. B) Consumers have a given income. C) Consumers have preferences over goods. D) B and C are not assumptions. E) All of t
- A consumer has preferences for two goods, 1 and 2, which can be represented with the utility function u(x_1, x_2) = 4x_1 + 3x_2. A. If a consumer has a budget of 20 AZN while prices of goods 1 and 2 are 2 AZN and 4 AZN, respectively, calculate the bundle
- A person has $120 to spend on two goods (x and y) whose respective prices are $3 and $5 per unit. (a) Draw the budget line showing all the different combinations of the two goods that can be bought w
- The utility from a specific product is: A) determined by a consumer's income. B) constant as one consumes more units of it. C) determined by the price of the product. D) a measure of one's preference or taste for it.
- Assume that a person's utility over two goods is given by: U(x,y) = x^(alpha)y^(1 - alpha). The price of Good X is p_x and the price of Good Y is p_y. The total income of the individual is given by M.
- Luke's choice behavior can be represented by the utility function u(x_1, x_2) = x_1 + x_2. The prices of x_1 and x_2 are denoted as p_1 and p_2, and his income is m. 1. Draw at least three indifferen
- According to the figure below, if the price of X is $5, what combination of X and Y will a utility-maximizing consumer choose? a. 80X, 20Y, b. 120X, 620Y, c. 120 X, 250Y, d. 200 X, 620Y, e. None of the above.
- Consider a rational utility maximizing consumer who is choosing between two goods clothing (C) and food (F), where the total utilities of the two goods are independent so that total utility (U) = Util
- Suppose that a consumer's preferences can be represented by the utility function u(x1, x2) = min {2x1 ,x2}. Suppose that the originally the price of good one is $2, the price of good two is $2 and the
- Consider the endowment economy. There are 2 goods, apples (A) and bananas (B). The price of apples (bananas) is P_A (P_B). Preferences are represented by the utility function U(D_A,D_B) = D_A^{\frac{1
- There are two commodities, h = 1, 2 with quantities x1 and x2. The consumer's preferences are represented by a utility function: u( x1, x2) = min {2 x1, x2}. Suppose the prices of the goods are given by (p1 , p2) = (1,2) and the income is m = 10. What
- Each of 100 people receives a random item from a grocery store and assigns it a value between 1 (low) and 10 (high). They trade those items among themselves for items they prefer rather than those they randomly received and then assign a second value (aga
- Assume that a consumer can buy only two goods X and Y, and has an income of $120. The price of X is $10, and the price of Y is $20. If the consumer spends all of her money on X and Y, which of the fol
- An individual's valuation of a good or service: a. is lower than the maximum value the individual will pay. b. can be expressed in the marketplace. c. is generally the same for most people. d. is known as the market price.
- To make a choice among combinations of goods with a cost in money, based upon the principle of rational choice, one need not know: a. the total utility of the combination of goods b. the marginal utility of each good c. the price of each good d. any of th
- Suppose there are two goods, X and Y. The utility function for these goods is given by U(X,Y) = 5X+2Y. Suppose I had $50 to spend on these two goods. Good X has a price of $5 per unit, while the price
- Suppose the total utility a person derives from two goods (x & y) can be described by the equation: U(x,y) = sqrt(xy) Units of y cost $10 each while the cost of each unit of x is dependent on the numb
- A consumption bundle that lies inside the individual's budget line is a consumption bundle that: A) does not maximize the individual's utility given their tastes, income, and the price of the goods. B) does not exhaust the individual's income. C) the indi
- Assume that a consumer can buy only two goods X and Y, and has an income of $120. The price of X is $10 and the price of Y is $20. If the consumer spends all of her money on X and Y, which of the following would be a possible combination: A. 4X and 2Y B
- Assume that the price of a 50-put on a single share of stock X has been determined to be $2, stock X share price today is $45, and the time premium is 10%. Find a (non-trivial) lower bound for the price of a 40-call.
