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Omar consumes only two goods, whose quantities are measured by x and y. His preferences are described by the utility function U(x, y) = xy + 10(x + y). His marginal utilities are MUx = y + 10 and MUy = x + 10. The prices of the goods are PX = $9 and Py = $3. He has a daily income of $30. (10 Marks) a) Show that Omar has a diminishing marginal rate of substitution of x for y. Why is this important in applying the method of Lagrange to the consumer choice problem? b) With Omar’s utility function, is it possible that the utility-maximizing basket (x, y) will be at a corner point, with either x = 0 or y = 0? Do you expect the budget constraint to be binding? c) Using the method of Lagrange, find Omar’s optimal consumption basket (x, y) when his income is $30. Also find the numerical value of the Lagrange multiplier, λ, which measures Omar’s marginal utility of income (the rate of change) when his income is $30. d) Find Omar’s optimal consumption basket (x, y) and the value of λ if his income is $31. e) Show that the increase in Omar’s utility when his income rises from $30 to $31 is close to the values of λ you found in parts (c) and (d).

Answer: Diminishing Marginal Rate of Substitution The marginal rate of substitution (MRS) is the rate at which one good must be substituted for another to maintain the same level of utility. As the quantity of one good increases while the

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Page 2 of 2e) Show that the increase in Omar’s utility when his income rises from $30 to $31 isclose to the values of λ you found in parts (c) and (d).3. Angela has a monthly income of $120, which she spends on MP3s and a composite good(whose price you may assume is $1 throughout this problem). Currently, she does not belongto an MP3 club, so she pays the retail price of an MP3 of $2; her optimal basket includes 20MP3s monthly. (10 Marks)For the past several months Asteroid, a media company has offered her the chance to jointheir “Premium Club”; to join the club she would need to pay a membership fee of $60per month, but then she could buy all the MP3s she wants at a price of $0.50. She hasdecided not to join the club.Asteroid has now introduced an “Economy Club”; to join, Angela would need to pay amembership fee of $30 per month, but then she could buy all the MP3s she wants at aprice of $1. Draw a graph illustrating (1) Angela’s budget line and optimal basket whenshe joins no club, (2) the budget line she would have faced had she joined the PremiumClub, and (3) her budget line if she joins the Economy Club. Will Angela surely want tojoin the Economy Club? If she were to join the club, how many MP3s per month mightshe buy? Show how you arrive at your answers using a revealed preference argument.

Answer: Angela’s Optimal Basket and Budget Line When She Joins No Club When Angela does not join any club, her budget line is determined by her monthly income of $120 and the cost of the MP3s, which is $2 each.

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Here is a table that illustrates some observed prices and choices for three different goods at three different prices in three different situations. Find these behaviours are inconsistent with the given choices. Check with the help of Weak Axiom of Revealed Preference (WARP) or Strong Axiom of Revealed Preference (SARP) about the behaviour. Does this violate any WARP or SARP.

Introduction to WARP and SARP WARP and SARP are two axioms used to determine whether observed economic behavior is consistent with underlying preferences. WARP states that if an individual prefers option A to option B in a given situation, then

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The chest-and-arm stretch squeezes __________. A. the pectoral muscles together B. the biceps simultaneously C. all muscles in the torso D. the shoulder blades together Please select the best answer from the choices provided. A B C D

Answer: The chest-and-arm stretch squeezes the pectoral muscles together The chest-and-arm stretch is a basic stretching exercise that is designed to target the chest and arm muscles. This stretch helps to increase flexibility, improve posture, and reduce strain on the

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Omar consumes only two goods, whose quantities are measured by x and y. His preferences are described by the utility function U(x, y) = xy + 10(x + y). His marginal utilities are MUx = y + 10 and MUy = x + 10. The prices of the goods are PX = $9 and Py = $3. He has a daily income of $30. (10 Marks) a) Show that Omar has a diminishing marginal rate of substitution of x for y. Why is this important in applying the method of Lagrange to the consumer choice problem? b) With Omar’s utility function, is it possible that the utility-maximizing basket (x, y) will be at a corner point, with either x = 0 or y = 0? Do you expect the budget constraint to be binding? c) Using the method of Lagrange, find Omar’s opti¬mal consumption basket (x, y) when his income is $30. Also find the numerical value of the Lagrange multiplier, λ, which measures Omar’s marginal utility of income (the rate of change) when his income is $30. d) Find Omar’s optimal consumption basket (x, y) and the value of λ if his income is $31. e) Show that the increase in Omar’s utility when his income rises from $30 to $31 is close to the values of λ you found in parts (c) and (d).

