Assume that a person's utility over two goods is given by: U(x,y) = x^(alpha)y^(1 - alpha). The...
Question:
Assume that a person's utility over two goods is given by:
{eq}U(x,y) = x^{\alpha}y^{1 - \alpha} {/eq}.
The price of Good X is {eq}p_{x} {/eq} and the price of Good Y is {eq}p_{y} {/eq}. The total income of the individual is given by M.
A) Write down the budget constraint of this person.
B) Determine the demand functions for x and y.
C) Is Good X a normal or inferior good? Is Good Y a normal or inferior good?
D) Calculate the own-price elasticities of demand for x and y.
E) Calculate the cross-price elasticities of demand for both goods.
Price elasticity vs cross price elasticity of demand:
Price Elasticity of Demand (PED) is characterized as the responsiveness of quantity demanded to a change in price. The demand for an item can be inelastic or elastic, contingent upon the rate change of demand with respect to change in its own price.
On the other hand, the cross elasticity of demand estimates the responsiveness in the quantity demanded of one commodity when the price for another product changes. Based on the sign of cross elasticity of demand, the related good can be classified as substitute or complement or neither.
Answer and Explanation: 1
Become a Study.com member to unlock this answer! Create your account
View this answerUtility function of the two goods is:
{eq}U(x,y) = x^{\alpha}y^{1 - \alpha} {/eq}.
Price of Good X = {eq}p_{x} {/eq}, price of Good Y =...
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
Demand in Economics: Definition & Concept
from
Chapter 7 / Lesson 11
97K
Learn about the demand curve and how the law of demand works with examples. See the demand definition, diagrams, and explanations.
Related to this Question
- The consumer is choosing between two goods: good 1 and good 2. Good 1 is priced at $2 and good 2 is priced at $3. The consumer has a total of $600 to spend on both the goods. 1. Let the utility function of the consumer be U (X1, X2) = X1(1/2)X2(1/2). a)
- The consumer is choosing between two goods- good1 and good2. Good 1 is priced at $2 and good 2 is priced at $3. The consumer has a total of $600 to spend on both the goods. Let the utility function of the consumer be U (X1, X2) = Min (X1,X2) a) Calculat
- If a consumer has a utility function of u(x_1,x_2)= x_1x_2^4 where MU_1 = x_2^4 and MU_2 = 4x_1x_2^3 , what fraction of her income will she spend on good 2? Assume that the person faces a downwar
- Consider three consumer goods: 100 of Good A, 100 of Good B, and 100 of Good C. In the base year, Good A sold at a price of $1, Good B sold at a price of $1, and Good C sold at a price of $1. In the current year, Good A sold at a price of $3, Good B sold
- A consumer has the utility function U(x1, x2) = x1x2 and an income of 24 pounds. Initially, the price of good 1 was 1 pound and price of good 2 was 2 pounds. Then the price of good 2 rose to 3 pounds while price of good 1 stayed the same. Find the consume
- An essential characteristic of a public good is that it is non-excludable. This means that A. public goods are of equal benefit to all consumers. B. there is no opportunity cost in the provision of public goods. C. people could consume the good without pa
- Maureen has preferences for two goods to be consistent with the utility function. The price of good 1 is $4 each, and the price of good 2 is $12 each. For what incomes will good 1 be normal?
- Suppose that Ashley likes 2 goods, good 1 (x_1) and good 2 (x_2). Her utility function is given by U(x_1, x_2) = x_1^2 + x_2. Ashley's income is denoted as M and the cost of good 1 (per unit) is P_1 and the cost of good 2 (per unit) is P_2. 1. Write down
- Consider a consumer that consumes only two goods, clothing and food. For this consumer, clothing is a normal good and Food is an inferior good. The consumer has weekly income of $400. In the initial s
- A consumer consumes good x and good y. She initially has an income of I = $1,000 and faces prices of px = $10 and py = $20. Then, the price of good x doubles. In response to the rising prices, the government gives the consumer a lump-sum payment of $300.
