An individual has the utility function U=4X 0.5Y 0.5 and can buy good X at £ 2 a unit and good Y at £ 8 a unit. If their budget is £ 100. Find the combination of X and Y that they should purchase to maximize utility

An individual has the utility function U=4X 0.5Y 0.5 and can buy good X at £ 2 a unit and good Y at £ 8 a unit. If their budget is £ 100. Find the combination of X and Y that they should purchase to maximize utility

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: Suppose, a glass of lemonade (x) sell for 10 taka each and a cupcake (y) cost 60 taka. Total income…

A: U(X,Y) = X0.15Y0.85 where X is a glass of lemonade Y is cupcake Px is the price of a glass of…

Q: Total utility is 0 when marginal utility is 0 True/False

A: # Utility is a concept which helps us calculate the satisfaction a consumer gets when a good or…

Q: You have the Cobb-Douglas utility function u(x,y) = xy over apples (x) and plums (y) and you have…

A: To construct a set of feasible set of bundle we need to keep both the budget income and weight…

Q: Suppose a consumer had a utility function given by: U = X²Y0.5. If the price of Good X (Px) is $3…

A: The utility function is given as The price of good X is $3.The price of good Y is $6. The budget for…

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 consumer has the following utility function: U(X,Y)= 400X2/5Y3/5 Suppose that the price of a spa…

A: To solve the above problem we construct Lagrangian in which Total cost function with constraint of…

Q: Suppose a consumer’s preferences can be represented by the utility function U(X,Y) = Min (2X,Y).…

A: Utility function: U = Min (2X, Y) --------------------- Budget constraint: Price of good X (Px) = $2…

Q: Liz has a utility function of U(X,Y)=30XY, where X is food and Y is the composite good. The price of…

A: utility function is an important concept that measures preferences over a set of goods and services.…

Q: Show how the budget constraint affects utility maximization.

A: Answer: Introduction: A consumer maximizes his/her utility by choosing the bundle of goods that…

Q: Suppose a consumer consumes two goods, x and y and has utility function U(x, y) = min{3x, 2y}. She…

A: Given information: U= min{3x,2y} -----------> Utility function The price of x is $35 => Px =…

Q: Joyce consumes x1 and x2 together in fixed proportions. She always consumes 1 unit of x2 for 2 units…

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

Q: compute the marginal utility of good X (MUX) and the marginal utility of good Y (MUY). b. U=U ( X…

A: Answer: Given, Utility function: U ( X ,Y )=X0.5Y0.4

Q: True/False Marginal utility is 0 for the Consumption of the very first unit.

A: the term marginal utility simply means the extra satisfaction which a consumer gets when he consumes…

Q: An individual values two goods, X and Y, according to the following utility function: U (X,Y)= 6…

A: Given Utility function: U(X,Y)=60.5X-0.88+0.5Y-0.88-1.14 .......(1) Price of X= 4 Price…

Q: Suppose a consumer has preferences described by the utility function u(x1,x2)=a In(x1)+(1-a) In(x2),…

A: We have given utility function for X1 and X2 in logarithmic form.

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: A consumer derives utility from good A and B according to the following utility function: U(A, B) =…

A: Utility maximization problem: With the given prices and income, a consumer chooses his consumption…

Q: then find out the quantity of x and y that will maximize utility.

A: Utility is defined as the total satisfaction that the consumer derives from consumption of the…

Q: U(x, y) = min(x, 5y) is the utility function of the consumer. In addition, px = 1, Py = 3 and M = 8.…

A: Given Utility function: U(x,y) =min(x,5y) ..... (1) The price of good x is 1 and the price of…

Q: (B) Same setup as (A) with u(x, y) = ax + y and ap<1. What is the demand for X? (a) x(p, m) = m (b)…

A: Given The utility function: u(x,y)=αx+y ....(1) Here αp<1 The price of good x is 1 and…

Q: Prove that if u is a reasonable utility function, then u(w) — u(w − h) > u(w+h)- u(w) for any w > 0…

A: A reasonable utility function assigns numerical values to outcomes based on personal preferences,…

Q: Question 1 Consider a consumer with utility x₁2/3x21/3 and a budget constraint of 3x1+6x2 $100. What…

A: To maximize utility, we can use the Lagrangian method by setting up the following function: L(x1,…

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: True/False Marginal utility is 0 for the Consumption of the very first unit.

A: Marginal utility can be defined as : The extra satisfaction which a consumer obtains when he…

Q: Suppose a consumer had a utility function given by: U= 2X + 5Y. If the price of Good X (Px) is $6…

A: Utility maximization refers to the process by which individuals or firms allocate their resources in…

Q: Suppose a consumer had a utility function given by: U= 9X + 4Y. If the price of Good X (Px) is $10…

A: The utility problem is given as The price of good X is $10.The price of good Y is $4.The budget for…

Q: 6. Show that your utility function is a CES utility function.

