Question

1. Praxilla derives utility from reading poems and from eating cucumbers. (For an introduction to the work of Praxilla, a female Greek poet in the fifth century B.C., see    http://ancienthistory.about.com/cs/praxilla/. But, this introduction to Praxilla is not important for solving this problem.) 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 3 units for each additional poem. Praxilla gets 6 units of marginal utility for each of her first three cucumbers consumed, 5 units of marginal utility for each of her next three cucumbers consumed, 4 units of marginal utility for each of the following three cucumbers consumed, and so on, with marginal utility declining by 1 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 1 poem and 15 cucumbers. Using this step-by-step process based on marginal utility, fill in the table below 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.

Choice	Marginal Gain from more Poems	Marginal Loss from fewer Cucumber	Overall Gain or Loss	Is Previous choice optimal?
0 poems, 18 cucumbers	Starting point	Starting point	—	—
1 poem, 15 cucumbers
2 poems, 12 cucumbers
3 poems, 9 cucumbers
4 poems, 6 cucumbers
5 poem, 3 cucumbers
6 poems, 0 cucumbers

Answer 1