- A consumer spends all her income on goods x and y. Her income is 400. Prices of x and y are px = 6 and py = 2. The preferences of the consumer are represented by U(x, y) = x3y, where x and y denote th
- Assume the price of good X is P X , price of good Y is P Y , and B is the budget. The formula for the budget line for these two goods is a. P Y Q Y P X Q X . b. P X B + P Y B = B . c. P X X + P Y Y = B . d. ( 1 P Y B ) P X .
- Suppose the price of apples is R3 each, the price of oranges is R5 each, and Bob's budget is R50 per week. What is Bob's utility-maximizing choice between these two goods?
- Suppose there is an economy with two individuals, A and B, and two goods, X and Y. The individuals' utility functions are: UA = 0.2lnX + 0.8lnY, UB = 0.8lnX + 0.2lnY For simplicity, let the price of
- A maximizing consumer with preferences described by the utility function u = xy has an income of 800 dollars and faces prices px = 10, py = 20. Next month prices will be px = 40, py = 20. A) Provide
- If, for a consumer choosing between two goods, the MRS equals the price ratio, then _____.
- Suppose that an individual consumes transportation (T) and all other goods (G). Assume that the price of G is pg, the price of transportation is pt, and Y is income. (a) If this consumer spends all of her income on transportation, how much could she buy?
- Suppose a consumer uses his income to buy food (F) and clothing (C) (note, his preferences are to not go without either). The current composite market price of food is $2.00 per unit and the current c
- Assume: TC = 5 + 2q + 0.5q^2, \ P = 20 - 3q. What is the profit max price, q, TR, cost?
- Consider commodity space where x1 is food and x2 is everything else. Allow food to have the price p1, and allow everything else to have the price of dollars, so p2 = $1. Denote income as m. (a) Write
- Consider an economy where the represetative consumer has a utility function u(c,l) over consumption c and leisure l. Assume preferences satisfy the standard properties. The consumer has an endowment o
- A maximizing consumer with preferences described by the utility function has an income of 800 dollars and faces prices Next month the prices will be a. Provide calculations and an Indifference Curve d
- Assume that all there is are movies (m) and food (f). The price of movies is $10, while the price of food is $5. Suppose you have $145 to spend on these two goods, and that your preference is described by the following utility function: u (m, f) = m + f +
- Consider a consumer with $10 to spend on these two goods where the price of apples is always $2 each. a) Find the utility maximizing combination of apples and oranges if oranges cost $4 each. Explain why the consumer didn't choose the bundle of 3 apples a
- Are opportunity costs based on a person's tastes and preferences?
- Suppose that the utility function is given as u(x) = 2ln(x_1) + 3ln(x_2). (Note: The preferences represented by this utility function is strictly convex and monotonic.) How much of commodity 1 (x_1) and commodity 2 (x_2) will the consumer purchase as a fu
- The firms practice menu pricing because: A) They cannot distinguish different consumers and menu pricing allows the consumers to self select the appropriate price. B) They have complete information about the individual valuation of the consumers for the p
- Assume that a consumer can purchase only two goods: R (recreation) and M (material goods). The market price of R is $2 and the market price of M is $1. The consumer spends all her income in such a way
- Suppose there are two goods, labeled x, y. A consumer has a budget of w = 220. Suppose the following two consumption bundles: (x = 4, y = 10), (x = 6, y = 4) all cost the consumer 220. (a) What's the
- Assume that an individual consumes two goods, X and Y. The total utility (assumed measurable) of each good is independent of the rate of consumption of other good. The price of X and Y are respectively $40 and $60. Use the following table of total utiliti
- Price elasticity, income elasticity, and cross elasticity are interesting concepts but no one really uses such considerations when making personal consumption or purchasing decisions; business firms might use such information, but individual people do not
- A person has $120 to spend on two goods (x,y), whose respective prices are $4 and $5. A) Draw a budget line showing all the different combinations of the two goods that can be bought with the given budget. B) What happens to the original budget line if th
- Consider a potential, voluntary exchange between two people. Assume that both people have complete information about each other?s preferences and that there are no transaction costs. Initially, Consum
