the next 6 hours of her free time. She could choose Aisha is considering how to allo between leisure (L) and helping her neighbour with the house chores. If she decides to help her neighbour, she is going to get paid at £25 per hour, which she can then spend on her favourite pizza (P). Suppose the price of pizza is £12.50. Aisha's preferences for leisure and pizza are given by the following utility function: U(L,P) = 3L + P. (MU₁ = 3, MUp = 1). a) Write down Aisha's budget equation and draw the corresponding budget line. Clearly label the axes and calculate the coordinates of the points of intersection of the budget line with each axis. b) Calculate Aisha's marginal rate of substitution between leisure and pizza. Explain the concept of MRS and interpret the figure obtained. c) Find Aisha's optimal consumption bundle, both algebraically and graphically. Explain your reasoning.

the next 6 hours of her free time. She could choose Aisha is considering how to allo between leisure (L) and helping her neighbour with the house chores. If she decides to help her neighbour, she is going to get paid at £25 per hour, which she can then spend on her favourite pizza (P). Suppose the price of pizza is £12.50. Aisha's preferences for leisure and pizza are given by the following utility function: U(L,P) = 3L + P. (MU₁ = 3, MUp = 1). a) Write down Aisha's budget equation and draw the corresponding budget line. Clearly label the axes and calculate the coordinates of the points of intersection of the budget line with each axis. b) Calculate Aisha's marginal rate of substitution between leisure and pizza. Explain the concept of MRS and interpret the figure obtained. c) Find Aisha's optimal consumption bundle, both algebraically and graphically. Explain your reasoning.

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: Mort consumes only beer and sausages. His income is $100. Beer costs him $0.50 per can and sausages…

A: Utility maximization refers to the process where individuals aim to allocate their resources in a…

Q: The utility function for Morris is U = min{4M, 2T}, where M is pints of milk and T is cans of tuna.…

A: In equilibrium: 4M = 2T [ as utility function is of perfect complement hoods] T = 2M Substituting…

Q: A consumer has set a budget of $400 for the consumption of good X and Y. The price of Good X is…

A: Utility function : U (X, Y ) = x y Price of x : Px Price of y : 5 Budget Set = 400 Therefore ,…

Q: A person has $25 to spend on apples, bananas, and cherries. Their respective prices are $2, $3, and…

A: The budget constraint for a person spending $25 on apples, bananas, and cherries, with prices of $2,…

Q: A consumer has $100 and would like to purchase food (F) and gas (G). Suppose their utility is given…

A: Given: U ( F,G ) = F 0.8 G 0.2 M= PF x F + PG x G 100 = PF x F + PGx G MUF= o.8 ( G / F ) 0.2 MUG…

Q: Romeo will purchase his original bundle. Romeo's budget line rotates inwards about the chocolates…

A: A Budget line represents different bundles of two goods that consumers purchase with the given…

Q: Each month Larry purchases household utilities. His preferences over gallons of heating oil (x) and…

A: A want satisfying power of a commodity or service is known as its utility. Utility is a significant…

Q: m 4.2 Nadia likes spare ribs, R, and Fried chicken, C. Her utility function is U(R,C)=10R^2 C…

A: The consumer's ideal blend of goods is where the spending plan line is a digression to an…

Q: Jessie has a budget of $50 and is attempting to draw her budget constraint for purchasing cookies…

A: Price of goods can be calculated by using the following formula.

Q: QUESTION 4 Linguini and Colette consume only éclair (x,) and profiterole (x,). Linguini has utility…

A: "Since you have posted multiple sub-part questions, I can only answer the first 3 parts, the rest…

Q: Your utility function is defined as U = x¹/3y2/3 where x and y are the only two goods you consume.…

A: Utility function represents the relationship between the utility and commodities that are consumed.

