q15 please help fast all info is there Suppose the utility function of U(x1, X2) = x, 1/2x21/2 and the budget constraint of p1x1+p2x2=m Let's assume that p1=$1, p2=$2, and m=$120. Find the optimal bundle.
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q15 please help fast all info is there
Suppose the utility function of U(x1, X2) = x, 1/2x21/2 and the budget constraint of p1x1+p2x2=m
Let's assume that p1=$1, p2=$2, and m=$120. Find the optimal bundle.
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- Is it possible for total utility to increase while marginal utility diminishes? Explain.Take Jeremys total utility information in Exercise 6.1, and use the marginal utility approach to confirm the choice of phone minutes and round trips that maximize Jeremys utility.7. Bob receives utility from days spent traveling on vacation domestically (D) and daysspent traveling in a foreign country (F) as given by the utilityU(D; F) = DFThe price of a day spent traveling domestically is 160 pounds and in a foreigncountry 200 pounds. Bobís annual budget for traveling is 8000 pounds. (a) Find Bobís utility maximising choice of days traveling domestically and of daystravelling in a foreign country. Find also his utility level from consuming thatbundle. Suppose that the price of domestic traveling increases to 250 pounds per day.Denoting his budget for traveling x, (suppose by now that it is unknown) findthe demand for D and F under the new prices as a function of x.
- Please no written by hand and no emage 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?I like drinking Smirnoff and Stoli Vodka, but I really only careabout the total amount of alcohol I get out of it. They areperfect substitutes. Smirnoff is sold in liter bottles that are100 proof (that’s 50% alcohol). Stoli is sold in liter bottlesthat are 80 proof (40% alcohol). What is my utility functionfor bundles of these two vodkas? What do my indifferencecurves look like?solutions. Question 1 Calculating MRS for CD Utility Functions (a) If a consumer has a CD utility function 0.4 0.6 U(91,92) = 994926, calculate MRS1,2. (b) If a consumer has a CD utility function Ima kdown1 calculate MRS1,2. (c) If a consumer has an utility function noltan asd Tor sympy ,1-α U(91,92) = 91 92 llib et (.) orde (hing aid tol bholup U(91,92) = a ln(91) + (1 - a) ln(92), diw sonuanos of calculate MRS1,2. Is it the same as the result in the previous part? (Note: Recall that we discussed the concept of ordinal utility in class, which means only the order of utility matters, not its magnitude. In function is a monotone transformation on the CD utility function. Notice that In (qq) = a ln(9₁) + (1 - a) ln(92). This example verifies that a monotone transformation does not change *(S) sidshav the consumer's indifference curves.) wobei/ (d)
- 9 of 15 Laura has an income of 100 and she has to spend it to buy daisies (x₁) and daffodils (x2). Her preferences are represented by a Cobb Douglas utility function u(x1,x2)= x1x2. If daisies are twice as expensive as the daffodils, what would her optimal bundle be? O Buy only daffodils O Buy only daisies O Buy twice as many daffodils as daisies O Buy twice as many daisies as daffodils O Buy same amount of daisies and daffodils O No answer.3. Finding the optimal combination of two goods - $2. Suppose that Larry buys Larry enjoys consuming both cheese and fruit. Each pound of cheese costs Pc = $1, and each pound of fruit costs PF 300 pounds of cheese and 200 pounds of fruit per year. The following graphs show his marginal utility curves for cheese and fruit. At his current consumption level, Larry's marginal utility from consuming the last pound of cheese he bought is MUC S 30 utils per pound, and his marginal utility from consuming the last pound of fruit he bought is MUF = 30 utils per pound. 60 40 30 IL 20 10 400 500 600 50 40 A 30 B C D 20 10 0 0 100 Is Larry currently maximizing his utility? Combination 200 300 CHEESE (Pounds per year) 300, 30 (Pounds per Year) 200 400 300 No; he could buy less cheese and more fruit, not spend any more money, and be better off. O No; he likes fruit and cheese more than other goods, so he should buy more of both. O No; he could buy more cheese and less fruit, not spend any more money,…8. Jane lives in a dormitory that offers soft drinks and chips for sale in vending machines. Her utility function is U 3SC (where S is the number of soft drinks per week and C the number of bags of chips per week), so her marginal utility of S is 3C and her marginal utility of C is 3S. Soft drinks are priced at £0.50 each, chips £0.25 per bag. a. Write an expression for Jane's marginal rate of substitution between soft drinks and chips. b. Use the expression generated in part (a) to determine Jane's optimal mix of soft drinks and chips. c. If Jane has £5.00 per week to spend on chips and soft drinks, how many of each should she purchase per week?
- Total utility O diminished as the quantity of a good increases increases as long as more goods are acquired increases as long as marginal utility increases O increases as long as marginal utility is positive diminishes as consumption of some good rises3. Suppose Mary enjoys Pepsi and Coke according to the functionU(P;C) = 4C + 5P. What does her utility function say about her MRS of Coke for Pepsi? What do her indi§erence curves look like? What type of goods are Pepsi and Coke for Mary? If Pepsi and Coke each cost $1 and Mary has $20 to spend on these products, how many units of each product should she buy in order to maximize her utility? Show this utility maximiz- ing combination combination of Pepsi and Coke on the graph. how would her consumption and utility maximizing bundle of Coke and Pepsi change if the price of Coke decreases to 50 cents. 4. Vera is an impoverished graduate student who has only $100 a month to spend on food. She has read in a government publication that she can assure an adequate diet by eating only peanut butter and carrots in the Öxed ratio of 2 pounds of peanut butter to 1 pound of carrots, so she decides to limit her diet to that regime. a) If peanut butter costs $4 per pound and carrots cost $2 per…A consumer is making purchases of products Alpha and Beta such that the marginal utility of product Alpha is 63 and the marginal utility of product Beta is 40. The price of product Alpha is $9, and the price of product Beta is $5. The utility-maximizing rule suggests that, to stay within a given budget constraint, this consumer should Multiple Choice O O O increase consumption of product Beta and increase consumption of product Alpha. make no change in the consumption of Alpha or Beta. increase consumption of product Beta and decrease consumption of product Alpha. increase consumption of product Alpha and decrease consumption of product Beta.