- Willingness to pay: A. is the lowest price that a buyer is willing and able to pay for a unit of good. B. is equal to the price of the highest-priced goods in a consumption bundle. C. is equal to the price of the lowest-priced goods in a consumption bundl
- The budget restraint that determines an individual's consumption refers to a. the average disposable income for a particular country. b. the income that an individual has to spend and the prices of the products the individual wants to buy. c. the maximum
- Suppose Players 1 and 2 are participating in a first-price sealed bid auction with private, independent valuations. Each player's valuation of the object to be sold, which is assumed to be worth 0 to
- To calculate price level, economists begin with the concept of a hypothetical group of different items, with specified quantities of each one meant to represent a 'typical' set of consumer purchases, used as a basis for calculating how the price level cha
- Suppose that Ben has $100 to spend on two goods, movie and hamburger(HD. (M) The price of a movie is S10 and the price of a hamburger is $2. Ben's preferences are represented by the utility function:
- The difference between the maximum amount a person is willing to pay for a good and its current market price is known as: a. the paradox of value b. profits c. revealed preferences d. consumer surplus
- Consider a consumer with the following preferences: U (x, y) = 20 log x + 5 log y who face prices px = 10, py = 10, and has wealth w = 100. Write the consumer maximization problem, with all constraints.
- Assume that there are two goods (X and Y). The price of X is $2 per unit, and the price of Y is $1 per unit. There are two consumers ( A and B). The utility functions for the consumers are: for consumer A: U (X,Y)= X^.5Y^.5 and for consumer B: U(X,Y)=X^.8
- Noriko has preferences over Good 1 and Good 2 given by u(x_1,x_2)=x_1+2sqrt(x_2). Suppose that P_1 = $2, P_2= $1, and that Noriko has $12 to spend. Compute her optimal consumption bundle. Now suppose
- Suppose that people consume only three goods, as shown in this table: | |Tennis | | | |Tennis Balls |Racquets|Gatorade |2014 price |$2|$40|$1 |2014 quantity |100|10|200 |2015 price |$2|$60|$2 |2015 q
- Suppose that an economist hypothesizes that the annual quantity demanded of a specific computer brand is determined by the price of the computer (P) and the average income of consumers (Y) according to: Q_D = Y - 3P. Which of these variables are exogenou
- Evaluate a pricing decision any company made that involved a product or service with fixed capacity. Do you think price was set optimally? If not, why not? How would you adjust the price, or would you
- The amount of profit that can be achieved using uniform pricing is {Blank} the profit that can be achieved from price discrimination because {Blank}. \\ Select one: \\ a. greater than; the cost of trying to determine every single consumer's individual d
- Utility function from consuming a bundle of goods (X,Y) is given as and Prices are given as =($2, $4), and income M=$100 1. Derive the optimum consumption bundle. 2. If prices now change to =($4, $4).
- Suppose that there are three beachfront parcels of land available for sale in Astoria and six people who would each like to purchase one parcel. Assume that the parcels are essentially identical and that the minimum selling price of each is $570,000. The
- The plan of the possible quantities that will be demanded at different prices by an individual is called (blank).
- Assume that the unit price of good A is $2, and the unit price of good B is $5. If an individual has income of $30, which of the following consumption bundles of (good A, good B) is on the edge of the budget constraint? A) (5,5) B) (5,4) C) (6,4) D (6
- Consider a consumer with the following preferences: U (x, y) = 20 log x + 5 log y who face prices px = 10, py = 10, and has wealth w = 100. Construct the Lagrangian, and solve for the optimal choices of x and y. Verify that you have included the approp
- Consider a second-price sealed-bid action. Suppose bidders' valuations are v_1 = 10 and v_2 = 10. Select all that apply. a) Bidding a value b_1 equal to her own valuation v_1 is a weakly dominated str
- The owner of a fast food chain determines that if x thousand units of a new meal item are supplied, then the marginal price at that level of supply is given by p prime (x) = x/(x + 3)^2 dollars per me
- Assume: TC = 5 + 2q + .5q^2, P = 20 - 3q. What is the profit max price, q, TR, cost?