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: Consider the consumer whose tastes and preferences for (X) and (Y) can be characterized by the…

A: The utility function can be written as follows: The budget constraint can be written as follows:

Q: Donna and Jim are two consumers purchasing strawberries and chocolate. Jim’s utility function is…

A: MUx (for Jim) = y MUy (for Jim) = xPx = $2 and Py = $4 ( as given in another subpart of…

Q: To maximize utility, Connie should buy pounds of meat and potatoes. (Enter your responses rounded to…

A: Utility maximisation is the process of maximising the utility of the consumer subject to the budget…

Q: Problem 1. Ted is an eight-year-old boy who loves Pokémon cards and Lego minifigures. His father…

A: Since you have posted multiple questions, we will provide the solution only to the first three…

Q: alculate the marginal rate of substitution (MRS12) for the following utility function: U(q1,q2)=…

A: Marginal rate of substitution refers to the slope of an indifference curve. It is calculated as the…

Q: Mia is a registered nurse. She has 18 hours per day to devote to labor or leisure, and has $20…

A: For maximizing utility, Mia has to select the combination of consumer goods and leisure that can…

Q: Carol needs to decide how to spend her wealth on fish and chicken. For Carol, 1 lb of fish is…

A: Given, u(x; y) = 2x + y

Question

EXERCISE 7
Aisha is considering how to allocate the next 6 hours of her free time. She could choose
between leisure (L) and helping her neighbour with the house chores. If she decides to
help her neighbour, she is going to get paid at £25 per hour, which she can then spend on
her favourite pizza (P). Suppose the price of pizza is £12.50. Aisha's preferences for
leisure and pizza are given by the following utility function: U(L, P) = 3L + P.
(MU₁ = 3, MUp = 1).
a) Write down Aisha's budget equation and draw the corresponding budget line.
Clearly label the axes and calculate the coordinates of the points of intersection of
the budget line with each axis.
b) Calculate Aisha's marginal rate of substitution between leisure and pizza. Explain
the concept of MRS and interpret the figure obtained.
c) Find Aisha's optimal consumption bundle, both algebraically and graphically.
Explain your reasoning.
d) Would Aisha's optimal choice change if she could get a discount on her pizza
purchases so that each pizza would cost £5? Explain.
e) Would Aisha's optimal choice change (as compared to c), if she could get a discount
on her pizza purchases so that each additional pizza beyond the first two, cost £5?
(In other words, the first two pizzas need to be purchased at a regular price of
£12.50 each, but the third, fourth, etc. can be purchased at a discounted price of
£5). Explain.

