Problem 2: Satiation point(s) There two goods, candy and soda, available in arbitrary non-negative quan- tities (so the consumption set is R²). A consumer has preferences over con- sumption bundles that are represented by the following utility function: u(x, y) = −|4 — x| − |4 − y| where x is the quantity of candy (in grams), y the quantity of soda (in liters), and |.| denotes the absolute value: for any real number r ≤R, |r| = r -r if r > 0 if r <0 The consumer has wealth of w> 0 Dirhams. The price of candy is p > 0 Dirhams/gram, and the price of soda is q > 0 Dirhams/liter. (a) Calculate the utility of the following consumption bundles: (4,4), (4, 5), (5, 4), (4,3), (3, 4), and a(4, 5) + (1 − a)(3, 4) for a € [0, 1]. (b) In an appropriate diagram, illustrate the consumer's map of indiffer- ence curves. (c) Are the consumer's preferences monotone? Provide an explanation for your answer.

Problem 2: Satiation point(s) There two goods, candy and soda, available in arbitrary non-negative quan- tities (so the consumption set is R²). A consumer has preferences over con- sumption bundles that are represented by the following utility function: u(x, y) = −|4 — x| − |4 − y| where x is the quantity of candy (in grams), y the quantity of soda (in liters), and |.| denotes the absolute value: for any real number r ≤R, |r| = r -r if r > 0 if r <0 The consumer has wealth of w> 0 Dirhams. The price of candy is p > 0 Dirhams/gram, and the price of soda is q > 0 Dirhams/liter. (a) Calculate the utility of the following consumption bundles: (4,4), (4, 5), (5, 4), (4,3), (3, 4), and a(4, 5) + (1 − a)(3, 4) for a € [0, 1]. (b) In an appropriate diagram, illustrate the consumer's map of indiffer- ence curves. (c) Are the consumer's preferences monotone? Provide an explanation for your answer.

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: An initial increase in investment spending will generate: Less of an increase in income…

A: The amount of desired investment would rise as a result of an increase in investment, which would…

Q: Q2. Suppose a consumer seeks to maximize the utility function U (x, y) = (x + 2) (y + 1), where and…

A: U(x,y) = (x+2)(y+1) Budget Constraint = Px*x + Py*y = I

Q: Suppose a consumer's utility function is u(x, y) = ;V+), with x and y the 6. amounts of two goods…

A: U(x,y) = 12x+12y2Px = 1Py = 2M = 300

Q: 3) A household has the budget constraint y = px₁ + x2 where the price of good 2 is normalized to…

A: The budget constraint is referred to the ideal combination of goods that an individual could…

Q: Suppose a person has allocated a monthly budget of 200 and they like to consume coffee (C) and…

A: A utility function is a thinking used in economics to signify how humans or buyers assign values or…

Q: Pete consumes goods 1 and 2. Pete thinks that 3 units of good 1 is always a perfect substitute for 4…

A: The utility function is the mathematical relationship between the utility and bundles of…

Q: A consumer with the following utility function U = xy2 faces two constraints. The first is the…

A: Consumer theory is important in economics because it investigates how consumers might maximize…

Q: Imagine you have a movie streaming platform that offers new movies at the time of release. Your…

A: Marginal utility is the additional utility derived from consuming an additional unit of the good.

Q: Which of the following utility functions represent preferences which do not satisfy monotonicity? U=…

A: Monotonic preferences refer to such consumer preferences towards the greater consumption of goods…

Q: marginal utility for custard (U.). What is Amelia's marginal rate of substitution (MRS)? Give a…

A: Different utility levels of consumers are taken to be independent. This means that utility obtained…

Q: Individual that consumes two goods (X and Y) and has a CES Utility Function of the form: U =…

A: "As per our policy, we can provide solutions to the first three subparts. Kindly raise the question…

Q: a) Assume that an individual consumes two goods, and achieves the benegàby çonsuming respectively i…

A: Individuals and businesses strive for the highest level of enjoyment from their economic actions,…

Q: 1. A consumer has m dollars. The price of ₁ is p₁ dollars, and the price of P2 dollars. The consumer…

A: Utility function represents the relationship between utility and commodities or goods that are…

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: uppose a consumer’s preferences for goods Y and X can be represented by the utility function,…

A: A rational consumer will consume where the MUx/MUy = Px/Py Here , MUx is the Marginal utility's of…

Q: Question 1 Consider an economy with two goods t = 1,2. Whenever an individual consumes ₁ units of…