- If one individual is willing to pay pound 20 for a unit of public good x, and another is willing to pay pound 40, given that the marginal cost of the good is MC(x) = 10 cdot x, the efficient provision of the public good will be: A. 8. B. 6. C. 4. D. 2.
- A good is nonexcludable if: a)The quantity of the good is affected by the price a consumer pays for the good. b)Consumption of the good by one person decreases the ability of other people to consume t
- Assume that the price of Good X is $5, the price of Good Y is $4, and the consumer's budget is $100 per month. a. Carefully construct and fully label the consumer's budget line. What is its slope? b
- Are all goods that are provided by the government, ?public goods?? Name one that is a public good and three that are not.
- By selecting a bundle of good X and good Y where MRS = MRT, the consumer is saying A) I value my last unit of each good equally. B) I will equate the amounts spent on all goods consumed. C) I am willing to trade one good for the other at the same rat
- A consumer purchased 10 units of good X and 6 units of good Y in year 1 (the base period) when the price of good X was $8 and the price of good Y was $5. The next year (year 2) the price of X fell to $7 and the price of Y increased to $8. a. Set the Lasp
- Is a small amount of money ($50) more valuable to a low-income person than a high-income person?
- Assume that there are only 2 goods, x, and y and that the price of each good is 1, i.e. px = py = 1. (a) Amanda spends $200 on x and $300 on y when her income is $500. She spends $180 on x and $420 on y when her income is
- Consumer surplus is best defined as: a) The amount a person is willing to pay for a good, b) The difference between what a person is willing to pay for a good and what a person actually has to pay for the good, c) The amount of total utility a person rece
- The utility that people experience from the consumption of a good depends on: A. total sales of the good. B. their income level. C. their tastes and preferences. D. how much shopping time they spent obtaining the good.
- Consider an intemporal exchange economy with two consumers, A and B, and one perishable consumption good. Person A is endowed with 4 units of the good in period 1 and 0 units in period 2. Person B is
- An individual's valuation of a good or service is: a. impossible for individuals to express. b. known as willingness to pay. c. lower than the maximum value the individual will pay. d. generally the same from person to person.
- If a consumer is willing and able to pay $20 for a particular good and she actually pays $16 for the good, then her consumer surplus is: a. $4 b. $16 c. $20 d. $36
- A person has a utility functions with MRSxy = change in Y/ change in X. The price of good X is $10 and the price of good Y is $20. The person has a budget of $1,000 for purchase of X and Y. a. What is the equation of the person's budget line? b. If this
- 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.
- Suppose Hodor and Bran are the only two consumers in society. Each has a utility function of the form U = X^{1/2}Y^{1/2}. Good X is a private good and good Y is a public good. The price of good X is P_x and the price of Y is P_Y. Each has an identical in
- A good is considered excludable in consumption if: individuals who do not pay for the good are kept from enjoying its benefits: one individuals consumption of the good results in less of it being avai
- If a producer offers a price that is below a consumer's valuation of the good, the consumer: A. will buy the good at that price. B. will refuse to purchase the good. C. will revalue the good. D. None of the statements associated with this question are cor
- Assume that there are only 2 goods, x, and y and that the price of each good is 1, i.e. px = py = 1. (a) Amanda spends $200 on x and $300 on y when her income is $500. She spends $180 on x and $420 o
- Assume that there are only 2 goods, x and y, with the price of each good is 1, i.e. p_x = p_y = 1. A) Amanda spends $200 on x and $300 on y when her income is $500. She spends $180 on x and $420 on y
- Jack treats goods x and y as perfect complements always combining 2 units of good x with 1 unit of good y. Suppose the price of good x is P_{x}=1, the price of good y is P_{y}=2, and Jack's income is
- An individual consumes two goods, clothing and food. Given the information below, illustrate the income-consumption curve. |Clothing Price |Food Price| Clothing |Food |Income |$3.00 |$12.00 |200 |5
- An agent's utility function is __U(X,Y) = 2X + Y__. The price of X is $5 and the price of Y is $2. The agent's total income is $100. What is the optimal bundle that maximizes utility?
