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- 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.. Consider a consumer with preferences defined over x and y. Demonstrate that it is possible theywould choose to consume some of both commodities when their income is I but would choose toconsume only x when their income is I’ > I. (Remember: if you can draw it without violating anyof the basic assumptions on preferences, it could happen.)Suppose that the following utility function is given (x,Y) xY. Which of the following is correct? OYis a good and X is a bad and indifference curve is positively sloped. X is a good and Y is a bad and indifference curve is negatively sloped. O Both X and Y are bads and indifference curve is negatively sloped. Both X and Y are goods and indifference curve is negatively sloped
- I like drinking Smirnoff and Stoli Vodka, but I really only careabout the total amount of alcohol I get out of it. They areperfect substitutes. Smirnoff is sold in liter bottles that are100 proof (that’s 50% alcohol). Stoli is sold in liter bottlesthat are 80 proof (40% alcohol). What is my utility functionfor bundles of these two vodkas? What do my indifferencecurves look like?Intialy mr. John is at equilibrium such that the last dollar spent on each of several products gives hi identical marginal utility i.e MUorange/porange=MUApple/pApple=...=MUn/pn where Mu orange =aditional utility derived from consuming one more unit of Apple ,pApple=price of a unit of Apple etc Q.how will Mr.Jhon react if the price of orange and other goods remain constant?and how can the equilibrium be restored?a. A consumer is willing to trade 3 units of x for 1 unitof y when she has 6 units of x and 5 units of y. She isalso willing to trade in 6 units of x for 2 units of y whenshe has 12 units of x and 3 units of y. She is indifferentbetween bundle (6, 5) and bundle (12, 3). What is theutility function for goods x and y? Hint: What is theshape of the indifference curve?b. A consumer is willing to trade 4 units of x for 1 unitof y when she is consuming bundle (8, 1). She is alsowilling to trade in 1 unit of x for 2 units of y when sheis consuming bundle (4, 4). She is indifferent betweenthese two bundles. Assuming that the utility function isCobb–Douglas of the form U (x, y) = xα y β, where α andβ are positive constants, what is the utility function forthis consumer?c. Was there a redundancy of information in part (b)? Ifyes, how much is the minimum amount of informationrequired in that question to derive the utility function?
- If we observe that a consumerâ s budget constraint has shifted inward, we can assume that the consumer will buy O fewer normal goods and fewer inferior goods O more normal goods and more inferior goods O fewer normal goods and more inferior goods more normal goods and fewer inferior goods¦ What can be the implications of a positively sloping indifference curve?Pls help with thsi question I am stuck Given the image attatched: 1.Given the above Marginal Utilities and prices to form the optimality condition for utilitymaximization. According to this optimality condition, what must be the ratio of Films toBooks in an optimal consumption bundle? 2. Given your answer to Q9, what must be the household’s optimal consumption of F & Bgiven their income (m)? 3. Suppose that the price of Films changed from $2 to $4. What would need to happen tothe MRS according to the optimality condition in Q9 if the household wanted to keepmaximizing its utility?
- 39. The following chart shows thec total utility-that Ammar receives from çonşuming various amounts-of chocolate.candy bars each day: Number candy, bars consumed për đay Total'utility 1' 40- 2 70 90 100 4. 80 Which of the following statements about Ammar's marginal utility is correct? Hiş marginal utility from the first candy bar is greater-than his marginalutility from the second candy' barTotal utility is maximized in the consumption oftwo goods by equating thea. prices of both goods for the last dollar spenton each good.b. marginal utilities of both goods for the lastdollar spent on each good.c. ratios of marginal utility to the price of bothgoods for the last dollar spent on each good.d. marginal utility of one good to the price ofthe other good.Five 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?
