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Five consumers have the following
The price of an apple is $1, and the price of a pear is $2.Which, if any,of these consumers are optimizing over their choice of fruit? For those who are not,how should they change their spending?
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- 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 utility—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.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.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 round—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.
- Explain why individuals make Choices that are directly on the budget constraint, rather than inside the budget constraint DI outside it.TU = Total Utilityf= is a function ofMU = Marginal UtilityO = units of consumptionA= infinitesimal change EMV= Equimarginal ValuePraxilla, who lived in ancient Greece, derivesutility from reading poems and from eating cucumbers.Praxilla gets 30 units of marginal utility from her firstpoem, 27 units of marginal utility from her secondpoem, 24 units of marginal utility from her third poem,and so on, with marginal utility declining by three unitsfor each additional poem. Praxilla gets six units ofmarginal utility for each of her first three cucumbersconsumed, five units of marginal utility for each of hernext three cucumbers consumed, four units of marginalutility for each of the following three cucumbersconsumed, and so on, with marginal utility declining byone for every three cucumbers consumed. A poem coststhree bronze coins but a cucumber costs only one bronzecoin. Praxilla has 18 bronze coins. Sketch Praxilla’sbudget set between poems and cucumbers, placingpoems on the vertical axis and cucumbers on thehorizontal axis. Start off with the choice of zero poemsand 18 cucumbers, and calculate the changes in…
- 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?Five consumers have the following marginal utility ofapples and pears:Marginal Utilityof ApplesMarginal Utilityof PearsClaire 6 12Phil 6 6Haley 6 3Alex 3 6Luke 3 12The price of an apple is $1, and the price of a pear is$2. Which, if any, of these consumers are optimizingtheir choices of fruit? For those who are not, howshould they change their spending?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
- Jill likes to consume coffee and cream in a very particular way: with every cup ofcoffee she always consumes two 0.5 oz. cream containers. Jill is a utility maximizer anddecides to spend her income is $120 per month on coffee and cream. If the price of eachcoffee cup is $2.50, and the price of each cream container is $0.25, she will consume______ cups of coffee and ______ cream containers per month.A) 48; 96.B) 96; 48.C) 240; 480D) 80; 40E) None of the above.maddy is a single mom with a weekly budget of $100. She can spend her weeklyincome on food and diapers for her son. Price of food is $1 and price of a diaperis 50 cents. Her son needs at least 5 diapers a day, therefore she must purchaseat least 35 diapers weekly. maddy utility function is U (f, d) = f 0.9d0.1,where f and d represent quantity of food and diapers, respectively.Part aFind Jennifer’s optimal consumption bundle. Make sure to draw her budgetconstraint and indifference curves and clearly demonstrate your solution.Part bmaddy uncle Sam, who is aware of her financial troubles, offers to help herout. Specifically, he offers to pay half of her weekly diaper expenses. Howmany diapers maddy would buy now? Again, demonstrate your solution bothgraphically and analytically.Wherein:TU = Total Utilityf= is a function ofMU = Marginal UtilityO = units of consumptionA= infinitesimal change EMV= Expected Monetary Value
