Suppose that your utility from pens (x) and notebooks (y) is given by U=xy+10x Your income is 80$, the price per pen is 30$ and the price per notebook is 10$. What are the optimal (utility maximizing) values of pens and notebooks?
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- 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.Would you expect marginal utility to rise or fall with additional consumption of a good? Why?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.
- Lee has calculated her marginal utility from buying pizza slices and soda (shown on the table in the worksheet) and wants to use these data to decide how to rationally spend the money she has. The price of pizza is $2.00 and the price of soda is $2.00 question 9 (a) given these prices and your worksheet calculations, what is the first product lee will buy? (b) would lee ever buy four slides of pizza? Why/why not? question 10Given the data in your worksheet, how many pizza slices and sodas lee should buy to maximize her total utility if she rationally spends her budget of 10.00? question 11 when the price of pizza changes, lee's MU/$P changes. If the price of pizza decreases to $1.50 and her budget decreases to $7.50, how many pzza slices and sodas lee should buy to maximize her total utility?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?5. Leila currently buys 6 trips using public transportation with a marginal utility of 2, and 4 trips using ride-share with a marginal utility of 8. Suppose that the price of a trip through public transport is 12 and the price of a trip through ride share is 56. Is Leila currently maximizing her utility? Explain why or why not. If not, what is the optimal action to improve her utility?
- 3. 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…Quantity X TUx MUX MUX/Px Quantity Y TUy MUY MUy/Py 1 75 1 96 135 60 B 72 185 50 3 234 66 4 230 45 A 4 294 60 270 5 348 54 2.Moe's income is $320 per week and he spends it on two goods, X and Y. Good X costs $8 and good Y costs $4 per unit. His utility function is U = 4.5XY. (a) Calculate Moe's utility-maximizing purchases of X and Y. (b) Calculate Moe's constrained utility- maximum if his income decreases by $2.00? (c) If the price of Y doubles, with no change in the price of X, by how much would his income have to increase to enable him to maintain his initial level of utility (as in part (a) above)?
- 1. A consumer has an income of $3024 to spend each day. The only two goods the consumer is interested in purchasing are goods A and B. The marginal-utility schedules for these two goods are shown in the table below. The price of B does not change and is $378. The marginal utility per dollar from B is also shown in the table. But the price of A varies as shown in the table. The marginal utility per dollar from A when the price of A is $1512 and $756 is shown in the following table. Good A Good B Quantity MU MU/$1512 MU/$756 MU MU/$378 1 24 2 15 3 12 4 8 5 6 6 4 48 32 24 16 8 4 ||||| ||||| |||1. Doreen is looking for a flat to rent in Brighton. a. In choosing a flat, she cares about two characteristics: the number of bedrooms (x), and the number of bathrooms (y). Her utility function is U(x,y) = min(x, 2y). She has £1000 to spent on rent per month. The rental price per bedroom in Brighton is £400, and the price per bathroom is £200. (For example, a flat with three bedrooms and two bathrooms would rent for £1600 per month.) How many bedrooms and bathrooms does Doreen choose to rent optimally? b. Doreen now needs to furnish her flat. She has £500 to spend. However, she would also like to buy some clothes for her new job. The cost of furniture f is £50 per unit and the cost of clothing c is £20 per unit. Her utility function over furniture and clothing is U(f.c) = f0.3c0.7. How much does she spend in total on furniture, and on clothing? c. The local furniture shop runs a flash sale of 50% off, on all prices. How much does Doreen now spend on furniture, and on clothing?…5. Jonas purchases only two goods, starfruit (S) and kiwi (K). He has an income of $60 and can buy starfruit at $2 per pound and kiwi at $3 per pound. His utility function is U(S,K)=3S+4K. That is, his (constant) marginal utility for starfruit is 3 and his marginal utility for kiwi is 4. What bundle of starfruit and kiwi should he purchase to maximize his utility? Why?