Answer: Diminishing Marginal Rate of Substitution of X for Y The marginal rate of substitution (MRS) is the rate at which a consumer is willing to substitute one good for another while maintaining a constant level of satisfaction. Omar’s preference

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The FITT principle stands for __________. A. frequency, intensity, time, and type B. fitness, intensity, toughness, and type C. frequency, ideal, time, and toughness D. frequency, ideal, time, and type Please select the best answer from the choices provided. A B C D

Answer: D. Frequency, Intensity, Time, and Type The FITT principle is a guideline for designing and implementing an exercise program. It stands for Frequency, Intensity, Time, and Type. The FITT principle can be used to help create a safe and

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Suppose the daily market demand for meat in a small town is given by QD=7/(2p^4) where QD is the quantity demanded (pounds of meat), and p is the price per pound of meat. Suppose this market is served by a profit-maximizing monopolist (that is, there is only one butcher in this town), and this seller obtains the meat at a marginal cost of $1.5 per pound. The price charged per pound of meat will be $

Answer The monopolist in this town must determine the price that maximizes their profits. Using the equation QD=7/(2p^4) to calculate the demand, and a marginal cost of $1.5 per pound, the monopolist can calculate the optimal price by finding the

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Suppose the daily market demand for meat in a small town is given by QD=72p4 where QD is the quantity demanded (pounds of meat), and p is the price per pound of meat. Suppose this market is served by a profit-maximizing monopolist (that is, there is only one butcher in this town), and this seller obtains the meat at a marginal cost of $1.5 per pound. The price charged per pound of meat will be $

Answer: How much will the monopolist charge for meat? The monopolist will charge $4 per pound of meat. This can be determined by setting the demand equation equal to the marginal cost and solving for the price. The demand equation

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Consider a monopoly facing the demand shown below. Assume that marginal costs of production are positive. Use the straight-line tool to show the range on the demand curve where we would, with certainty, not expect a profit-maximizing monopolist to produce any output.

Answer: Demand Curve and Profit Maximization for Monopoly A monopoly is a market structure with a single firm that produces all of the output in a given market. Facing a downward sloping demand curve, a monopolist will set price and

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Brian consumes units of electricity (E) and a composite good (Y ), whose price is always equal to 1. He likes both goods. In period 1, the power company sets the price of electricity at $7 per unit, for all units of electricity consumed. Brian consumes his optimal basket, 20 units of electricity, and 70 units of composite goods. In period 2, the power company then revises its pricing plan, charging $10 per unit for the first 5 units and $4 per unit for each additional unit. Brian’s income is unchanged. Brian’s optimal basket with this plan includes 30 units of electricity and 60 units of composite goods. In period 3, the power company allows the consumer to choose either the pricing plan in period 1 or the plan in period 2. Brian’s income is unchanged. Which pricing plan will he choose? Illustrate your answer with a clearly labeled graph.

Answer: Brian will choose the pricing plan in period 2. This plan charges $10 per unit for the first 5 units and $4 per unit for each additional unit. This pricing plan allows Brian to optimize his consumption and benefit

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Brian consumes units of electricity (E) and a composite good (Y ), whose price is always equal to 1. He likes both goods. In period 1, the power company sets the price of electricity at $7 per unit, for all units of electricity consumed. Brian consumes his optimal basket, 20 units of electricity, and 70 units of composite goods. In period 2, the power company then revises its pricing plan, charging $10 per unit for the first 5 units and $4 per unit for each additional unit. Brian’s income is unchanged. Brian’s optimal basket with this plan includes 30 units of electricity and 60 units of composite goods. In period 3, the power company allows the consumer to choose either the pricing plan in period 1 or the plan in period 2. Brian’s income is unchanged. Which pricing plan will he choose? Illustrate your answer with a clearly labeled graph.

Answer: Brian will choose the pricing plan from period 2 Brian will choose the pricing plan from period 2 because it is the more cost-efficient option for him. In period 1, Brian consumed 20 units of electricity at a price

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Brian consumes units of electricity (E) and a composite good (Y ), whose price is always equal to 1. He likes both goods. In period 1, the power company sets the price of electricity at $7 per unit, for all units of electricity consumed. Brian consumes his optimal basket, 20 units of electricity, and 70 units of composite goods. In period 2, the power company then revises its pricing plan, charging $10 per unit for the first 5 units and $4 per unit for each additional unit. Brian’s income is unchanged. Brian’s optimal basket with this plan includes 30 units of electricity and 60 units of composite goods. In period 3, the power company allows the consumer to choose either the pricing plan in period 1 or the plan in period 2. Brian’s income is unchanged. Which pricing plan will he choose? Illustrate your answer with a clearly labeled graph.