- Suppose there are two citizens whose value for a public good in terms of private good X given up are MRS1XG (G)=50-G, MRS2XG (G)=100-2G. Suppose also that each unit of the public good provided costs
- Refer to the above table. If the price of Good X is $2, the price of Good Y is $1, and the consumer has $9, the rational consumer will purchase:
- A good is non-excludable if: a. when you pay for the good, you are guaranteed to be the sole consumer. b. nobody can be excluded from enjoying the benefits of the good. c. it is also non-rival. d. when you consume a unit, that means there is no less for s
- A consumer may not necessarily choose to buy a good based solely on which item has the greatest utility. Two other highly important factors are Blank. a. need and income. b. price and desire. c. income and price. d. size and color.
- The price of Good x is P_x = 1 for the first 50 units, and P_x = 0.50 thereafter. The price of Good y is P_y = 1 for the first 50 units, and P y = 0.50 thereafter. Income is I = 100.
- Determine whether each of the following goods is a private good, a public good, a common resource, or a club good. || ||Private Good||Public Good||Common Resource||Club Good |A new guitar for you to p
- Show two consumers, purchasing a basket of goods, each that maximizes their happiness, subject to their budget line. Make sure they face the same prices, but otherwise, their incomes and preferences can be different. Do not violate any properties of ICs.
- Suppose there are two consumers, A and B, and two goods, X and Y. Consumer A is given an initial endowment of 6 units of good X and 1 unit of good Y. Consumer B is given an initial endowment of 2 unit
- The absolute price of a good is its? a. money price. b. projected price. c. relative price. d. subjective price.
- If your income goes up by 2% and, in response, the quantity demanded of good x rises by 3%, good x can be considered: a. An inferior good. b. A normal good. c. A public good. d. A private good.
- You are the manager of firm X. The demand for your product is given by Qd = 300 - 3Px + 4Pz - 4I. Good Z is the alternative good and I stands for income. Which of the following statements is true? A. Good x is an inferior good and good x and z are complem
- The nominal value of a good is: A. the good's value expressed in purchasing power terms. B. the price of the good in today's dollars, minus an anticipated inflation premium. C. the good's anticipated value one year from now. D. the price of the good in t
- A consumer is trying to make up her mind about what market basket to purchase. She's got so much good 1 in her shopping cart and so much good 2. The cost of those quantities adds up to her income. When she consumes those quantities of goods 1 and 2, her M
- If the value of the consumer price index (CPI) in 2013 was 135 and the value of the CPI in 2012 was 117, it would be correct to say that: A. typical basket of goods was about 18 percent more expensive in 2013 than in 2012. B. typical basket of goods was
- Items bought by individuals to provide personal enjoyment are called: a. personal goods b. consumption goods c. consumption or investment goods d. standard goods
- A consumer consumes one consumption good x and hours of leisure h. The price of the consumption good is p, and the consumer can work at a wage rate of s=1. What is the consumer's Walrasian budget set?
- List five sets of two goods each (i.e., each set is composed of two goods; for example, diamonds and water make up one set) such that the good with the greater value in use has a lower value in exchange than does the good with the lower value in use.
- Willingness to pay may not be an accurate measure of a consumer's benefit from a product because the consumer: a. may not find the product sufficiently expensive. b. may dislike the product. c. may be too poor to pay very much. d. may have an elastic dema
- Items bought by individuals to provide personal enjoyment are termed: a. personal goods. b. consumption goods. c. consumption or investment goods. d. standard goods.
