18. Aisling eats turkey and bread sandwiches for lunch and regards turkey and bread as perfect complements. For every 2 slices of bread (B), she requires exactly 3 slices of turkey (T). Aisling has $14 to spend on bread and turkey, each slice of bread costs 50 cents, and each slice of turkey costs 25 cents. Her utility function is and her optimal bundle is
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- 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) 21 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.Question 2 David spends his budget on chocolate and chip. His utility function is given by ?(?1,?2)= 2?1?2, where ?1 is the number of chocolates he consumers per week, and ?2 is the number of chips he buys per week. A chocolate costs 10 SEK, and a chip costs 20 SEK. David’s weekly budge for consuming on these two goods is 120 SEK. (1) What is David’s budge line? Draw the budget line on a graph with chocolate amounts on the horizontal axis and chip amounts on the vertical axis. Write explicitly at which points budget line crosses the axis. (2) What is David’s marginal utilities for the two goods, respectively? What is his marginal rate of substitution between the two goods? (3) What is David’s optimal choice? Calculate the numerical answer for the optimal bundle. Also draw an indifference curve for David on the same graph as question(1) and show the optimal bundle.
- Nadia likes spare ribs, R, and fried chicken, C. Her utility function is U = 10R-C. Her weekly income is Y = $180, which she spends on only ribs and chicken. 8- If she pays $20.00 for a slab of ribs and $10.00 for a chicken, what is her optimal consumption bundle? 7- Nadia's optimal consumption bundle contains 6 slabs of ribs and 6 fried chickens. (Enter numeric responses using integers.) 6- Suppose the price of chicken increases to $20.00. How does her optimal consumption of chicken and ribs change? 2160 fried Nadia's optimal consumption bundle contains chickens. (Enter numeric responses rounded to one decimal place.) slabs of ribs and 2 1- 0- 9 10 11 12 13 14 15 16 17 18 Chicken ост tv 24 Help . ..... MacBook Air 80 DII F1 F2 F3 F4 F5 F6 F7 F8 F9 F10 @ #3 2$ & 一 2 6. 7 8. 9. Q W E T Y U A S D F G H J K L C V V * 00 另: NNadia likes spare ribs, R, and fried chicken, C. Her utility function is U = 10R C. Her weekly income is Y = $180, which she spends on only ribs and chicken. 8. If she pays $20.00 for a slab of ribs and $10.00 for a chicken, what is her optimal consumption bundle? Nadia's optimal consumption bundle contains 6 slabs of ribs and 6 fried 6- chickens. (Enter numeric responses using integers.) Suppose the price of chicken increases to $20.00. How does her optimal consumption of chicken and ribs change? 4- 3- Nadia's optimal consumption bundle contains slabs of ribs and fried chickens. (Enter numeric responses rounded to one decimal place.) 10 11 12 13 14 15 16 17 18 14) Chicken etv 21 MacBook Air DI DD 30 F10 FB F9 F6 F7 F5 F4 F3 F1 F2 & ! @ # 2$ 7 8 1 2 3 4 { Y Q W J K F A く > C V command opti ption command .. .- * 00 コ エ **6. Anthony spends his income on fishing lures (L ) and guitar picks (G ). Lures are priced at $2, while a package of guitar picks costs $1. Assume that Anthony has $30 to spend and his utility function can be represented as U(L,G) = L 0.5 GO5. a. Given the utility function in this problem, use calculus to derive the marginal utilities of fishing lures and guitar picks. b. Using the tangency condition, what is the MRSL,G? c. What is the optimal number of lures and guitar picks for Anthony to purchase? d. At the optimal bundle, how much utility does Anthony have? e. If the price of guitar picks doubles to $2, how much income must Anthony have to maintain the same level of utility? f. Suppose that the prices of lures and guitar picks are $2 and $1 (as they were before the price change) and that Anthony still has only $30 to spend. Use a Lagrangian to solve his constrained utility maximization problem and confirm that the answer is the same as that to part (c). g. Now suppose that the…
- Jackie has a budget of $36 per month to spend on snacks. She can spend this budget on bags of potato chips (C) and Hershey chocolate bars (H). Potato chips cost $4 per bag, while Hershey bars cost $1 per bar. The utility that Jackie receives from consuming potato chips and Hershey bars is represented by the following utility function: U=3C2 H. Given that Jackie seeks to maximize her utility, find the number of potato chip bags and Hershey chocolate bars that Jackie will purchase each month.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? $Consider a consumer that consumes 2 teaspoons of sugar with each cup of coffee. For each cup of coffee with sugar the consumer gains 10 utils. a)Write down the utility function that gives the total utility if the consumer consumes S teaspoons of sugar and C cups of coffee. The consumer has assigned £7 per week to be spent on drinking coffee with sugar. The current price of coffee is £0.50 per cup and each spoon of sugar costs £0.10. b)Calculate the optimal weekly consumption bundle for this consumer. c)Does the consumer view C and S as complements or substitutes?
- 2 COOKIES AND TEA Consider a consumer, Jennie, who only consumes tea (t) and cookies (c). Jennie's utility func- tion is U(t, c) = min{5t, c}. The min function gives you the smaller of the two arguments.¹ For example, the min{1,3} = 1 since 1 is less than 3. She has $10 to spend, the price of a cup of tea is normalized to $1, and the price per cookie is $2. Assume she can buy tea and cookies in fractions. a. Graph the set of the tea and cookie pairs that yield the utility level of 5 with tea on the x-axis and cookies on the y-axis. Now graph an indifference curve associated with the level of utility equal to 7. b. Given the market prices that Jennie faces and her income, how much tea and how many cookies will Jennie choose to consume? Show her optimal choice graphically with cookies on the x-axis and tea on the y-axis. [Note: You cannot use the standard Lagrangian technique here because the slope of the indifference curve is not defined at the kink. Try working with the graph of the…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. Jesper consumes granola (g) and whole milk (w). His utility function is u(g, w) = 2/g+ 2 yw, and he has $120 to spend. Giant sells granola for $4 per pound and milk for $2 per gallon. Safeway sells granola for $2 per pound and milk for $4 per gallon. (i) Find the optimal bundle if Jesper shops at Giant. (ii) Find the optimal bundle if he shops at Safeway. (iii) Explain why the bundle Jesper purchases at Giant would cost more at Safeway, and vice versa. (iv) Suppose that Jesper can purchase from Sam's Club instead by paying an “entry fee," f, and then paying prices $1.50 for granola and $3 for milk. Under what conditions will Jesper choose to shop at Sam's Club? (Your answer will be an algebraic expression involving f.) 2. Manuel consumes pints of strawberries (s) and blueberries (b). His utility function is u(s, b) = s + 2b, the prices are ps 2 and pB = 3, and Manuel has $60 to spend. (i) Find Manuel's optimal bundle. (ii) Suppose that pB rises to 5, all else equal. Find the new…