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
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.
