A utility maximizing consumer with preferences u(x, y)-x¹/2y1/2 allocates 60 dollars towards the purchase of goods x and y. Prices are py-0.5 and px - 1. With the purchase of a discount card prices are py-0.5 and px - 0.25. Calculate the maximum fee the consumer should pay to purchase this card. Provide an Indifference Curve and Budget Line Diagram to illustrate and quantify the Substitution Effect (a to b) and Income Effect (b to c) of this price change. Quantify all intercepts and intersections.

A utility maximizing consumer with preferences u(x, y)-x¹/2y1/2 allocates 60 dollars towards the purchase of goods x and y. Prices are py-0.5 and px - 1. With the purchase of a discount card prices are py-0.5 and px - 0.25. Calculate the maximum fee the consumer should pay to purchase this card. Provide an Indifference Curve and Budget Line Diagram to illustrate and quantify the Substitution Effect (a to b) and Income Effect (b to c) of this price change. Quantify all intercepts and intersections.

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: Given above are some of the indifference curves for a student who consumes Burritos and Pizzas and…

A: Since you have posted a question with multiple sub parts, we will provide the solution only to the…

Q: You consume music (M) and concert tickets (C). Your utility function is U(M, C) = M1/4C3/4. The…

A: Any combination of commodities that gives the consumer the same level of enjoyment is represented by…

Q: The elementary school has one candy machine in the cafeteria. Candy at the vending machine costs…

A: An indifference curve, with respect to two commodities, is a graph showing those combinations of the…

Q: Harry's indifference curve for popcorn (X1) and butter (X2) is U-min(X1, 3X2). Sketch two…

A: We have two statements which could be true or false and one is for plotting the Indifference curve.

Q: QUESTION 8 If the ulitity function is: U=41x₁ + 11x2 and considering the following bundles:…

A: A mathematical depiction of an individual's preference or level of happiness from using a good or…

Q: Draw two indifference curves for two goods (Gunna Tickets and Drake Tickets) at utility level 2 and…

A: Economists utilize a jargon of boosting utility to depict individuals' inclinations. In Buyer…

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: To remain in consumer optimum, a price decrease requires V in consumption. A price increase requires…

A: To remain in consumer optimum, a price decrease requires an increase in consumption. A price…

Q: Drawing indifference curves: Carl likes taking the rides at Disneyland, but dislikes standing in…

A: Production possibility frontier (PPF) shows a probable combination of two commodities produced in an…

Q: You run a foundation that provides help to families during the holiday season. You distribute both…

A: Budget line shows various combination of 2 goods that a person can buy, given the prices of the…

Q: Suppose a consumer has utility function U(X, Y) = X2/3Y1/3. Suppose the consumer has M = $90 to…

A: Utility function : U = X2/3 Y1/3Income : M = 90 Price of X : Px = 15 Price of Y :Py = 6

Q: Question 31 Clothing (units per week) Figure 3.1.2 Food (units per wook) Refer to Figure 3.1.2. The…

A: Indifference curve refers to the graphical representation of all possible combination of two goods…

Q: y function: u = x0.64x2.36. He h by $1.00. Calculate t increases

Q: Greg has the following utility function: u = x1^0.361x 2^0.642. He has an income of $74.00, and he…

A: Utility function is the function that shows or represents the level of satisfaction or degree of…

Q: Jana is interested in only two goods, X and Y, which she views as "perfect complements". Write down…

A: In order to derive the preference:- 4.5 x = 3.5 y U( x , y ) = min { 4.5 x , 3.5 y }

Q: Donald derives utility from only two goods, carrots (Q.) and donuts (Qa). His utility function is as…

A: Utility is the satisfaction that a consumer derives from the consumption of a good. Indifference…

Q: Milo spends £27 on stamps (S) and maple candy (C). His preferences for these goods are given by the…

A: Given , Milo income = 27 Utility function : U = min { S , 3C } Price of Stamps = 1.1 Price of…

Q: a)Assume that the typical consumer always spends a small share of her overall budget on Vietnamese…

