Suppose the weighted marginal utility for two goods, x and y, at a position of consumer equilibrium is 70. If the price of good x is R10 and the relevant marginal utility for y is 140, what is the price of good y and the relevant marginal utility for good x?
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- 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-maximizingPraxilla, 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.Who determines how much utility an individual will receive from consuming a good?
- Would you expect total utility to rise or fall with additional consumption of a good? Why?Income Effects depend on the income elasticity of demand for each good limit you buy. If one of the goods you buy has a negative income elasticity, that is, it is an inferior good, what must be true of the income elasticity of the other good you buy?Mylie’s total utility from singing the same song over andover is 50 utils after one repetition, 90 utils after tworepetitions, 70 utils after three repetitions, 20 utils afterfour repetitions, 250 utils after five repetitions, and 2200utils after six repetitions. Write down her marginal utilityfor each repetition. Once Mylie’s total utility beginsto decrease, does each additional singing of the songhurt more than the previous one or less than the previousone?
- 9: Is il fossible for marginal utility To be negetive and yet Tolal Utilily To positive ? INhy be why not ? orFive consumers have the following marginal utility ofapples and pears:Marginal Utilityof ApplesMarginal Utilityof PearsClaire 6 12Phil 6 6Haley 6 3Alex 3 6Luke 3 12The price of an apple is $1, and the price of a pear is$2. Which, if any, of these consumers are optimizingtheir choices of fruit? For those who are not, howshould they change their spending?Figure 4.2 P3 P2 P1 A C Q Q2 Q3 Q4 Qs Qs Q7 Refer to Figure 4.2. The demand curve A indicates that O the smallcst price change will cause consumcrs to change their consumption by a large amount, O therc is no change in quantity demandcd as the price changes. consumcrs can purchase any quantity they want regardless of the price, Oithc smalcst price incrcasc wil.causc.consuners to switch to the producer with thc lowest
- Units of the Good 0 1 5678AWN2 3 4 Total Utility Total Utility of X of Y 0 0 620 1740 1120 3030 1500 3960 1820 4710 2080 5280 2300 5730 2460 6060 2580 6300 For the next 3 questions, assume that an individual consumes two goods X and Y. The total utility (assumed measurable) of each good is independent of the rate of consumption of other goods. The prices of X and Y are, respectively, $20 and $30. If the consumer buys the fourth unit of X the Marginal Utility per Dollar Spent on X is 16 I If the consumer has $210 to spend on X and Y, the utility-maximizing bundle is The minimum budget necessary to move to a higher equilibrium consumption of X and Y is $ unit(s) of X and unit(s) of Y.Question 9 If we observe that a consumerâ s budget constraint has shifted inward, we can assume that the consumer will buy O more normal goods and fewer inferior goods O more normal goods and more inferior goods O fewer normal goods and more inferior goods fewer normal goods and fewer inferior goods O OFor normal goodsA) the substitution effect of a price decrease will decrease the quantity of the good demanded while theincome effect of a price decrease will increase the quantity of the good demanded.B) the substitution and income effects of a price decrease will both increase the quantity of the gooddemanded.C) the substitution and income effects of a price decrease will both decrease the quantity of the gooddemanded.D) the substitution effect of a price decrease will increase the quantity of the good demanded while theincome effect of a price decrease will decrease the quantity of the good demanded.