A: As given utility function is u(x1,x2) = αlnx1 +lnx2 Where α>0

Q: Consumer satisfaction from consuming goods X and Y is as follows: U=10X+14Y-X2-Y2 and consumer…

A: Consumer equilibrium is the situation where he gets maximum satisfaction level of utility with given…

Q: Ms Smith likes to drink wine; in particular, a french bordeaux (f) at $40 per bottle and a…

A: The utility is maximized where the indifference curve tangents the budget line. or slope of the…

Q: Ms Smith likes to drink wine; in particular, a french bordeaux (ƒ) at $40 per bottle and a…

A: Utility function : U = f2/3c1/3Price of f (Pf) = 40 Price of c (Pc = 8 New price of (Pf ) =…

Q: a good is normal, then an increase in the price of the good will lead to which of the following to…

A: We are approached to consider the effect of a price increase on a normal good within a two-good…

Q: Do the preferences represented by this utility function satisfy monotonicity? Why or not? D. why

A: A function is monotonic if it is increasing throughout without any change or decreasing throughout.…

Question

For each part (a), (b) and (c), illustrate the demand for candy as a
function of wealth in an appropriate diagram.
Now consider a different consumer who has preferences represented by the
following utility function.
-12 – x| – |8 – yl if x <y
u(x, y)
-18 – x| – |2 – y| if x > y
where x is the quantity of candy (in grams) and y is the quantity of soda
(in liters).
(e) In an appropriate diagram, illustrate the consumer's map of indiffer-
ence curves.
(f) Are the consumer's preferences monotone? Are the preferences convex?
Provide an explanation for each answer.

Problem 2: Satiation point(s)
There two goods, candy and soda, available in arbitrary non-negative quan-
tities (so the consumption set is R). A consumer has preferences over con-
sumption bundles that are represented by the following utility function:
u(x, y) = -|4 – x| – |4 – y|
where x is the quantity of candy (in grams), y is the quantity of soda (in
liters), and |.| denotes the absolute value: for any real number r E R,
if r >0
|r| =
if r < 0
-r
The consumer has wealth of w > 0 Dirhams. The price of candy is p > 0
Dirhams/gram, and the price of soda is q > 0 Dirhams/liter.
(a) Calculate the utility of the following consumption bundles: (4, 4),
(4,5), (5,4), (4, 3), (3,4), and a(4, 5) + (1 — а) (3,4) for a € [0, 1].
(b) In an appropriate diagram, illustrate the consumer's map of indiffer-
ence curves.
(c) Are the consumer's preferences monotone? Provide an explanation for
your answer.
(d) Find the demand for candy and soda as a function of wealth w > 0
for the following specific prices, explaining how you arrived at your
answers:
(i) when p = 1 and q = 2,
(ii) when p
2 and q = 1,
(iii) when p = q = 1.

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

Step 2

Step 3

Step 4

Step 5

Trending now

This is a popular solution!