- A private good is a good that: A) is available for everyone to consume, regardless of who pays. B) cannot result in external benefits or costs to those who don't consume. C) is consumed by a single person or household. D) cannot be used by private citizen
- Consumers A and B consume good 1 and good 2 in an exchange economy. A's utility function is U^A = min(q_1^A, 2q_2^A) while B's utility function is U^B = q_1^B(q_2^B)^2. Their endowments are (e_1^A ,
- An asset is: a. anything of value owned by a person or a firm. b. a payment by a corporation to its shareholders. c. a nonmonetary opportunity cost. d. anything owed by a person or a firm.
- Assume you win a lottery. If you now purchase a smaller quantity of some item, what label would an economist attach to this good? Give personal examples of such an item. What kind of good is it if you buy more when your income rises? Which elasticity is i
- In the table below you will find the Quantity Consumed and Price of Good A and Good B. || ||Base Year||Later Year |Price of good A|100|200 |Quantity of good A|100|200 |Price of good B|100|100 |Quantit
- Can utility be measured as the price you're willing to pay divided by your total wealth?
- A consumer's budget is M=300, which she spends on buying two goods, X and Y. Her utility from consuming x units of good X and y units of good Y is given by the following Cobb-Douglas utility function
- Imagine that preferences of a given individual are presented with U(X1 ,x 2 )=X 1 -e^ ? x 2. Assume that the prices of the two goods consumed by this individual are given by p1 and p2. Normaliz
- 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 beer is an inferior good and the price of beer falls, then the substitution effect results in the person buying _____ (less/more) of the good and income effect results in the person buying _____ (less/more) of the good.
- If the price of X is set at $1 per unit, the quantity of the good purchased by this consumer each month will be _____. a. 10 b. 16 c. 24 d. 36 e. 48 f. 56 g. 60 h. 64 i. 72 j. 96
- Suppose Naomi consumes two goods: good 1 and good 2. Last year, the price of good 1 was $2.00 and the price of good 2 was $5.00. Given these prices, Naomi maximized satisfaction consuming bundle A. H
- In year 1, the prices of goods alpha, beta, delta are $2, $4, and $6 per unit, respectively. In year 2, the prices of alpha, beta, delta are $3, $4, and $7, respectively. In year 2, twice as many unit
- Do public goods come under the umbrella of merit goods?
- Suppose there are two consumers, A and B, and two goods, X and Y. Consumer A is given an initial endowment of 6 units of good X and 1 units of good Y. Consumer B is given an initial endowment of 2
- The absolute price of a good is its: a. subjective price b. money price c. relative price d. projected price
- Mary has utility over Goods 1 and 2 given by U(x1, x2) = x12x2. What is the value of MRS(2, 3)?
- If the absolute (or money) price of good A is $40 and the absolute price of good B is $60, what is the relative price of each good?
- Consider a consumer choosing between two goods, food and gasoline. Suppose her monthly income is $1500 and average price of food per unit is $30. Price of gasoline per liter is $50. What is the opportunity cost of food?
- Suppose Jane has chosen a combination of two goods, A and B, such that MU/P of good A is 10 (MUA/PA = 10), and the MU/P of good B is 10 (MUB/PB = 10). To increase utility with the same amount of money
- Suppose a consumer buys 10 units of good X and 20 units of good Y every year. The following table lists the prices of goods X and Y in the years 2005-2007. Assume that these two goods constitute the typical market basket. Calculate the price indices for t
- Suppose a consumer buys 10 units of good X and 20 units of good Y every year. The following table lists the prices of goods X and Y in the years 2005-2007. Assume that these two goods constitute the typical market basket. Calculate the price indices for
- In the use of contingent valuation under cost-benefit analysis: A.people's travel costs determine the value of a public good. B.the value of similar market-traded goods estimates the value of a publ
- 27.) For Questions a-f, consider a household that consume only two goods ? food and ?other goods? ? that are each normal goods The income of the household is $120, the price of food is $10 and the pri
- A public good is one that once produced and provided to one person, provides benefits to: a. other persons who didn't necessarily pay for it. b. only the person who bought it. c. only U.S. citizens. d. no one.
