Praxilla lives in Athens and derives utility from readingpoems and from eating cucumbers.Praxilla gets 30 units of marginal utility from her first poem, 27 units of marginal utility fromher second poem, 24 units of marginal utility from her third poem, and so on, with marginalutility declining by three units for each additional poem. Praxilla gets six units of marginalutility for each of her first three cucumbers consumed, five units of marginal utility for eachof her next three cucumbers consumed, four units of marginal utility for each of the followingthree cucumbers consumed, and so on, with marginal utility declining by one for every threecucumbers consumed. A poem costs three bronze coins, but a cucumber only costs onebronze coin. Praxilla has 18 bronze coins.1. Define the concept of utility (10 marks)2. Sketch Praxilla’s budget set between poems and cucumbers, placing poems on thevertical axis and cucumbers on the horizontal axis. Start off with the choice of zeropoems and 18 cucumbers and calculate the changes in marginal utility of movingalong the budget line to the next choice of one poem and 15 cucumbers. Using thisstep-by-step process based on marginal utility, create a table and identify Praxilla’sutility-maximizing choice. (20 marks)Assessment Brief3. Compare the marginal utility of the two goods and the relative prices at the optimalchoice 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? (15 marks)4. 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 6Cucumbers, 6) 5 Poems and 3 Cucumbers, 7) 6 Poems and 0 Cucumbers (15 marks)Task B (40% = 40 marks)Average cost curves (except for average fixed cost) tend to be U-shaped, decreasing and thenincreasing.Marginal cost curves have the same shape, though this may be harder to see since most ofthe marginal cost curve is increasing. Why do average and marginal cost curves have thesame general shape? Motivate your answer with necessary references.
