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.

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter5: Income And Substitution Effects

Section: Chapter Questions

Problem 5.12P

See similar textbooks

Related questions

Q: Hasmi has an income of $100. a. Draw their budget constraint when the price of Ais $1and the price…

A: A budget line which represents the budget constraint shows various combinations of two goods a…

Q: Why do mainstream institution theories have a highly problematic understanding of the relationship…

A: The mainstream institution theories have a highly problematic understanding of the relationship…

Q: Customs administrations play several roles in national development, in protecting society and in…

A: National Development National development is the capacity of a country to raise the standard of…

Q: Define the term 'opportunity cost'. 2. Explain why the NHS has to make 'tough choices' about what it…

A: Health care economics deals with various factors that converge to influence the health care…

Q: Barriers to entry exist for perfectly competitive firms. restrict the entry of new firms into the…

Q: 2.5 The only variable input a janitorial service firm uses to clean offices is workers who are paid…

A: The cost that varies per unit of output is known as a variable cost, as the name suggests. The…

Q: True or False: In the case of a discount bond, the bond's return matches the rate of capital gain

A: All the instruments employed in various markets for speculation or other similar reasons are covered…

Q: Five friends plan to establish a consulting firm after 5 years. The plan is for each to make…

A: Net present value or NPV can be defined as the capital budgeting tool that is used to make a…

Q: 5

A: “Since you have posted a question with multiple sub-parts, we will solve the first three sub-parts…

Q: Economic activity that is above potential output signals that potential output is about to increase…

A: “Potential output is defined as the maximum amount of goods and services an economy can produce or…

Q: Kiwidale Dairy is considering purchasing a new ice- cream maker. Two models, Smoothie and Creamy,…

A: To solve this problem, let us assume that the minimum acceptable rate of return (MARR) which makes…

Q: 1. The Grossman Model envisions consumers deciding between investments in health H and investments…

A: Production possibility curve: It refers to a curve that shows the combinations of goods to buy. It…

Q: In the diagram to the right, we have five different combinations of movies and books. Combination A…

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Chen's family is saving for a home renovation that they would like to pay for with cash. They would…

A: According to this question P= $150,000 A1=10,000 i=5% per year n=15 years We have to find the…

Q: is cheap and requires fewer workers to run. Demonstrate the effect this equipment has on the and for…

A: Equilibrium in the labour market is where demand for labour and supply of labour are equal. This…

Q: Importance of price elasticity

A: Price elasticity measures how responsive a good's supply and demand are to price changes. It is…

Q: The table below shows the per unit prices and marginal utility for the last unit of waffles and…

A: In economics, it is assumed that individuals are rational and take the decision which is in their…

Q: 1. Below is the price and quantity information a firm. For example, at a price of $2.80, 60 units…

A: A demand curve refers to a graphical depiction of the connection between the price of a product and…

Q: Draw CASH FLOW DIAGRAMS for the GIVEN AND REQUIRED/FIND. Begins the solutions by writing the…

A: The formula that will be used to solve the given question: Equal payment series compound amount…

Q: Discuss the major shortcomings of the Basle I accord.

A: Basel I was the first global agreement on adequate amount of bank capital. Criticisms include that…

Q: A vertical demand curve or supply curve would be called:

A: In a vertical supply or demand, the amount that is being supplied or demanded is fixed and does not…

Q: Consider a market for books. Demand is given by QD=120-P. Supply is given by Qs=5P. The equilibrium…

Q: Given the following demand function: Q=15.6-0.5 p (a) Graph the demand curve. (b) Calculate for…

A: Given Demand function: Q=15.6-0.5p To draw the demand curve, we just require x-intercepts and…

Q: Can You show the sollution for letter C please? Thank you!

A: We have given that the $400 will be paid over a period of 7 years That means the future value (FV)…

Q: Consider the following hypothetical income tax brackets for a married couple. Assume for simplicity…

A: Tax is the compulsory levy which is imposed by the government. There is no quid pro quo associated…

Q: In a market with perfect competition, 1. Prices are set by businesses. 2. Businesses confronting an…

A: Theoretically, perfect competition creates a monopoly that enables a business to set any price…

Q: 2) Suppose the following game of "Matching Pennies." In this game, each player chooses heads or…

A: In a Nash equilibrium each player choose the approach that, given the approaches taken by their…

Q: What year end payment is equivalent to the monthly payments that would be paid on a $2,000 loan that…

A: Present value P=2000 r=1% per week We have to calculate the year-end payment which is equivalent to…

Q: A consumer of two goods has indirect utility v(p, w) = -1/2 +P₂ (a) Find the indirect money-metric…

A: Indirect utility function means a combination of the function of prices of goods and income of…

Q: Which individual is cyclically unemployed?