Answer: Brian Will Choose the Period 1 Pricing Plan Brian will choose the period 1 pricing plan because it yields a higher level of utility (happiness/satisfaction) for him. Under period 1 pricing, he consumes 20 units of electricity and 70

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When did Michael Jackson die

Michael Jackson’s Death Michael Jackson, the iconic pop star, passed away on June 25, 2009, due to a drug overdose. He was only 50 years old. Cause of Death Michael Jackson died of a drug overdose caused by propofol, a

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rewrite THE FIRST TWO paragraphs of the Declaration of Independence, replacing confusing or antiqued words with accurate modern language conveying the same meaning. Be careful not to distort or change the intent and meaning behind each sentence. As you are doing this, consider carefully the intend the author had which his word choice

Answer: Modern Rewrite of First Two Paragraphs of the Declaration of Independence When in the course of human events, it becomes necessary for one people to dissolve the political bonds that have connected them with another, and to assume, among

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nike credit rating

Nike’s Credit Rating Nike is currently rated A2 by Moody’s and A by S&P Global. This rating indicates that Nike has a strong capacity to meet its financial commitments, but is somewhat more susceptible to the adverse effects of changes

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Disney credit rating

Disney Credit Rating Overview Disney is a diverse entertainment conglomerate with businesses such as its film studio, theme parks, and broadcasting networks. The company’s credit rating is an assessment of its creditworthiness, which is based on its ability to pay

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Disney credit score

Disney Credit Score Disney offers a variety of credit cards that can help consumers build or improve their credit score. These cards are designed to help consumers build a strong credit history and improve their financial situation. The cards offer

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Consider the following regression model: yi=β0+β1x1i+β2x2i+ui Data for the variables are in this file. Estimate the model by OLS and use a Breusch-Pagan test to test the null hypothesis that ui is homoskedastic using a 5% significance level. (a) Enter the value of the F-statistic in the box below (accurate to 3 decimal places). Answer 1 Question 2 5.478 (b) Enter the critical value in the box below (accurate to 3 decimal places) Answer 2 Question 2 3.841 (c) Do you find evidence of heteroskedasticity? Multiple choice 1 Question 2 Yes. No.

Answer: Estimating a Regression Model with OLS and Testing for Heteroskedasticity Using the Breusch-Pagan Test Consider the following regression model: yi=β0+β1x1i+β2x2i+ui Data for the variables are in this file. Estimate the model by OLS and use a Breusch-Pagan test to

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Paraphrase Sometimes in your lowest moments, when you least expect it, when you feel most helpless, He reveals a treasure. It could come in many forms, a helping hand, a gentle reminder, advice or even a smile. Surely when He takes something away from you, He gives you something greater in its place3

Answer: Treasures in Lowest Moments In our lowest moments, when we feel most helpless, it is often when God reveals a treasure to us. This treasure can come in many forms, such as a helping hand, a gentle reminder, advice,

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New tax related information in Nigeria

Summary Of Tax Related Information In Nigeria Taxation in Nigeria is based on the provisions of the Personal Income Tax Act (PITA) of the Federal Government of Nigeria. The Act provides for the imposition of taxes on the income and

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Prerequisites of a tax club

What Are the Prerequisites of a Tax Club? Tax clubs, also known as tax study groups, are a great way for individuals to learn more about taxes and how to file them. Many tax clubs are led by professional tax

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Aims and objectives of a tax association

Summary of Aims and Objectives of a Tax Association Tax Associations are organizations that promote the interests of tax professionals, from tax attorneys to accountants and tax preparers. The main aims and objectives of a tax association are to provide

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5. Address each of the following true, false or uncertain short statements from a microeconomics perspective. Label the statement as true, false or uncertain and clearly explain your choice using clearly labelled and appropriate diagrams. (Use a maximum of 250 words for each part.) (a) An individual who consumes two products, X and Y, could not be maximising utility subject to the usual budget constraint if: Marginal Utility of Product X Marginal Utility of Product Y ———————————— > ———————————— Price of Product X Price of Product Y In particular, the individual should consume less of product X and/or more of product Y. (40 marks)

Answer: True, false or uncertain? The statement in question is True. This is because, according to the law of diminishing marginal utility, the marginal utility of a good decreases as more of it is consumed, meaning that if the marginal

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Suppose a firm’s total cost function is C(Q) = 4Q2 + 100Q + 800. a) How much is the total fixed cost (TFC) if this firm? b) How much is the average variable cost (AVC) of this firm? c) What is the marginal cost of production (MC)? d) If P = 116, what is the profit-maximizing quantity? e) What is the lowest price for which the firm will make economic profits?

Answer: Total Fixed Cost (TFC) The Total Fixed Cost (TFC) of a firm is the cost of production that does not change with the level of output. In this case, the total fixed cost is the constant part of the

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