1. Jill acts as if she maximizes the utility function U = cx where c represents 'other consumption'. Jill plans to spend $12. The price of c is pe = 1 while the price of x is p₂ = 2. What quantity of c and x maximizes Jill's utility function? Ju If Jill chooses this level of c and x, how much additional utility does one 'x' give Jill (what is at this level of consumption), and how much additional utility does one unit of 'other consumption' give Jill ()? How many units of consumption would Jill give up to get one more 'x' (Marginal Rate of Substitution)? How many units of consumption does Jill have to give up to get one more x?

If people do not have a complete mental picture of total utility for every level of consumption, how can they find their utility-maximizing consumption choice?

Is it possible for total utility to increase while marginal utility diminishes? Explain.

As a college student you work at a part-time job, but your parents also send you a monthly allowance. Suppose one month your parents forgot to send the check. Show graphically how your budget constraint is affected. Assuming you only buy normal goods, what would happen to your purchases of goods?

Would you expect marginal utility to rise or fall with additional consumption of a good? Why?

Who determines how much utility an individual will receive from consuming a good?

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 next 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 cucumber consumed. A poem costs three bronze coins hut a cucumber costs only one bronze coin. Praxilla has 18 bronze coins. Sketch Praxillas 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-by-step process based on marginal utility, create a table and identify Praxillas 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.

What is the rule relating the ratio of marginal utility to prices of two goods at the optimal choice? Explain why, if this rule does not hold, the choice cannot be utility-maximizing