Unit of product (1) Marginal utility, A (2) Marginal utility, B (3) Marginal utility, C First 18 39 12 Second 16 36 10 Third 14 33 9 Fourth 12 30 8 Fifth 10 27 7 Sixth 8 24 5 Seventh 6 21 3 If the prices of A, B, and C are $2, $3, and $1, respectively, and the consumer has $26 to spend on these three products, what combination of the three products should be purchased in order to maximize utility?

Unit of product (1) Marginal utility, A (2) Marginal utility, B (3) Marginal utility, C First 18 39 12 Second 16 36 10 Third 14 33 9 Fourth 12 30 8 Fifth 10 27 7 Sixth 8 24 5 Seventh 6 21 3 If the prices of A, B, and C are $2, $3, and $1, respectively, and the consumer has $26 to spend on these three products, what combination of the three products should be purchased in order to maximize utility?

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter4: Utility Maximization And Choice

Section: Chapter Questions

Problem 4.12P

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Jeremy is deeply in love with Jasmine. Jasmine lives where cell phone coverage is poor, so he can either call her on the land-line phone for five cents per minute or he can drive to see her, at a roundâ€”trip cost of 2 in gasoline money. He has a total of 10 per week to spend on staying in touch. To make his preferred choice, Jeremy uses a handy utilimometer that measures his total utility from personal visits and from phone minutes. Using the values in Table 6.6, figure out the points 011 Jeremys consumption choice budget constraint (it may be helpful to do a sketch) and identify his utility-maximizing point.
Praxilla, who lived in ancient Greece, derives utility from reading poems and from eating cucumbers. Praxilla gets 30 units of marginal utility from her first poem 27 units of marginal utility from her second poem 24 units of marginal utility from her third poem, and so on, with marginal utility declining by three units for each additional poem. Praxilla gets six units of marginal utility for each of her next three cucumbers consumed, five units of marginal utility for each of her next three cucumbers consumed, four units of marginal utility for each of the following three cucumbers consumed, and so on, with marginal utility declining by one for every three cucumber consumed. A poem costs three bronze coins hut a cucumber costs only one bronze coin. Praxilla has 18 bronze coins. Sketch Praxillas budget set between poems and cucumbers, placing poems on the vertical axis and cucumbers on the horizontal axis. Start off with the choice of zero poems and 18 cucumbers, and calculate the changes in marginal utility of moving along the budget line to the next choice of one poem and 15 cucumbers. Using this step-by-step process based on marginal utility, create a table and identify Praxillas utilityâ€”maximizing choice. Compare the marginal utility of the two goods and the relative prices at the optimal choice to see if the expected relationship holds. Hint: Label the table columns: 1) Choice, 2} Marginal Gain from More Poems, 3) Marginal Loss from Fewer Cucumbers, 4) Overall Gain or Loss, 5) Is the previous choice Optimal? Label the table rows: 1) 0 Poems and 18 Cucumbers, 2) 1 Poem and 15 cucumbers, 3) 2 Poems and 12 cucumbers, 4) 3 Poems and 9 Cucumbers, 5) 4 Poems and 6 cucumbers 6) 5 Poems and 3 Cucumbers, 7) 6 Poems and 0 Cucumbers.
Mylie’s total utility from singing the same song over andover is 50 utils after one repetition, 90 utils after tworepetitions, 70 utils after three repetitions, 20 utils afterfour repetitions, 250 utils after five repetitions, and 2200utils after six repetitions. Write down her marginal utilityfor each repetition. Once Mylie’s total utility beginsto decrease, does each additional singing of the songhurt more than the previous one or less than the previousone?
Wherein:TU = Total Utilityf= is a function ofMU = Marginal UtilityO = units of consumptionA= infinitesimal change EMV= Expected Monetary Value
Suppose the linear demand curve for shirtsslopes downward and that consumers buy 500 shirts per yearwhen the price is $30 and 1,000 shirts per year when the priceis $25.a. Compared to the prices of $30 and $25, what can you sayabout the marginal valuation that consumers place on the300th shirt, the 700th shirt, and the 1,200th shirt they mightbuy each year?b. With diminishing marginal utility, are consumers derivingany consumer surplus if the price is $25 per shirt? Explain.c. Use a market demand curve to illustrate the change in consumersurplus if the price drops from $30 to $25.
