not use ai please don't Constrained optimization: michaels preferences over acai owls (A) anf burritos (B) are given by the followingutility function U(A, B) where U(A, B) 5A^.3B^.7. Micaels budget is 100, while acai bowls cost $5 each,and burritos cost $7 each.=a) calculate the optimal consumption A* and B* using the Larange method.b) draw the optimal consumption point (A*, B*) along with the associated indifference curve (I*) with theequation for 1*

Part a: Calculate the Optimal Consumption (A* and B*) Using the Lagrange Method Part b: Draw the…

Answered: Constrained optimization: michaels…

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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11) Stanley consumes only white and red wines and his utility function can be describedby U(R,W) = R0.40∙W0.60, where R is the number of bottles of red wine and W is the4number of bottles of white wine that he consumes per month. Suppose that his income is$500 and the price of a bottle of red wine $20 and the price of a bottle of white wine is$15. In this case, Stanley will purchase _____ bottles of red wine and _____ bottles ofwhite wine per month. Next, suppose that the price of red wine goes up to $35 per bottle.In this case, Stanley would consume ______ quantity of bottles of white wine comparedto the original situation.A) 10; 20; smallerB) 20; 10; smallerC) 10; 20; the sameD) 20; 10; the sameE) None of the above.
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?
A9
A utility function is given as U = √MB where B represents the quantity of books consumed and M represents magazines. This uülity is shown via indifference curves in the diagram to the right. Holding the number of magazines constant at 20 units, as we increase our consumption of books from 5 units to 10 to 15 and to 20 units, marginal utility with respect to books. is CIES Magazines (Y) 50- 45 40 35 30 25- 20- 15- 10- 5 0- 10 15 RSTV a quie 10 15 20 25 30 35 40 Books (X) 45 5 eboo SCOR scor scor score score
Hi, I need some help with the attached question. It is taken from an optimisation problem set in my intermediate maths for economists course.
On a given evening, J. P. enjoys the consumption of cigars (c) and brandy (b) according tothe functionU(c, b) = 20c− c²+ 18b − 3b²a. How many cigars and glasses of brandy does he consume during an evening? (Cost isno object to J. P.)b. Lately, however, J. P. has been advised by his doctors that he should limit the sum ofglasses of brandy and cigars consumed to 5. How many glasses of brandy and cigarswill he consume under these circumstances?
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) ?
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1 Consider a consumer who consumes only two goods, 21 and z2. His utility function is u (21, 22) = In z1 + 2. where In represents the natural logarithm. 1.a Derive the consumer's MRS of good 1 for good 2 using calculus to calculate his marginal utility from z and his marginal utility from z2. 1.b If the price of z1 is $2 per unit and the price of z2 is $4 per unit, and the consumer's income is $100, What is the equation of this consumer's budget line? 1.c What are the optimal consumption choices, z and z5, for this consumer? Show your work.
Aji Fatou's utility function for Blueberry (b) and Raspberry (r) is given as follows: U = f(b, r); Budget constraint: 100 = 4b + 5r. If Blueberry is graph in the horizontal axis and Raspberry on the Vertical axis. Which of the following is true? %3D a. If Aji Fatou spend her entire income on Blueberry, she will get 25 Blueberries. b. If Aji Fatou spend her entire income on Raspberry, she will get 20 Raspberries. c. The slope of her budget line is 4/5. d. All of the above.
Kate’s utility function includes coffee (c) and sugar (s). She only consumes coffee and sugar together, and she only consumes in the ratio of one unit (cup) of coffee with two units (spoons) of sugar. Her utility function is What is her marginal utility of sugar if she has 4 cups of coffee and 6 spoons of sugar? Remember that unit are infinitely divisible (you can have parts of units). (a) 0 (b) 1 (c) ½ (d) 2
Hot-dogs (P = $1) Apple pie slices (P=$2) Hot-dogs Total MUMU/P Apple pie Total MUMU/P ConsumedUtility ConsumedUtility 1 7 1 14 2 13 26 3 18 3 36 4 22 4 44 5 25 5 50 6. 27 54 7 28 7 56 Assume that hot-dogs cost $1 and apple pie slices cost $2. Your budget is $9. (MU is marginal utility; MU/P is marginal utility divided by price) 1) Fill in the table. For each good, calculate the marginal utility (MU) and the marginal utility per dollar (MU / P). 2) The marginal utility of consuming the second hot dog is 3) The marginal utility of consuming the 6th apple pie slice is The optimal bundle of goods that maximizes 4) your total utility (and you don't overspend) is: dogs and hot- apple pie slices. Explain how you found it.

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