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Principles of Economics 2e

2nd Edition
Steven A. Greenlaw; David Shapiro
ISBN: 9781947172364

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BuyFindarrow_forward

Principles of Economics 2e

2nd Edition
Steven A. Greenlaw; David Shapiro
ISBN: 9781947172364
Textbook Problem

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 Praxilla’s 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 Praxilla’s 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.

To determine

Praxilla’s utility-maximizing choice based on the marginal utility.

Explanation

In the given question, Praxilla gets the utility from two goods which are Poems and Cucumber. The poem costs three bronze coins and cucumber derives the costs of one bronze coin. Hence, the budget constraint equation will be seen as done below:

3P + C =18

Where, P is Poems and C is Cucumber.

The marginal utility derived from poems is given as first unit to be 30, second unit to be 27 and so on. Similarly, the marginal utility of Cucumber declines one for every three cucumber consumed.

The choice of the table can be seen as below:

Cucumber Poems MU of Poems MU of Cucumber Total Utility
18 0

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