- 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?
- 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
- Frank's utility function is U = 10X + 6Y. Frank has a budget of $60 to spend on goods X and Y. The price of good X is $3 and the price of good Y is $2. How many units of good X and good Y does Frank purchase?
- When one person uses a common pool resource: a. an externality arises. b. other people are worse off. c. it is difficult to charge him or her for the usage of it. d. that person gets the benefits of usage. e. all of these answers are correct
- Suppose that Angie's MUx=Y^2 and MUy=2XY. The price of good X is $ 10 and the price of good Y is $ 2. If Angie is consuming 8 units of good X and 16 units of good Y, is she maximizing utility?
- Consider a consumer choosing between two goods, food and gasoline. Suppose her monthly income is $1500 and average price of food per unit is $30. Price of gasoline per liter is $50. What is the opportunity cost of gasoline?
- Suppose that a person's utility is given by: Where a = 1.1 and b = 0.5. Additionally, we know that m = 168. If this is the case, and we are purchasing 17 units of good 1(x1), then what must p1 eq
- There are 2 consumers and 2 commodities. Consumer A's initial endowment is 4 units of good x and 1 unit of y, and the utility function is U=x*y. Consumer B's initial endowment is 0 units of x and 7 units of B,and the utility function is U = min{x,y}. 1)
- Public goods tend not to be sold in the marketplace because: A. they are, by nature, so inexpensive that everyone would be able to afford to buy them if offered in the marketplace. B. the benefits w
- If a good that is excludable but is also non-rival in consumption, then it is [{Blank}]. a. a private good b. a club good c. a common resource d. a public good
- If a good that is both excludable and rival in consumption, then it is [{Blank}]. a. a private good, b. a club good, c. a common resource, d. a public good.
- Goods are rival if: a) It is not possible to prevent an individual from using the good. b) Consumption of a good by one person decreases consumption by another person. c) It is possible to prevent an individual from using the good. d) The quantity of the
- A good or service that a business can charge for, and consumption by one person does not reduce the ability of others to consume the same product is considered a a) public good. b) quasi-public good. c) private good. d) public-private partnership.
- If good X is normal and good Y is inferior, following an increase of income: a. the new optimal bundle will contain more X and less Y. b. the new optimal bundle will contain more Y and less X. c. the consumer's utility will be unchanged. d. the consum
- What condition must be satisfied in order for an individual to be at their optimal income-leisure bundle?
- If a consumer lives in poverty, his/her reservation price for food A.is a reliable measure of the benefit you will be receiving from consuming that good. B. is not a reliable measure of the benefit
- Suppose there are two goods, food, c, and leisure, L. The prevailing prices of c and L are p = $1/unit and w = $10/hr:, respectively. Suppose you can consume no more than 24 hours of leisure per day a
- The money used to purchase goods or services is functioning as a: a) store of value. b) medium of exchange. c) unit of account. d) standard value.
- The tragedy of the commons is that: a. too few individuals have access to high quality healthcare. b. common people overconsume public goods. c. the quality of life for lower income people is generally lower than that of higher income people. d. a res
- Common property a. is owned by specific people b. is inexhaustible c. refers strictly to land resource d. refers to goods "owned" by society at large and freely usable by anyone
- The Consumer Price Index is a measure of the {Blank} of the prices paid by {Blank} consumers for a fixed market basket of consumption goods and services. A. average; urban B. sum; urban C. sum; rural D. average; rich
- In 2011, Product X costs $2 and a consumer, Tom, bought 500 units of this good. Additionally, a related good, Product Y, cost $10 and Tom purchased 200 units of this good. In 2012, X still costs $2, b
- Are there any products that have an appreciating value, rather than a depreciating value?
Explore our homework questions and answers library
Browse
by subject