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

Step 2

Step 3

Step 4

Step 5

Step 6

Step by step

Solved in 6 steps with 2 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

Anna has an income of 1000 euros and utility function U(x,y)=x²y³. The prices of the two goods are P₁=5 and Py-20. a) Define the budget constraint and represent it graphically. (
Logan consumes olives (x₁) and ice cream (x₂). He prefers to eat them only separately (never together). In particular, his utility function is given by: u(x₁,x2)= x₁²+x₂². If his income is $10 and the price of olives is $1 and the price of ice cream is $2. Which of the following is FALSE? The optimal bundle Logan will choose to consume is (2,4) None of the above The utility level at a bundle (2,4) is 20 The utility level when he spends all of his income on good 1 is 100 The utility level when he spends all of his income on good 2 is 25
Consider the following utility function for goods x1 and x2: u(x1,x2)=(x1+x2)2 What type of preferences does this utility function represent and why?
Loise spends £20 on tea (T) and coffee (C). Her preferences for these goods can be described by the following utility function: U(T, C) = 2T + C² − C (MU, = 2, MUc = 2C − 1). Suppose that one cup of tea costs £1.60 while one cup of Loise's favourite coffee costs £4.00. a) Find Loise's optimal consumption bundle. Provide both algebraic and graphical solution. Explain your reasoning. b) Discuss how Loise's optimal consumption choice would change when her disposable budget changes. c) If the price of tea increases to £2.00 per cup, how should the price of coffee change so that Loise can be as well off as before this change in prices? d) Discuss the implications of the price change from c) on Loise's optimal choice. In your discussion, include the analysis of the substitution and income effects as well as Loise's demand for tea and/or coffee.
Aji's utility function for Blueberry (b) and Raspberry (r) is given as U = f(b, r); Budget constraint: 100 = 4b + 5r, If Blueberry is graph in the horizontal axis and Raspberry on the Vertical axis, the slope of this budget line is (Please put your answer in fraction form like 3/7). The maximum number of Raspberry Aji could afford is (Please put your answer in numerical forms without comma and decimal place). The maximum number of Blueberry Aji could afford is (Please put your answer in numerical forms without comma and decimal place). Aji is considering 3 different bundles X, Y & Z. Bundle X contains 10 Blueberry and 15 Raspberry, bundle Y contains 7 Blueberry and 13 Raspberry, bundles Z contain 5 Blueberry and 16 Raspberry. Bundle X cost bundle Y cost & bundle cost (Please put your answers for all these 3 bundle cost in numerical forms without dollar sign, comma or a decimal place). What is the optimal bundle? (Please choose X,Y or Z, upper case only)
Maya is doing her undergrad at Queen's University. She loves donuts and chocolate chip cookies (CCC). Her utility function is given by u(x, y) = √8x +5 + 2y, where x denotes her consumption of donuts and y denotes her consumption of CCC. Her budget is $10/day. The price of a donut is $1. (a) When the price of CCC is $1, what is Maya's optimal choice of donuts and CCC? (b) When the price of CCC is $8, what is Maya's optimal choice of donuts and CCC? (c) When the price of CCC increases from $1 to $8, calculate Maya's substitution effect and income effect. (d) According to your calculation in part (c), is CCC a normal good or an inferior good? Explain. Is CCC an ordinary good or a Giffen good? Explain.
In Workout problem 5.1, Charlie has a utility function U(xA, xB) = xAxB, the price of apples is $1, and the price of bananas is $2. If Charlie's income were $160, how many units of bananas would he consume if he chose the bundle that maximized his utility subject to his budget constraint?
You consume music (M) and concert tickets (C). Your utility function is U(M, C) = M1/4C3/4. The marginal utility for concert tickets, MUC is MUC =3/4C-1/2M1/4 and the marginal utility for music, MUM is MUm = 1/4C3/4M-3/4 (a) Calculate MRSMC using only the given marginal utilities. (b) Solve for the utility of bundle A where M = 16 and C = 16. Solve for your utility at bundle B where M = 128 and C = 8. Are the utilities the same? (c) Calculate MRSMC at bundle A and at bundle B. Are they the same? (d) Are your indifference curves convex? Draw the ICs. Make sure to label the quantities of the consumption bundles, the axis, and the MRS at those bundles.
Suppose that the price of good X is $6 and the price of good Y is $2. You have $144 to spend and your preferences over X and Y are defined as: U(x,y) = x2/3y1/3 Calculate the marginal utility of X Calculate the Marginal Utility of Y What is the optimal Choice of X and Y given the PX = $6, PY = $2 and I = $144 If Income is increased to $150 calculate how the optimal choice of X and Y change
QUESTION 1 Let qa be the quantity of apples and qo the quantity of oranges. A consumer's utility is described by the function u(qA.90)= 39A + 590 This consumer curently consumes 2 apples and 4 oranges. For this consumer, the marginal utilities are MUA= and MUO= Moreover, the marginal rate of substitution is MRSA O=
QUESTION 4 Linguini and Colette consume only éclair (x,) and profiterole (x2). Linguini has utility function UA = x4x4 and Colette has utility function UB = 2xfx. Linguini is endowed with 10 éclair (x,) and 3 profiterole (x), while Colette is endowed with 20 éclair (x,) and 9 profiterole (x2). (a) Draw an Edgeworth box with x, on the horizontal axis and x, on the vertical axis. Position Linguini on the bottom left corner and Colette on the top right comer. Indicate the total number of units of x, and x2. Label the endowment allocation. (b) Derive the equation of the contract curve, ie., find x(x). In your graph in (a), draw the contract curve.
Let u(x) be a utility function that represents the preferences of a household. We say that the function v(x) is a monotonic transformation of u if f(·) is a strictly increasing function and v(x) = f(u(x)). (a) Show that if v(x) is a monotonic transformation of u, it represents the same preferences. (b) Can you explain why taking a monotonic transformation of a utility function does not change the marginal rate of substitution? (c) What kind of preferences are represented by a utility function of the form U(x1,x2) = ? What about the function U(x1,x2) = 13x1+13x2?