A: The Constant Elasticity of Substitution (CES) utility function is a functional form that is commonly…

Q: The consumer's total budget is S300. How many units of C and F will they consume?

A: Utility is the level of satisfaction that a consumer gets when consuming a good. Utility…

Q: The utility function of a consumer regarding two goods x and y is given by U(x,y) = x^(7.9)y^(9).…

A: U(x,y) = x7.9y9 Price of x (Px) = 19 Price of y (Py) = 80 Total Income (M) = 10800

Q: A consumer derives his utility from two goods, the amounts of which are x and y, according to the…

A: Given Utility function U=2lnx+lny .......(1) Px=$2 and Py=$4 Consumer income =$48 We have…

Q: Suppose a consumer had a utility function given by: U = X³Y. If the price of Good X (Px) is $6 and…

A: Utility maximization refers to the process by which individuals or firms allocate their resources in…

Q: a. Find Sam's utility maximizing choice of ice cream and video games. Also find his utility level…

A: In economics, the utility function measures the welfare or satisfaction of a consumer as a function…

Q: A consumer utility function is U = 1 log x1 + log x2. His budget constraint is given by 2x1 + 4x2 =…

A: The consumer is in equilibrium when he gets maximum satisfaction out of his expenditure. The…

Q: 8. A consumer bas utility function u(z, y) = VIy, for two goods, X and Y, where c is some positive…

Q: 10 9 IC, 8 IC, 10 12 Good Y The utility a person gets from consuming an additional unit of Good Y at…

A: An indifference curve shows the various combinations of two goods that give the consumer equal…

Q: MU, = and 2. If the utility I get from good x and y is u(xy) = 2 x + 2 y, then MU, = V. If x costs…

A: We are going to use Marginal rate of substitution method to answer this question.

Q: Jack’s preferences are represented by the utility function U = XY^2. PX = 1, PY = 1.5 and his budget…

Q: Suppose a consumer has the following utility function: U(x1,x2) = alnx1 + (1-a)lnx2. The price of…

A: We have Ux1, x2=alnx1+1-alnx2 When a= 1/2 or a=0.5 Ux1, x2=0.5lnx1+0.5lnx2 ............…

Q: Tom went to a pizza by the slice bar with Jerry. Tom loves pizza (x), and prefers it, even more,…

Q: A consumer’s budget set for two goods (X and Y) is 500 ≥ 4X + 5Y. a. The budget set is illustrated…

A: The budget constraint is given by the inequality: 500≥4X+5Y.To find the values of A (the intercept…

Q: Consumer utility function is, U(XY) = X 75 Y 0.5. The price of X good 2 AZN and Y good 4 AZN. If…

A: A consumer maximizes utility by consuming at the point where slope of indifference curve given by…

Q: (A) Suppose an individual who derives utility u(x, y) from consuming a units of the good X and y…

Q: Hui's utility function is U(x,y) = 4x+y+6.6. Suppose Hui has x = 30 units of good X and good y =…

A: Utility refers to the satisfaction attained from the consumption of combination of two goods. The…

Question

An individual has the utility function
U=4X 0.5Y 0.5
and can buy good X at £ 2 a unit and good Y at £8 a unit. If their budget is £ 100. Find the combination of X and
Y that they should purchase to maximize utility

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 by step

Solved in 4 steps

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

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).
f
For the utility function U = Qx0.46Qy(1-0.46) and the budget 100 = 11Qx + 11Qy find the CHANGE in optimal consumption of X if the price of X increases by a factor of 1.5. 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).
Consumer has the following utility function U(x,y) = x1/2y1/2 , where the price of good x is 1$ per unit, the price of good y is 4$ per unit, and the consumer’s income is 800$. Find the utility maximizing consumption levels of x and y.
The total utility from two products is maximized at the optimal consumption bundle. True or False?
Every month, a family of three spends $2,000 on food (F) and other items (O). The family’s preferences are represented by the utility function U(F,O) = F1/5O4/5. The unit price of food and the unit price of other items are both $1. Find this family’s monthly food expenditure.The family could join a consumers’ club. At the club, food costs 20% less than in other stores (i.e., at the food club PF = $0.8)
= x 2 y. This Consider a consumer with the utility function U (x, y) = Vxy 글3글2-iy and MU, Vx = x? They have 1 function gives MU Va a budget of $60, and pr 1 and Py 2. Find optimal consumption of x and y.
Assume that a person’s utility depends on two products, x and y. The utility function is given by U(x, y) = (x + 2)^2(y + 3)^3. Find the marginal utility of x and marginal utility of y.
5
suppose a consumer consumes two goods x and y with utility function u=x^0.5+y^1.5, does the utility funciton exhibit diminishing marginal utility for (i) x (ii)y?
1
You currently have (x, y) = (8, 2) and the utility function U(x, y) = min(x, 4y ). How many units of X are you willing to give up to get another unit of Y?