A consumer has preferences represented by the utility function:with 0 < a < 1.U (x₁, x2) = aln(x₁) + (1 − a)ln(x₂)(a) Derive demand functions (optimal choice of x1 and x2 as a function of income and price(s)).(b) Derive price and income elasticities.

A consumer has preferences represented by the utility function: U(x₁, x₂) = aln(x₁) + (1 − a)ln (x₂) with 0 < a < 1. (a) Derive demand functions (optimal choice of x1 and x2 as a function of income and price(s)). (b) Derive price and income elasticities.

A consumer has preferences represented by the utility function: U(x₁, x₂) = aln(x₁) + (1 − a)ln (x₂) with 0 < a < 1. (a) Derive demand functions (optimal choice of x1 and x2 as a function of income and price(s)). (b) Derive price and income elasticities.

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

See similar textbooks

Related questions

Q: Consider a system of banking in which the Federal Reserve uses required reserves to control the…

A: This can be described as the central authority of the banking system of that particular nation. The…

Q: Suppose a profit-maximizing monopolist faces no threats from possible new entrants to its industry.…

A: There are many sellers, however, the products produced by each seller are different. The products…

Q: Chapter 13: Cost of Production Questions: 1. Which is bigger... accounting profit vs. economic…

A: Total cost is the total cost of production, which includes both fixed and variable costs. Marginal…

Q: As the price of cookies increases, firms that produce cookies will: Multiple Choice O O O increase…

A: With regards to the market for treats, the law of supply recommends that makers, like treat…

Q: Show the possible effect of this free entry and exit by shifting the demand curve for a typical…

A: Monopolistic competitive market is the hybrid of perfect competition and monopoly where there are…

Q: Year Unemployment Rate Inflation Rate Economic Growth Rate 2009 18.9% 0.4% -1.38% 2010 19%…

A: The economic performance of developing countries, particularly those in the Caribbean, has been…

Q: OPTION 2: The Cheesiest: Consider a competitive market for cheese, with two producers and four…

A: A perfectly competitive market is a theoretical economic model that describes an idealized market…

Q: Hanging out the side of the helicopter, he slowly dumps the bag containing a total of $100 million…

A: Helicopter money is the large amount of money being printed and distributed among the people in the…

Q: Tea Shoppe More Advertising Less Advertising Coffee. Co. More Advertising $2,500 $2,500 $1,000…

A: Dominant strategy is an expression in game theory that implies the optimal option for a player among…

Q: In period t, a parental household (indexed by i) equipped with human capital hit earns a labour…

A: Utility FunctionBudget ConstraintHousehold Income - Cost of educating children = .

Q: Refer to Figure 7.4 (above) for a perfectly com O Average variable costs at the output E. Total…

A: A perfectly competitive firm is a price taker. This means the price in a competitive market is…

Q: 3. Consider the relative PPP. If Foreign country's inflation rate is 5% and E changes by 2%, how…

A: The movement of currency from one country to another country through exchange is called the exchange…

Q: 10. Problems and Applications Q10 Suppose firms become very pessimistic about future business…

A: The total amount of goods and services produced in an economy at all potential price points at a…

Q: Using the framework of the supply and demand of loanable funds, analyze the possible effect on the…

A: The objective of the question is to analyze the possible effect on the equilibrium interest rate in…

Q: Market A B C D Characteristic Demand is very clastic relative to supply. Demand is very inelastic…

A: The demand curve shows an inverse relationship between price and quantity demanded. Demand is a…

Q: 1) In period t, a parental household (indexed by i) equipped with human capital h earns a labour…

A: Utility FunctionBudget ConstraintHousehold Income - Cost of educating children =

Q: Use the supply and deman Price $5 8 11 14 17 Quantity Demanded 75 65 55 45 35 Instructions: Enter…

A: Supply and demand is an economic model of price determination in a market. It postulates that,…

Q: QUESTION 1 For the production function Q=K0.6L0.1 and the budget 144 = 8K + 3L find the NEW LEVEL of…

A: INTRODUCTION: the production function Q = K0.6L0.1 represents a Cobb-Douglas production function,…

Q: Initial deposit ($100) $ The Money Multiplier Process Loan Loan University Bank $ Excess reserves:…

A: A loan is a form of borrowing in which a lender provides an amount of money to a borrower with the…

Q: Question 1 According to a researcher at the FDA, vegan foods are “the way if the future”. More…

A: Demand is the quantity of a good or service that consumers are willing and able to buy at a given…

Q: The following table shows demand and marginal cost for a monopolist. Calculate marginal revenue (MR)…

A: This can be defined as a cost that shows the type of cost that an individual, business, or any other…

Q: Judy allows her friend Tim to use her car whenever he’s in town on business. Which economic practice…

A: Judy allowing her friend Tim to use her car presents an economic scenario involving the sharing of…

Q: Because this market is monopolistically competitive, you can tell that it is in long-run equilibrium…

A: A monopolistically competitive market is a type of market structure where there are many firms…