A: Total customers = 120,000 Price of other products = Pm= $1 Price of Vietnamese Meals = Pv The…

Q: A cup of Starbucks coffee is just as good as a cup of Dunkin Donuts coffee for me (assuming equal…

A: Two goods are substitutes in microeconomics if they may be utilised for the same purpose by the…

Q: 3.11. Consider a consumer who is demanding goods 1 and 2. When the price of the goods are (2, 4), he…

A: Demand: It refers to the things that people consume. The increase in demand makes the increase in…

Q: Suppose Alex has the following utility function defined over goods x and y. U (x, y) = xy +10x a.…

A: Since you posted a question with multiple sub-parts, we will provide the solution to only the first…

Q: As a consumer moves along an indifference curve, then each point to the right will show higher…

A: Indifference curve is an indicative curve for any firm which shows combination providing equal…

Q: Determine the monotonicity and convexity of these preferences and briefly define what they mean.…

A: Utility refers to the level of satisfaction a consumer obtains from the consumption of goods or…

Q: Greg has the following utility function: u = x0.69x2.31. He has an income of $60.00, and he faces…

A: Utility function: ..........(1)Price of good x1 (p1)=1Price of good x2…

Q: Susan buys bagels and falafels. The price of a falafels is £1 and the price of a bagels is £3. Susan…

A: Price of F=1Price of B=3M=12Budget constraintPF*F+PB*B=<M1*F+3*B=<12

Q: A consumer with income I=120 facing prices pX = 4 and pY = 8 for two goods X and Y (for each good…

A: In utility maximization problem, a consumer attains his equilibrium or optimal consumption bundle…

Q: 6. Draw indifference curves for two goods and y, where y is a "bad" good. Specify each axis, show…

A: The indifference curve shows the different combinations of two goods that provide the same level of…

Q: Suppose that the price of good A and good B are $3 and $2 respectively. Suppose a consumer is…

A: In a market, when a consumer consumes two products, he will be at equilibrium when the Marginal…

Concept explainers

Marginal Rate of Technical Substitution

MRTS reaches a manufacturer when a part of the product is lowered to sustain the manufacturing level when the other part is extended. It is the level of the quantity that is lowered when one extra volume is used, and the output is unchanged.

Preferences and Utility Analysis

Before understanding what is preference and utility analysis, it is very important to understand the terms preference and utility separately.

Question

A utility maximizing consumer with preferences u(x, y) - x2y1/2 allocates
60 dollars towards the purchase of goods x and y. Prices are py - 0.5 and px
– 1. With the purchase of a discount card prices are py - 0.5 and px - 0.25.
Calculate the maximum fee the consumer should pay to purchase this card.
Provide an Indifference Curve and Budget Line Diagram to illustrate and
quantify the Substitution Effect (a to b) and Income Effect (b to c) of this
price change. Quantify all intercepts and intersections.

