1. Hagrid spends his income on Acid Pops and Butterbeer, two treats enjoyed widely in the wizarding world. Hispreferences can be represented by the following utility function: U(a, b) = 4a² + b.a. Set up Hagrid's utility maximization problem without solving it. Denote the price of Acid Pops by pa andthe price of Butterbeer by p, and income by Y. Clearly identify the objective function, the constraint,and the variables that represent the things Hagrid can choose when picking his optimal bundle.b. Solve for Hagrid's Marshallian (uncompensated) demand for both goods, that is, the quantity demandedfor any possible prices and income level. Assume an interior solution. Note: The substitution method isrecommended but any approach is fine.Use your answer to part b and calculus to determine how Hagrid's Marshallian demand responds tochanges in income. Give a brief (intuitive) description of what each equation implies about Hagrid'sdemand of Acid Pops and Butterbeer.C.

The objective of this question is to set up and solve Hagrid's utility maximization problem, given…

Answered: 1. Hagrid spends his income on Acid…

Exploring Economics

8th Edition

ISBN:9781544336329

Author:Robert L. Sexton

Publisher:Robert L. Sexton

Chapter10: Consumer Choice Theory

Section: Chapter Questions

Problem 6P

See similar textbooks

Similar questions

Suppose that the consumer maximizes his utilitysuch that the marginal utilities of goods X and Y are; MUx=80-16x MUy=60-2y Let Px=P4,Py=P2 and I=P80 Find the utility maximizing quantities X and Y
Suppose Al is currently consuming five movies and two concerts per month. If his utility function is given by U = 15MC, where Mrepresents the number of movies seen and C represents the number of concerts attended, Al's total utility is equal to: 75 15 150 10 30
2. Eren's two main hobbies are taking vacations overseas (V) and eating expensive meals (M). His utility function is given as: U(V,M) = V²M Last year, the average price of taking a vacation overseas was US$200 and the average price of an expensive meal is $50. However, due to supply problems in Onions, the average price of an expensive meal rose to $75. The average price of a vacation did not change. His income, which is $1500, did not change. a. b. C. Calculate the change in consumer surplus from consuming the expensive meals considering the price change (Hint: you need to compare his optimal consumption bundle before and after the price change to get the change in CS). Suppose that the Department of Welfare wants to know how much should be given to Eren to offset his change un utility due to the price increase of an expensive meal. Calculate the compensative variation (CV). Calculate for the equivalent variation (EV) for the price change.
1 Alice has a monthly lunch budget of 360 dollars which she spends on either burgers (B) or pizza (Z). The price of each pizza is 16. dollars and the price of each burger is 8 dollars. Alice's utility is given by: u(B, Z) = B'/2 +4Z!/2 + 47!/2 a) Find Alice's budget constraint. Set up the Lagrangian and find her optimal consumption. What is her new consumption if the price of burgers becomes 16 dollars?
2. Tom spends all his $100 weekly income on two goods, apples and bananas. His utility function is given by U (A, B) = AB, where A and B stand for the quantity of apples and bananas consumed by Tom. If PA = $4 and PB= $10, how many apples and bananas will he consume? Make sure you write out the utility maximization problem explicitly, including the decision variable(s). What if his utility function is given by U (A, B) = A0.5B 0.5?
Devon's utility function can be written as ?1^0.50?2^0.50, where ?1 is the quantity of hamburgers consumed and x2 is the quantity of milk shakes. His income is $2,400.00. 1) Hamburgers cost $8.00 each and the price of one milk shake is $4.00. If he is maximizing his utility, how much will Devon spend on hamburgers? $ 2)The price of hamburgers decreases to $7.37 each. Now, how much will Devon spend on hamburgers if he is maximizing his utility? $
2. Suppose John's utility function is UX,Y) = 4/XY , where X is consumption of beer and Y is consumption of pizza. For this utility function, ( Calculus Kahuna say: MUx = 2Y/X and MUy = 2\X/Y ) a) Suppose Y=3. Calculate John's utility for X=4,9,16, and 25. For a given level of Y, does good X display diminishing marginal utility?
I need help with my homework assignment that i dont undertsand. Suppose a consumer has a utility function given by U(X,Y) = MIN(X, 2Y). The consumer has $90 to spend (M = $90). The Price of good Y is PY = $1. Using a graph, sketch the consumer’s demand curve for Good X. Make sure to identify three points on the demand curve. Make sure your graph is neat, accurate, and scaled properly.
4 Emily goes camping on the weekend and eats marshmallows (M) and crackers (C) there. She wants to match 1 marshmallow with 2 crackers, but does not eat in different proportion (i.e., perfect com- plement). The price of a marshmallow is 10 cents and the price of a cracker is 5 cents, and she spend up to $3 in total. a) Write down a utility function which represents Emily's preferences over marshmallows and crackers. b) How many marshmallows and crackers is she going to consume? (Hint: the first-order conditions will not help; draw the budget constraint and the indifference curves and look at the highest one that intersect the budget constraint). c) What is the exact value of Emily's indirect utility?
In a simple but delicious world, Joey eats only sandwiches, s, and jam, j. He has a Cobb-Douglas utility function ?(?,?) = ??!"#?#, where 0 < ? < 1 and ? > 0. The price of jam is ?$, the price of sandwiches is ?%, and Joey has a monthly budget ? to spend on lunch. a. Explain why you can safely use a simpler Cobb-Douglas utility function, ?(?,?), to represent Joey’s preferences, which is the same as ?(?,?) except for replacing N with 1. b. Transform ?(?,?) by taking natural logs and bringing down exponents. Explain why it is useful to do this for a Cobb-Douglas utility function, but not for a quasi-linear utility function. c. Use ln(?(?,?)) and the substitution method to derive the formulas for Joey’s optimal amount of jam, j*, and sandwiches, s*, to buy and consume per month. d. What fraction of his income does Joey spend on jam, and what fraction on sandwiches?
A consumer has a utility function U(X,Y ) = X1/2 Y1/2 . Prices of the goods are pX = £10 and pY = £5, respectively, and the consumer has income M = £200 to spend on X and Y. Currently, she buys 2 units of good X and spends the rest of her income on good Y.a) Determine this consumer’s current utility level. b) Computetheconsumer’smarginalutilitiesofgoodsXandY. c) Explain why the consumer’s current consumption of goods X and Y is not optimal. Should she substitute X for Y or vice versa? The consumer’s marginal rate of substitution is MRS = Y/X.d) Determine this consumer’s optimal consumption of both goods. e) By how much does the consumer’s utility increase when she consumes the optimal bundle?
Suppose Susan has to choose between purchasing high-definition televisions and milk. Which of the following is the utility-maximizing rule that Susan 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 Milk = MU of HDTVS O (MU of Milk) × (Price of Milk) = (MU of HDTVS) × (Price of HDTVS) MU of Milk MU of HDTVS Price of HDTVS Price of Milk MU of Milk MU of HDTVS Price of Milk Price of HDTVS Since milk costs little and high-definition televisions are expensive, it must follow that when people choose their optimal quantities of milk and high- definition televisions to purchase, the marginal utility they receive from the last high-definition television they buy is v than the marginal utility they receive from the last gallon of milk they buy.

SEE MORE QUESTIONS

Recommended textbooks for you

Exploring Economics

Economics

ISBN:

9781544336329

Author:

Robert L. Sexton

Publisher:

SAGE Publications, Inc

Exploring Economics

Economics

ISBN:

9781544336329

Author:

Robert L. Sexton

Publisher:

SAGE Publications, Inc

SEE MORE TEXTBOOKS