Q: In a monopolistically competitive market, A strategic interactions among the firms are very…

A: A market system with several enterprises operating and each selling somewhat different items is…

Q: Suppose you are the manager of a watchmaking firm operating in a competitive market. Your cost of…

A: The firm is operating in a competitive market.The cost of production is given by C = 400 + 2q2The…

Q: using an interest rate of 3% per year(effective), calculate feasibility of each option (I),(II). use…

A: Present Worth Analysis involves discounting future cash flows to their present value using a…

Q: While the salaries for all three countries (for the three industries shown) are all smaller than…

A: Wage refers to the sum of money given by employers or owners of a business to their employees in…

Q: The AD-AS graph below illustrates the U.S. economy at the end of 2021. Actual real GDP was $18.4…

A: The AS-AD model in macroeconomics is used to comprehend and explain how changes in aggregate demand…

Q: 1. A 3-year 10% coupon bond has $1000 face value. What is the duration of this bond? (Assume this…

A: A type of debt instrument used by governments or corporations to raise finance from the public is…

Q: Maya is doing her undergrad at Queen's University. She loves donuts and chocolate chip cookies…

A: a) When the price of CCC (chocolate chip cookies) is $1, which is the same as the price of donuts,…

Q: a. Monetary Policy involves changing (Click to select) (Click to select) b. (Click to select)…

A: Monetary policy is the policy of the central bank through which the money supply and the interest…

Q: The following graph illustrates a shift of the aggregate demand curve to the right. It can be caused…

A: The aggregate demand (AD) curve shows the total quantity of goods and services demanded in an…

Q: Given the following supply, demand and marginal revenue fi QS = 5P-25 Q = 100-5P MR = 20-2/5Q (a)…

A: Competitive equilibrium occurs when demand and supply forces are equal. Firms are price taker in…

Q: BND11.1 Why Do Externalities Cause Deadweight Loss?

A: The externality is defined as the cost or benefit that is unrelated to the third party involved. It…

Q: Figure 8-2 Price Level (P) a a Q, Real GDP (Q) Refer to Figure 8-2. A movement from point A to point…

A: The curve AD1 represents the aggregate demand curve. The aggregate demand curve is a curve that…

Q: The market for toothpaste is a monopolistically competitive market. The graph below depicts the…

A: Monopolistically competitive market can be defined as a market situation in which there are many…

Q: $16T $14T $12T SIOT S8T 2010 2011 2012 2013 2014 2015 2016 2017 2018 2019 2020 a) Calculate the rate…

A: Inflation is the general increase in price level over a period of time.

Q: hat is the total cost and marginal cost when fixed cost is 25, average cost is 57, total revenue is…

A: The marginal cost refers to change in total cost when one additional unit of output is produced. The…

Q: At output Q₂2 and price P2, which of the following is TRUE? OA. The firm suffers some diseconomies…

A: The study and analysis of commercial difficulties impacting businesses using abstract economic…

Q: 11. The use of online banking would A) increase; menu B) decrease; shoe-leather C) increase;…

A: The given question tends to the effect of web based depending on the cost related with a high…

Q: An economy's GDP is $2000 billion, desired consumption spending $1200 billion, desired investment…

A: National income estimates provide informed viewpoints on a country's economic health, challenges,…

Q: A UK-manufactured car sells for GBP 14.000. A french-manufactured car sells for EUR 15.750. If the…

A: The objective of this question is to convert the price of a UK-manufactured car from GBP to EUR…

Q: In general, consider the following three market structures: (a) perfectly competitive market (b)…

A: Perfect competition is a type of market where there are very large number of firms, which have no…

Q: Gizmo, Inc. has just announced year-end results as follows: alculate the book value per share.…

A: The entire sum of money that would be distributed to shareholders in the event that the business…

Q: For problem 1 and 2, consider the following game : C D A (0,5) (5,-5) B (3, 1) (1, 0) 1. Show that…

A: There are two players : { Player 1 , Player 2 }Strategy Set : { A , B }Strategy Set : { C ,B }…

Q: Question 1 A consultant recently provided the firm's marketing manager with this estimate of the…

A: The demand curve represents the quantity demanded by consumers at different price levels. The supply…

Q: Question 12 Higher barriers to entry and exit are generally associated with O lower profits higher…

A: A single firm operating in the market often does not want other firms to enter the market to…

Q: The graph shows the demand for university education. The marginal cost of educating a student is a…

A: When an activity have external benefits, social benefits will be higher than private benefits.

