Suppose a consumer had a utility function given by: U= 2X + 5Y. If the price of Good X (Px) is $6 and the price of Good Y is $2 then what is the utility maximizing quantity of Good X the consumer will purchase with a budget of $12? (Round to the nearest two decimal places if necessary.)

Suppose a consumer had a utility function given by: U= 2X + 5Y. If the price of Good X (Px) is $6 and the price of Good Y is $2 then what is the utility maximizing quantity of Good X the consumer will purchase with a budget of $12? (Round to the nearest two decimal places if necessary.)

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: Amanda consumes three different products: apple (x), orange (y) and banana (z). Her utility function…

A: Budget constraints shows the relationship between the two goods, their prices and the income of…

Q: Q10. Consider a utility function: U (F,C) = FC so MU_F = C and MU_C = F. In Case 1, Total income is…

A: We are going to use Consumser decision theory to answer the question.

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: 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 a utility function 9*sqrt(x1)+x2 and a budget constraint of 8x1+6x2 ≤10000. How much…

A: Utility means satisfaction. Utility is maximized where the MRS is equal to the price ratio of two…

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: For the utility function U = (Qx0.5+Qy0.5)2 and the budget 190 = 5Qx + 12Qy find the CHANGE in…

A: The utility function is given as The budget constraint is given as The price of X is increased by a…

Q: 2) A consumer’s utility function is: U(x,y) = sqrt(9xy). The price of each good is: (PX,PY) =…

A: Optimal consumption bundle: The optimal consumption bundle is such that at that bundle the…

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: Let a1 and a2 denote the quantities consumed. The consumer's preferences are represented by the…

A: We have Utility function U(x1,x2)=x1+x2 ... (1) Consumer income m=100 Price of good 1:…

Q: QUESTION 1 For the utility function U = Qx0.43Qy(1-0.43) and the budget 102 = 13Qx + 11Qy find the…

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

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: For the utility function U = Qx0.68Qy(1-0.68) and the budget 103 = 10Qx + 13Qy find the CHANGE in…

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

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: 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: suppose a consumer's utility function is given by U(X,Y) = X*Y. Also the consumer has $288 to spend,…

A: Given: U(X,Y) = XYPrice of XPx=16Price of YPy=16

Q: For the utility function U = (Qx0.5+Q,0.5)2 and the budget 167 = 10Qx+8Qy find the CHANGE in optimal…

A: Utility functionU = (Qx0.5+Qy0.5)2Budget Constraint167 = 10Qx + 8QyTherefore , Price of x = 10Price…

Q: If the consumer's utility function is given by U(x, y) = 10x0.5 0.5, solve for the optimal quantity…

A: Consumer theory is important in economics because it investigates how people maximize their…

Q: Utility Function: U(X,Y)=X1/2Y1/2 Budget Constraint: 2X+2Y=16 If the price of good X changes…

A: Utility function: ..........(1)Budget constraint: ......…

Q: Assume there is consumer, his utility function is U(x,y)=y/(100-x). If px = 1, py = 1, please show…

A: Utility function U (x, y) = y/(100-x) .... 1) (MUx) / (MUy) = Px /Py.…

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: For the utility function U = (Qx0.5+Q,0.5)2 and the budget 122= 8Qx + 8Qy find the CHANGE in optimal…

A: Utility function : U = (Qx0.5 + Qy0.5)2Budget Constraint : 122 = 8Qx + 8 QyTherefore , Price of x…

Q: 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…

A: Utility function U = 4X0.5 Y0.5PX = £2 PY = £8 M = £100

Q: For the utility function U = (Qx0.5+Qy0.5)2 and the budget 167 = 10Qx + 8Qy find the CHANGE in…

A: Utility functionU = (Qx0.5+Qy0.5)2Budget Constraint167 = 10Qx + 8QyTherefore , Price of x = 10Price…

Q: Suppose a consumer had a utility function given by: U = XY². If the price of Good X (Px) is $6 and…

A: Suppose a consumer had a utility function given by: U = X * Y ^ 2 . If the price of Good X (Px) is…