Step by step

Solved in 5 steps with 5 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

10
Suppose Carlos has to choose between purchasing jewelry and water. Which of the following is the utility-maximizing rule that Carlos should follow while choosing the optimal quantities of these two goods? (Note: In the answer options that follow, MU stands for "marginal utility.") O (MU of Water) x (Price of Water) = (MU of Jewelry) x (Price of Jewelry) O MU of Water = MU of Jewelry MU of Jewelry %3D Price of Water MU of Water Price of Jewelry MU of Jewelry Price of Jewelry MU of Water %3D Price of Water Since water costs little and jewelry is expensive, it must follow that when people choose their optimal quantities of water and jewelry to purchase, the marginal utility they receive from the last piece of jewelry they buy is than the marginal utility they receive from the last gallon of water they buy.
Rick consumes 2 goods, Chicken McNuggets (M) with Szechuan sauce (S). His utility function is U(M, S) = M2/3S1/3 and his income is m. The price of Chicken McNuggets is p, and the price of Szechuan sauce is 1. g. On the same graph, show the (hypothetical) budget constraint that is tangent to the indifference curve from part (e) but parallel to the budget constraint in part (f). h. On the same graph, show the income and substitution effects of the increase in p from 1 to 2 on Rick’s consumption of Chicken McNuggets. Are Chicken McNuggets a normal or inferior good for Rick? Explain your answer. i. Find the equation representing the (hypothetical) budget constraint drawn in part (g). Hint: you know this budget constraint has the same prices as in part (f), so you need to find the income level m that makes the budget constraint just tangent to the indifference curve passing through Rick’s chosen consumption bundle in part (e).
There two goods, candy and soda, available in arbitrary non-negative quantities (so the consumption set is R2+). A consumer has preferences over consumption bundles that are represented by the following utility function:u(x, y) = −|4 − x| − |4 − y|where x is the quantity of candy (in grams), y is the quantity of soda (inliters), and |.| denotes the absolute value: for any real number r ∈ R, |r| = r if r ≥ 0 −r if r < 0. The consumer has wealth of w > 0 Dirhams. The price of candy is p > 0 Dirhams/gram, and the price of soda is q > 0 Dirhams/liter. (a) Calculate the utility of the following consumption bundles: (4, 4), (4, 5), (5, 4), (4, 3), (3, 4), and α(4, 5) + (1 − α)(3, 4) for α ∈ [0, 1]. (b) In an appropriate diagram, illustrate the consumer’s map of indifference curves.
Help!
A consumer consumption bundle contains good X and Y. Suppose the price of good X goes up and a consumer goes on consuming the exact same amount of X as before. Check the correct statement(s).A) Both X and Y are inferior. B) X is an inferior good.C) In the special case where X is Leisure, and Y is "all other goods", X is an inferior good.D) The consumption of Y decreases.E) It is impossible that the consumption of X remains unchanged when the price of × goes up.F) The substitution effect is negative
A consumer’s utility only depends on the consumption of goods A and B according to the following Cobb-Douglass utility function: U(A, B) = A1/4 B 3/4. The price of goods A and B are $20 and $40, respectively. The consumer has a budget of $1200 that he can use to consume the two goods. a. Write down the budget constraint and plot it. b. Calculate the optimal bundle and maximized utility for the consumer. c. A new tax of $10 is imposed on the price of good B. Compute the new optimal bundle of good A and B for the same consumer. What is the utility loss due to the tax? d. Show that the consumer would prefer a lump sum income tax that raises the same revenue as the tax on good B. Note:- Do not provide handwritten solution. Maintain accuracy and quality in your answer. Take care of plagiarism. Answer completely. You will get up vote for sure.
Peter's preferences over two goods, x and y, are represented by the utility function u(x, y) = y + 2x. a) Peter is currently consuming bundle A = (2,4) with 2 units of good x and 4 units of good y. Calculate his current level of utility from consuming this bundle. b) Write the expression the indifference curve representing Peter's current level of utility (i.e., the one you found in part (a). Next draw this indifference curve. c) By looking at the indifference curve you drew in part (b), answer the following questions: Does Peter like good x? Good y? Explain. What can you say about the marginal rate of substitution of good x for y, MRSxy? Is it positive? Negative? Constant? Increasing? Decreasing? Interpret/explain your answer in terms of the tradeoffs Peter is willing to make between goods to keep the same utility level. d) On the same graph you drew in part (b), draw the indifference curve for a utility level of 10. Plot and label in the graph bundles B = (1,2), C = (1,6), and D =…
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.
Gino derives utility from only two goods, carrots (Qc) and donuts (Qd). His utility function is as follows:U(Qc,Qd) = (Qc)(Qd)The marginal utility that Donald receives from carrots (MUc) and donuts (MUd) are given as follows:MUc = Qd MUd = QcGino has an income (I) of £120 and the price of carrots (Pc) and donuts (Pd) are both £1. - suppose a lump sum tax of the same dollar amount, of a 1 pound tax per unit on donuts, is levied on Gino. what is Gino's utility maximising market basket? - why would Gino prefer a per unit tax over the lump sum tax, or vice versa, or why is he indifferent between the two taxes.
3) The utility function of a consumer who consumes quantities x and y of two goods is defined by the expression U(x, y)=√xy subject to the constraint 7x+3y=84 where $84 is the consumer's overall budget. Assuming marginal utilities U,,U>0, maximize the utility function of the consumer. What are the optimal values of x, y and U(x,y) ?
Gino derives utility from only two goods, carrots (Qc) and donuts (Qd). His utility function is as follows:U(Qc,Qd) = (Qc)(Qd)The marginal utility that Donald receives from carrots (MUc) and donuts (MUd) are given as follows:MUc = Qd MUd = QcGino has an income (I) of £120 and the price of carrots (Pc) and donuts (Pd) are both £1. - what is Gino's budget line and what quantities of Qc and Qd will maximise Gino's utitlity? - holding income and Pd constant, what is Gino's demand curve for carrots? - suppose a tax of 1 pound per unit is levied on donuts. how will this alter Gino's utility maximisinzing market basket of goods?