A: Unemployment is the situation where a person who is willing abd able to work is not getting a job.…

Q: The local goverment unit is planning to construct a steel foot bridge in Davao City. The estimated…

A: Given Construction cost (initial cost at t=0) = P400M Annual maintenance cost of the bridge…

Q: 56

A: We know that As economies and societies developed, the study of economics got more complicated.…

Q: You are a policy maker who is interested in increasing tax revenues in order to reduce the Federal…

Q: You are considering going to a football game. However, the roads are cover in ice due to bad…

A: Utility Function : U(Z) + U(D) = ln (Z - 3) - ln(2-D) Also it is given that , D = 1 So utility…

Q: Goal 10: Reduced Inequalities. Income inequality is on the rise the richest 10 percent have up to 40…

A: We are aware of the significant difficulties we confront in the modern world, including the pressing…

Q: produce a discussion paper for a group exercise with other candidates which analyses the…

A: The cultural and regulatory diversity of international markets can present both challenges and…

Q: Year Price of strawberries 2014 $0.75 Quantity of strawberries 100 Price of cream $3.00 Quantity of…

A: Nominal GDP = ∑Output * Current Price Real GDP = ∑Output * Base year Price GDP Deflator = Nominal…

Q: A consumer of two goods has indirect utility v(p,w) = 1/2 -1/2 √w + P₂ P₁ (a) Find the indirect…

A: Money Metric utility Both income and expenditure metrics will be the center of the research on…

Q: Suppose, the current year is the base year for the price index calculation, and a. Calculate the…

A: The inflation rate refers to the increase in the prices of a bunch of different goods and services…

Q: #4. Agriculture in india is mostly characterized by perfectly competitive market why? Short answer…

A: Agricultural economics is a branch of economics that focuses on using economic theory to improve…

Q: The following graph shows the market for croissants in Philadelphia, where there are over 1,000…

A: Given:

Q: What would happen if the government started regulating product prices, and how would that affect…

A: The fundamental building block of economics is the determination of market prices through the…

Q: Suppose that when the price of a burger decreases from $2.00 to $1.75 and other things remian the…

A: The cross-price elasticity assists to measure the correlation between the price of one good and the…

Q: 5. The _______________ is the quantity where quantity demanded and quantity supplied are equal at a…

A: The markets are the place where the buyers and the sellers of different goods, and services are…

Q: When the price of good Y increases from $2 to $3, the quantity demanded for good X decreases from 20…

A: "Cross-Price elasticity of demand between two commodities indicates how responsive is the demand for…

Q: Why aren't greater resources given to prudential regulation of the financial sector because it is…

A: It is difficult for regulators to effectively coordinate and collaborate with the financial…

Q: Question 07 The figure below shows the supply and demand of two related markets: college degrees and…

A: Here, when analyzing given graphs, it can be said that the first graph indicates market for College…

Q: Ellen is downloading labor market data for the most recent month, but her connection is slow. So far…

A: Given that,Unemployment rate = 5.2%Participation rate = 62.5%Not in labor force = 60 million

Q: a. What is the sample range? b. If you would like to construct a frequency distribution table with 6…

A: Sample range = maximum value - minimum value = 13.5 - 5.2 = 8.3

Q: 4. Find the total differential of z = (5x³-12xy-6x5)

A: The total differential of a function with two or more independent variables is equal to the sum of…

Question

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.

Expert Solution

This question has been solved!

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

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 2 steps

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

Derive demand functions for x and y for the general class of Cobb-Douglas preferences represented by the utility function u(x, y) = x α y β . As functions of px, py, I, α, and β, calculate price elasticities, cross-price elasticities, income elasticities, and expenditure shares for x and y.
Suppose that an individual has a Utility function represented by a CES function. The utility function of the individual is given as: U(x,y) = x1/2 + y1/2 b. Calculate the own price elasticity using the "share elasticity" of any good. Let us assume that the prices of both goods are equal.
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
If the utility function for a consumer is defined by U=6X^0.6Y^0.7 . Given that the consumer's income is 300 currency units and unit price of goods X and Y are 12 and 15 currency units respectively, calculate the equilibrium quantity of both goods. Compute the price elasticity of demand for both goods and interpret your results. If income and prices of the two goods increase by 50%, calculate the equilibrium quantities of both goods
Suppose the utility function is represented by the following equation: U (X, Y) = XY + X + 2Y + 2 and the budget constraint (I = PxX + PyY) is represented by (I = 95; PX = 10 and PY = 5): 95 = 10X + 5Y a. Determine the optimal quantity to buy of X and Z subject to the budget constraint. b. What is the total profit under the optimal combination? c. By how much will total profit increase if income increases by one dollar?
If the utility function for a consumer is defined by U=f(X,Y)=3√(X^2Y), Given that the consumer's income is 900 currency units and unit price of goods X and Y are 20 and 30 currency units respectively, find the combination of X and Y which optimize the consumer satisfaction.
What is the demand for goods L and Y given the utility function U(L,Y) = L+2Y where the price of L is $1 dollar per unit and the price of y is $Z per unit.
True/False Utility refers to the total satisfaction or happiness that an individual get from consuming a product.
Suppose a consumer’s utility function u is given by u(x) = x1 x22 where x1 and x2 are amounts of two commodities consumed a) Find the utility-maximing demand for x1 and for x2. b) Are the second-order sufficient conditions for a maximum satisfied?
A consumer's preferences are represented by the utility function If the budget constraint is P1X1 + P2X2 = M, determine the demand functions q1(P1, P2, M) and Q2(P1, P2, M). Determine also the indirect utility function V(P1,P2,M).
Assuming a linear budget constraint, consider the following utility maximization problem:U (x1, x2) = 2x10.5 + 4x20.5 1. Compute the Marshallian demand functions for goods 1 and good 2.2. Find the compensated demand function.3. Derive the expenditure function and verify that h (p, u) = ∇pe (p, u)4. Derive the indirect utility function and verify Roy's Identit
Upon graduating from UT this May, you take on a management position working at UtMax theater. You will consider the utility of seeing performance over 1 month, and suppose that at a regular price of $$$ per ticket (my assigned ticket price is 145), customers will see no performance, however with the price reduced by $5, customers will see one performance per month and when reduced by $10, customers will see two performances. As long as the number performances, x, is small, your demand function for performance can be modeled by p=D(x). Write down your demand function.