- Suppose a consumer's preference are represented by the utility function \\ U(X,Y) = X^3Y^2 \\ Therefore, \\ MU_x = 3X^2Y^2\\ MU_y = 2X^3Y \\ Also, suppose the consumers has $200 to spend (M = $200) , P_y = 1, and that they spend all of their money on goo
- In a Cournot game with homogeneous commodities, players are firms who simultaneously announce quantities they want to produce. Suppose there are two firms, 1 and 2, whose chosen quantities are q1 and q2, respectively. The market price is given by P = 31 -
- If you assign one worker per computer, what is the cost of inventorying a single item? If you assign two workers per computer, what is the cost of inventorying a single item? If you assign three wor
- For the typical gas station the profit-maximizing price would be: a. P_4 b. P_3 c. P_2 d. P_1
- An individual utility function is given by U(x,y) = x�y. This individual demand (optimal purchase) equation for x is a factor a of I/px: x* = a (I/px). In this specific case, factor a is equal to....
- Suppose that Sally s preferences over baskets containing milk (good x), and coffee (goody ), are described by the utility function U(x, y ) = xy + 2x. Sally s corresponding marginal utilities are, MUx = y + 2 and MUy = x. Use Px to represent the price of
- Consider a Pure Exchange economy with two consumer's and two goods. Let UA(xA,yA) = xAyA with an initial allocation of xA=20 and yA=80. Let UB(xB,yB) = xB + yB, with an initial allocation of xB=80 and
- Suppose an insured individuals willingness-to-pay for a medical good is $100 while the market price of that product is $400. What has to be the coinsurance rate so that the person can buy the product?
- Consider how a tax on a goods affect the price paid by buyers, the price received by sellers, and the quantity sold.
- Assume that we can treat all automobiles as more or less the same. The demand for cars worldwide is P = $140 - 20Q, where P is the price of cars in thousands of dollars and Q is the number of cars sol
- Kelly's preferences over goods X and Y can be represented by the following utility function: U(X,Y) = X^0.75 Y^0.25 Given prices and income, Kelly optimally chooses to consume X* = 3 and Y* = 2. There
- A Consumer has preferences represented by the utility function: U = xy; the Prices are: Px = 1 and Py = 2. I. Expenditure minimization problem: determine the optimal consumption vector and the minimu
- Given an individual's current consumption patterns, we know that the person is consuming in such a manner that he is maximizing his satisfaction. Given a decrease in the price of one of the goods he normally purchases, what will happen to the consumer's t
- A factor that most directly affects the demand for automobiles is: A) the individual tastes and preferences of buyers. B) the cost of raw materials and natural resources. C) the availability of workers in automobile factories. D) a company's ability t
- Sam has preferences for weekly video games (V) and sodas (S) described by the utility function U(V, S) = V^2S^2. Suppose the prices are denoted by pV and pS and Sam has income given by I. Assume that in Sam's optimal bundle, he consumes strictly positive
- Refer to the figure below. Assume that the consumer depicted in the figure has an income of $10. The price of Skittles is $1 and the price of M&M's is $2. This consumer Kill choose a consumption bundle a. A b. B c. C d. D
- Sam has preferences for weekly Video Games (V) and Sodas (S) described by the utility function U ( V, S) = V ^2S^2. Suppose the prices are denoted by p_V and p_S and Sam has income given by I. Assume that in Sam's optimal bundle, he consumes strictly posi
- Consider two goods, x and y. Suppose the quantity of x is measured on the horizontal axis and the quantity of y is measured on the vertical axis. Suppose the consumer likes both goods. Further suppose that the price of x is Px and the price of Y is Py per
Explore our homework questions and answers library
Browse
by subject