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: Define utility

VIEW

Step 2: Maximum fee

VIEW

Step 3: Substitution and income effect

VIEW

Solution

VIEW

Step by step

Solved in 4 steps with 22 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

Greg has the following utility function: u=x10.75x20.25. He has an income of $68.00, and he faces these prices: (p1,p2)=(8.00,4.00). Suppose that the price of x1 increases by $1.00. Calculate the equivalent variation for this price change. $
Multiple Choice 1. 8 2. 10 3. 12.50 4. 14 5. 15
A maximizing consumer with preferences u = 12x^(1/2)+ y pays pY= 2 and spends 64dollars per month on these goods. The store where she purchases good x has two pricing plans. Plan A has a unit price of pX= 6 with a monthly subscription fee of 4dollars. Plan B has a unit price of pX= 4 but the monthly fee is 8 dollars. Provide an Indifference Curve Diagram to illustrate and quantify her choice between Plan A and Plan B. Quantify all intercepts and intersections.
Alex has a monthly budget of $72 to spend on commuter train trips and organic pasta. Each train trip costs $12; each box of pasta costs $6. Alex's preferences for train travel and pasta are represented by the indifference map on the following page. a. Determine which line (L1, L2, L*, or L**) represents Alex's budget constraint. b. Find their utility-maximizing bundle (E1, E2, e*, or e**). How many train trips will Alex take? Suppose the state government establishes a program to subsidize public transportation for commuters, such that each train trip now costs Alex $6. c. Determine which line (L1, L2, L*, or L**) represents Alex's new budget constraint. d. Find their new utility-maximizing bundle (E1, E2, e*, or e**). Determine how many train trips Alex will now take. e. Find the size and direction (positive or negative) of the substitution effect for train trips. As part of your answer, state the starting quantity and ending quantity of train trips that represent this effect. f. Find…
There are two goods x and y. A consumer has utility function U(x, y) min(2x, y). The price of good x is 2 and the price of good y is 1. The consumer has income | = 10. 1) Draw a graph that illustrates the indifference curves for the consumer. 2) Find the bundle of goods (x * y*) that maximizes the consumer's utility subject to the budget constraint.
For the utility function U = Qx0.28Q (1-0.28) and the budget 137 = 11Qx+6Qy find the CHANGE in optimal consumption of X if the price of X increases by a factor of 1.6. Please enter your response as a positive number with 1 decimal and 5/4 rounding (e.g. 1.15 = 1.2, 1.14 = 1.1).
preferences are represented by the utility function The prices of X1 and x₂ are p₁and p2 u(x₁, x₂) = x²x² 1. What is the slope of the indifference curve at the point (x₁, x₂) 2. Find the budget line tangent to the indifference curve (x₁, x₂) 3. When consuming the best bundle that can afford, what fraction of his income does Ken spend on point x₁ 4. Find x and x2
ONly parts D-G
Mr. Rational has $27 that he plans to spend purchasing 5 units of good X (priced at $3 per unit) and 6 units of good Y (priced at $2 per unit). The marginal utility of the fifth unit of X is 30, and the marginal utility of the sixth unit of Y is 18. If Mr. Rational is a utility maximizer, he should: buy less of X and more of Y. buy X and Y in the quantities indicated. buy more of X and less of Y. not buy anything. buy less of X and even lesser than that of Y.
Abby likes tangerines and oranges. For every 4 tangerines, Abby is equally happy to consume 2 oranges instead. Let x be the number of tangerines, and y be the number of oranges. (a) Graph Abby's indifference curves. Make sure to mark the direction of the preferred bundles. (b) Write down an utility function that represents Abby's preferences. (c) Write down another utility function different from your previous answer but also represents Abby's preferences. (d) Does v(x, y) = x + y represent Abby's preferences? (e) What is Abby's marginal rate of substitution? (f) Suppose that px = 1, py = 1, and Abby has Y = 20. Compute Abby's optimal consumption bundle.
Given above are some of the indifference curves for a student who consumes Burritos and Pizzas and the relevant budget line. Equilibrium is defined as the maximum utility or satisfaction given the consumer’s budget. The consumer has more indifference curves above I3, below I1, and between I1 and I2 and between I2 and I3. Out of all the indifference curves the consumer has, only I1, I2, and I3 are shown. The given budget line touches I2 at the point where I2 touches the y-axis (Burritos axis). a) If the price of Pizzas decreased and the price of Burritos remained unchanged, would the quantity of Burritos consumed at equilibrium increase or decrease compared to the equilibrium point A in the graph given above? (b) If the price of Pizzas increased and the price of Burritos remained the same, would the consumer equilibrium point be different from point A or the same as point A in the graph given above?
Q5. Jason has preferences defined over novels (good x) and DVDs (good y) described by the utility function U(x,y)= x2y2. He has an income of $120; novels cost $5 each, while DVDs are priced at $15 each. [Hint: MUx=2xy2, MUy=2x2y] a) Sketch Jason's budget constraint, indifference curves and the interior solution in a graph. b) Calculate Jason's optimal consumption bundle, and his maximized utility level. Suppose the price of novels increases to $7.5, while the price of DVDs and income are unchanged. c) Calculate his new optimal bundle, show it in the same graph from a), and interpret the Marginal Rate of Substitution (MRS) at this new optional bundle (point).