Explain how an optimal decision of a consumer can be achieved by using utility-maximizing theory and revealed preference theory, please explain about how they are different and how they will get the same outcome!
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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.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.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.
- Would you expect total utility to rise or fall with additional consumption of a good? Why?Is it possible for total utility to increase while marginal utility diminishes? Explain.Explain why individuals make Choices that are directly on the budget constraint, rather than inside the budget constraint DI outside it.
- No written by hand solution Assume Fred has the following preference relation on [0, 1]: x ≿ y if and only if x ≤ y for all x ̸= 1 and y ̸= 1; and 1 ≻ z for all z ∈ (0, 1), 1 ∼ 1 and 0 ≻ 1. Does there exists a utility representation for this preference relation? If yes, provide a utility function. If no, explain. Show your work.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 2Explain the consumer equilibrium point by using Indifference Curve Approach andthe Budget Line. What is the necessary condition for the consumer equilibrium? Explain whyconsumer is not in equilibrium if this condition does not fulfil
- 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?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.