Suppose that a consumer has a choicebetween two goods, X and Y. If the price of X is $2 and the priceof Y is $3, how much of X and Y does the consumer purchaseper period, given an income of $17 per period? Use the followinginformation about marginal utility:Units MUX MUY1 10 52 8 43 2 34 2 25 1 2
heABCCompanyLtd.HasapproximatedthemarginalrevenuefunctionforoneofitsproductsbyMR=20x – 2x 2 .ThemarginalcostfunctionisapproximatedbyMC=81 – 16x+x 2 .Determinetheprofitmaximizingoutput,thetotalprofit,thetotalrevenuefunction,anddemandfunction
Total utility is maximized in the consumption oftwo goods by equating thea. prices of both goods for the last dollar spenton each good.b. marginal utilities of both goods for the lastdollar spent on each good.c. ratios of marginal utility to the price of bothgoods for the last dollar spent on each good.d. marginal utility of one good to the price ofthe other good.
Consider a town with a single street of 1 km long with 3,000 people spread uniformly along it. Two stores, 1 and 2, are located at the opposite ends of the street and sell the same product (store 1 is locatedattheleftend).Thecostofwalkingist1 =$6perkmtostore1andt2 =$9perkmtostore2for each consumer. The net utility of a consumer located at point x from buying a product at store 1 is U1(x) = 100 – p1 – t1x, where pi is a price of the product at store i = 1,2. The net utility from buying at store 2 is U2(x) = 100 – p2 – t2(1 – x). The average cost of the product for each store is c = 4. (a) Assume that all consumers buy product from the sellers. Find the demand functions Di(p1,p2) and the profit functions πi(p1,p2) for each store i = 1,2 as functions of prices p1,p2.(b) Find the equilibrium prices.
A consumer finds only three products, X, Y, and Z, are for sale. The amount of utility which their consumption will yield is shown in the table below. Assume that the prices of X, Y, and Z are $10, $2, and $8, respectively, and that the consumer has an income of $74 to spend. Product X Product Y Product Z Quantity Utility Marginal Utility per $ Quantity Utility Marginal Utility per $ Quantity Utility Marginal Utility per $ 1 42 NA 1 14 NA 1 32 NA 2 82 4 2 26 6 2 60 3.5 3 118 3.6 3 36 5 3 84 3 4 148 3 4 44 4 4 100 2 5 170 2.2 5 50 3 5 110 1.25 6 182 1.2 6 54 2 6 116 0.75 7 182 _0 7 56.4 _1.2 7 120 _0.5_ Why would the consumer not be maximizing utility by purchasing 2 units of X, 4 units of Y, and 1 unit of Z?
A consumer finds only three products, X, Y, and Z, are for sale. The amount of utility which their consumption will yield is shown in the table below. Assume that the prices of X, Y, and Z are $10, $2, and $8, respectively, and that the consumer has an income of $74 to spend. Product X Product Y Product Z Quantity Utility Marginal Utility per $ Quantity Utility Marginal Utility per $ Quantity Utility Marginal Utility per $ 1 42 NA 1 14 NA 1 32 ___NA__ 2 82 4 2 26 6 2 60 __3.5_ 3 118 3.6 3 36 5 3 84 __3___ 4 148 3 4 44 4 4 100 __2___ 5 170 2.2 5 50 3 5 110 _1.25___ 6 182 1.2 6 54 2 6 116 _0.75__ 7 182 0 7 56.4 1.2 7 120 _0.5_ How many units of X, Y, and Z will the consumer buy when maximizing utility and spending all…
What combination of units of products U, W, X, Y, and Z will maximize total utility for a person whose budget is P1,500 and whose marginal utility schedule is shown in the following table. Marginal Utility Qty. MUu MUw MUx MUy MUz 1 50 30 35 90 75 2 50 15 28 84 65 3 35 15 25 80 63 4 25 10 12 75 60 5 15 10 5 62 54 6 10 5 5 48 50 7 5 0 5 35 40 8 0 0 5 30 30 Price Pu = 80 Pw = 20 Px = 45 Py = 200 Pz = 100 Legend: Pi = Price per unit of product i (i= u, w, x, y, z) MUi = Marginal Utility of product i (i= u, w, x, y, z) Upload an Excel file that shows the following: (1) Number of units to buy for u, w, x, y, and z (2) Total money to spend (3) Total utility of buyer

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Unit of product	(1) Marginal utility, A	(2) Marginal utility, B	(3) Marginal utility, C
First	18	39	12
Second	16	36	10
Third	14	33	9
Fourth	12	30	8
Fifth	10	27	7
Sixth	8	24	5
Seventh	6	21	3