Q: Table: Demand Schedule of Gadgets Price of a Gadget $10 9 8 7 6 5 4 3 Quantity of Gadgets Demanded…

A: Demand is the desire of an individual ability and willingness to pay for a product. The demand is…

Q: Figure: Aggregate Demand and Aggregate Supply 1 Inflation rate 10 9 8 7 6 5 4 3 2 1 0 0 A. B. 1 O c.…

A: The total supply of goods and services produced in an economy within an aspect time period is called…

Question

A consumer has preferences represented by the utility function:
with 0 < a < 1.
U (x₁, x2) = aln(x₁) + (1 − a)ln(x₂)
(a) Derive demand functions (optimal choice of x1 and x2 as a function of income and price(s)).
(b) Derive price and income elasticities.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1: Introduction

VIEW

Step 2: a) Derive the demand curve

VIEW

Step 3: b) Price and income elasticities

VIEW

Solution

VIEW

Step by step

Solved in 4 steps with 28 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, economics and related others by exploring similar questions and additional content below.

Similar questions

Ricky has utility function u=x'y. This implies that MUx=2xy. MUy=x². His income is 100. The price of y is 10. (a) Find his demand for x at price 20. (b) Find his demand for x at price 30. (c) Write down his demand function for x: that is, write down his demand for x as a function of the price of x.
A consumer with I dollars budget has the utility u(x,y) = x(y+1) over amounts of cake (x) and ice cream (y) she consumes. The prices are px , py respectively. (a) Derive her demand for cake (x), as a function of prices px , py and her budget I. (b) Looking at the demand function in (a), is cake a normal good or an inferior good? Are cake and ice cream complements or substitutes? (c) Calculate the (i) (own) price, (ii) income, (iii) cross- price elasticity of demand for cake at the point where I = 80, px =10, py = 20.
Utility Maximization A consumer faces income constraints and has CES preferences of the following form: U(x, y) =x y Find the consumer’s demand for x as a function of prices and income
A consumer has utility (see image) on ice creams (x) and cakes (y). (a) Are the indifference curves bowed towards the origin? (b) Derive his demand function (as a function of prices px, py and budget I) for ice cream (x). (c)(Looking at the demand function you found in (b), Is ice cream a normal good? Are ice cream and cakes substitutes or complements? Calculate the income elasticity of market demand at the point px = 2, py = 1 and I = 12.
Consider the utility function: U(x,y)= -4(3x-12)² - (2y-10)² Determine the marginal utility for the two commodities
your answer. 2. The utility function of a consumer over two goods x and y is given by u(x,y) = 20 ln x + 2y The price of y is 1. Let p denote the price of x. The consumer has an income of M> 10. The consumer's price elasticity of demand for x has a lower absolute value compared to the income elasticity of demand for y. Is this true or false? Explain by calculating both elasticities.
Given the utility function U = X0.5+Y0.5 and budget constraint I=Px X+ Py Y,(a) Is this utility function is homothetic?(b) Derive the consumer’s demand functions for goods X and Y.(c) Obtain the numerical values of the own-price elasticity, cross-price elasticity, and the income elasticity of demand for X and Y.(d) Derive the indirect utility function and the expenditure function for this consumer.e) Obtain the compensated demand functions for goods X and Y. (f) Prove that the Slutsky equation holds in this case.
1. For each of the following three utility functions below, find the demand function by explicitly solving each utility maximization problem. (a) u(x1,x2) = xx. (b) u(x1, x2) = Inx1+2lnx2. (c) u(x1,x2) = x7x3.
Exercise Suppose the utility function of a person consuming two commodities X and Ywith income Birr 600 is given by U = 2 X 06Y 04 If the per unit price of X is Birr 20 and per unit price of Y is Birr 40 a) What is the utility maximizing level of consumption of X & Y ? b) Find the MRSyy at the optimum ?
The consumer’s utility function is u(x1, x2) = 2√x1 + √(x2/4) (a) Determine the equilibrium condition for MRS21 and prices p1, p2. (b) Express the general form of D1(p1, p2, m), D2(p1, p2, m). (c) Calculate the desired amounts x1, x2 for p1 = 8, p2 = 2, m = 80. (d) Express the general form of income elasticity for commodity x1. Please show working step by step for b,c,d with final values of solution like in a
(A) Suppose an individual who derives utility u(x, y) from consuming a units of the good X and y units of the good Y. Prices of goods X and Y are respectively p = 1 and Py = p. Furthermore, the individual has a budget m. What is the demand for Y if the utility function is: u(x, y) = min{x, ay}. (a) y(p, m) = am (b) y(p, m) = = (c) y(p, m)= (d) y(p, m) = = am a+p m a+p m 1+p (B) Same setup as (A) with u(x, y) = ax + y and ap Pr. The quantity demanded of good X is q. Which of the following is true ? (a) The substitution effect increases q but the income effect decreases q and over- come the substitution effect. Overall q decreases. (b) The substitution effect decreases q but the income effect increases q come the substitution effect. Overall q increases. and over- (c) Both the income and substitution effects increase q. Overall q increases. (d) Both the income and substitution effects decrease q. Overall q decreases. (D) Suppose an inferior good X (not Giffen). Its price increases from…
Constant Elasticity of Substitution utility function U(x. y) = (x^a*y^ (1-a))^b + y. I am looking for a this form of CES utility function to derive demand functions. (Note = > a is alfa, b is lambda).