Praxilla, 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 marginalutility of moving along the budget line to the next choiceof one poem and 15 cucumbers. Using this step-bystep process based on marginal utility, create a table andidentify Praxilla’s utility-maximizing choice. Comparethe marginal utility of the two goods and the relativeprices at the optimal choice to see if the expectedrelationship holds. Hint: Label the table columns: 1)Choice, 2) Marginal Gain from More Poems, 3)Marginal Loss from Fewer Cucumbers, 4) Overall Gainor Loss, 5) Is the previous choice optimal? Label thetable rows: 1) 0 Poems and 18 Cucumbers, 2) 1 Poemand 15 Cucumbers, 3) 2 Poems and 12 Cucumbers, 4) 3Poems and 9 Cucumbers, 5) 4 Poems and 6 Cucumbers,6) 5 Poems and 3 Cucumbers, 7) 6 Poems and 0Cucumbers.
Praxilla, who lived in ancient Greece, derives
utility from reading poems and from eating cucumbers.
Praxilla gets 30 units of
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 first 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 cucumbers consumed. A poem costs
three bronze coins but 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-bystep 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.
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