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.