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: The utility function of a buyer for x units of tea and y units of coffee is given by u(x, y) = x…

A: we are given with a utility maximization problem of a buyer for x units of tea and y units of…

Q: For the utility function U = (Qx0.5+Q,0.5)2 and the budget 125 = 11Qx + 14Qy find the CHANGE in…

A: Utility function : U = (Qx0.5 + Qy0.5)2Budget Constraint : 125 = 11Qx + 14 QyTherefore , Price of…

Q: QUESTION 1 For the utility function U=Qx0.340,(1-0.34) and the budget 174= 5Qx+5Qy find the CHANGE…

A: Utility:The utility is want satisfying power of a commodity. It can be expressed in cardinal and…

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: ralph has a utility function u(x,y) = 0.5x + y and an income of $M. Let the price of x be $4 and the…

A: Consumer, consumes the good from which he get maximum $ marginal utility. If $ MUx = MU/px is more…

Q: Maya is doing her undergrad at Queen's University. She loves donuts and chocolate chip cookies…

A: a) When the price of CCC (chocolate chip cookies) is $1, which is the same as the price of donuts,…

Q: 2) A consumer’s utility function is: U(x,y) = sqrt(9xy). The price of each good is: (PX,PY) =…

A: ***Since the student has asked to solve a specific part of the question, hence, the expert is…

Q: For the utility function U = Qx0.48Qy(1-0.48) and the budget 188 = 11Qx + 11Qy find the CHANGE in…

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

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

Q: Suppose Jasmine's utility function is U(x,y) = 15x -5.3x² + y. Her income is 5.8 dollars, the price…

A: Utility maximization refers to the process of determining the combination of goods and services that…

Q: For the utility function U = Qx0.28Q (1-0.28) and the budget 137 = 110x + 6Qy find the CHANGE in…

A: Utility: The purpose of the utility is to satisfy the power of a commodity. It is possible to say it…

Q: 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…

A: Utility function U = 4X0.5 Y0.5, PX = £2, PY = £8, M = £100 His budget line would be XPx * YPY =…

Q: Find the quantities of each product that the consumer should buy, subject to the budget, that will…

A: Answer to the question is as follows :

Question

Suppose a consumer had a utility function
given by: U= 2X + 5Y. If the price of Good X
(Px) is $6 and the price of Good Y is $2 then
what is the utility maximizing quantity of
Good X the consumer will purchase with a
budget of $12?
(Round to the nearest two decimal places if
necessary.)

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 the problem:

VIEW

Step 2: Determine utility maximizing quantity for good X and good Y:

VIEW

Solution

VIEW

Step by step

Solved in 3 steps with 6 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

Find marginal utility MU for a consumer consuming x amount of a given commodity, where his total utility function is TU = x²ln (x² + 1).
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.
Question 2. A consumer has the utility function U(q1,q2) = q10.5 + q2Assume p2 = 1 and Y = 100. What is the equivalent variation of a price increase for good 1 from 1 to 4?
QUESTION 1 For the utility function U = (Qx0.5+Qy0.5)² and the budget 133 = 8Qx + 10Qy find the CHANGE in optimal consumption of Y if the price of X increases by a factor of 1.1. 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).
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.
suppose the utility function of Vivian is U=602/3Y1/3. The unit priice of Good X is $10 while the unit price of Good Y is $30. Vivian has a budget of $1,800 to be spent on Good X and Good Y. Find the optimal consumption bundle of vivian show your calculations.
Mary has the following utility function: u(x, y) = 3 ln(x) + 2y. Her income is given by I = 10 and the prices originally are p = 1 and py = 2 (b) How much of each good is Mary currently consuming?
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.
For the utility function U = (Qx0.5+Qy0.5)² and the budget 122 = 8Qx + 8Qy find the CHANGE in optimal consumption of X if the price of X increases by a factor of 1.7. 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).
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) ?
Suppose a consumer had a utility function given by: U=X + 4Y. If the price of Good X (Px) is $1 and the price of Good Y is $8 then what is the utility maximizing quantity of Good X the consumer will purchase with a budget of $4? (Round to the nearest two decimal places if necessary.)