i need 22 and 23 only plz!!! 22. Cameron's preferences can be represented by the utility function u(X,Y) = X02y04 If the market pricesare px = 1 and py = 1, what is Cameron's optimal mix of goods X and Y?a. X= Yb. X = 2Yс. 2X %3D Yd. X= 4Ye. 4X = Y23. Which of the following will is most likely to lead to a decrease in the market price of nuts?a. The cost of hiring nut pickers decreases.b. Nut butters and jelly are complements, and the price of jelly decreases.c. The New England Journal of Medicine reports that people who eat two ounces of nuts per day livefive years longer than those that do not.d. A devastating flood occurs on nut farms in California, destroying many nut trees in the process.e. None of the events above will cause the market price of nuts to decrease.Price70p° = 53P= 50p = 4810D70 8024. The graph above depicts the effect of a $5 per unit (excise) tax on the market for sweaters. Based on thisinformation, which of the following is true?a. Consumers will pay $0 of the $5 tax.b. Consumers will pay $1 of the $5 tax.c. Consumers will pay $2 of the $5 tax.d. Consumers will pay $3 of the $5 tax.e. Consumers will pay $5 of the $5 tax.25. A firm uses capital, K, and labor, L, to produce output, q, in a perfectly competitive market. The firm'sproduction function is q = f(K, L) = 0.1L + 0.2K. The prices of labor and capital are w = 4 and r = 1,respectively. Compute the cost function for this firm.a. C(q) = 0.8qb. C(q) = 2qc. C(q) = 5qd. C(q) = 10qe. C(q) = 40q

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Answered: 22. Cameron's preferences can be…

Exploring Economics

8th Edition

ISBN:9781544336329

Author:Robert L. Sexton

Publisher:Robert L. Sexton

Chapter10: Consumer Choice Theory

Section: Chapter Questions

Problem 9P

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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. 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?
12) A consumer’s preferences are given by U(X,Y) = X0.6Y0.4. The price of X is 4, and the price of Y is 5. The consumer has an income of $2000.a) What is the utility maximizing choice of X and Y?b) How would the utility maximizing choice change if price of X falls to 3 because of a pricesubsidy?c) Given the answers to the previous parts plot a linear demand function for X.d) Show that the consumer would prefer the cash equivalent of the price subsidy in part b.
12) A consumer's preferences are given by U(X,Y)= Xo6y04. The price of X is 4, and the price of Y is 6. The consumer has an income of $2200. a) What is the utility maximizing choice of X and Y? b) How would the utility maximizing choice change if price of X rose to 8? c) Given the answers to the previous parts plot a linear demand function for X.
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.
4. Tim wants to maximise his utility given his utility function of U (A, B) = A² B¹. He faces the following prices and income: PA = 25; PB = 20; M = 250. However, a change in the price of good A to PA 22 will change his optimal bundle. If he is only interested in being able to consume his original bundle of goods, how much income would he need after the price change? = (a) Tim would require £54 less income (b) Tim would require £18.33 more income (c) Tim would require £10 less income (d) Tim would require £16.66 more income (e) Tim would require £16.66 less income
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
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.
5. Janice consumes two goods, X and Y. Janice has a utility function given by the expression: U=4X05Y05 and current prices of X and Y are $25 and $50, respectively. Janice currently has an income of 750 unit per time period. a. Write an expression for Janice's budget constraint. b. Calculate the marginal rate of substitution of X for Y. (horizontal line X, vertical line Y). c. Calculate the values of X and Y that will maximize utility. d. Graph your answers (budget line, indifference curve)
Mylie's total utility from singing the same song over and over is 70 utils after one repetition, 110 utils after two repetitions, 140 utils after three repetitions, 160 utils after four repetitions, 120 utils after five repetitions, and 60 utils after six repetitions, as shown in the table below. a. Write down her marginal utility for each repetition. Instructions: Enter your answers as a whole number. If you are entering any negative numbers be sure to include a negative sign (-) in front of those numbers. Repetitions 0 1 2 3 4 5 6 Total Utility Marginal Utility 0 70 110 140 160 120 60 b. Once Mylie's total utility begins to decrease, does each additional singing of the song hurt more than the previous song or less than the previous song? O More than the previous song O Less than the previous song
13. Shawn likes to consume pineapple smoothies and hotdogs. His preferences are represented by the utility function U(x,y) = 34x - x²/2 + y where x is his consumption of pineapple smoothies and y is his consumption of hotdogs. The price of pineapple smoothies is $2 and the price of hotdogs is $1. If the price of pineapple smoothies increases to $6, the change in Shawn's consumer surplus is: A) -144 B) -128 C) -120 D) -112 E) -90
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?

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22. Cameron's preferences can be represented by the utility function u(X, Y) = X0.2y04, If the market prices are px = 1 and py = 1, what is Cameron's optimal mix of goods X and Y? a. X= Y b. X= 2Y c. 2X = Y d. X = 4Y e. 4X = Y