Armando consumes two goods: grapes and wine. He can purchase both at the market and also possesses a technology that allows him to costlessly convert any quantity of grapes into the same number of units of wine. This technology is not reversible: there is no quantity of wine that he can convert to grapes. Thus, for example, if he purchases 4 units of grapes and 3 units of wine, he could consume any bundle (4-s,3+s) with s € [0,4]. Armando's utility from consuming a units of grapes and y units of wine is u(x, y) = r²y. For each of the following questions, you may use, without proof, any results from the lectures for this course. (a) Find Armando's Marshallian demand expressed in terms of the bundle he consumes (i.e., of monon into min
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- John likes Coca-Cola. After consuming one Coke, John has a total utility of 10 utils. After two Cokes, he has a total utility of 25 utils. After three Cokes, he has a total utility of 50 utils. Does John show diminishing marginal utility for Coke, or does he show increasing marginal utility for Coke? Supposethat John has $3 in his pocket. If Cokes cost $1 each and John is willing to spend one of his dollars on purchasing a first can of Coke, would he spend his second dollar on a Coke, too? What about the third dollar? If John’s marginal utility for Coke keeps on increasing no matter how many Cokes he drinks, would it be fair to say that he is addicted to Coke?Alexi has a budget of $21 to spend on toaster and breads. He does not directly gain any utility from owining a toaster but for every slice of toasted bread he consumes he gain 2 units of utility, that is if he owns a toaster. Without the toaster, he gain 0 units of utility from consuming plain bread. Suppose the toaster has inferior quality and will break after toasting only 10 slices, then Alexi needs to buy a new one. The current market price for cheap toaster is $5 and the price for a single slice of bread is $1. Assume that Alexi aims to maximize consumer surplus. Find Alexi's income-consumption curve for slices of bread for incomes between $0 and $21, assuming a price of $1 per slice.Alexi has a budget of $21 to spend on toaster and breads. He does not directly gain any utility from owining a toaster but for every slice of toasted bread he consumes he gain 2 units of utility, that is if he owns a toaster. Without the toaster, he gain 0 units of utility from consuming plain bread. Suppose the toaster has inferior quality and will break after toasting only 10 slices, then Alexi needs to buy a new one. The current market price for cheap toaster is $5 and the price for a single slice of bread is $1. Assume that Alexi aims to maximize consumer surplus. In a graph, draw total utility as a function of number of toasted slices, assuming that Alexi buys 1 toaster.
- Jeremy is deeply in love with Jasmine. Jasmine lives where cell phone coverage is poor, so he can either callher on the land-line phone for five cents per minute or he can drive to see her, at a round-trip cost of $2 in gasolinemoney. He has a total of $10 per week to spend on staying in touch. To make his preferred choice, Jeremy uses ahandy utilimometer that measures his total utility from personal visits and from phone minutes. Using the values inTable 6.6, figure out the points on Jeremy’s consumption choice budget constraint (it may be helpful to do a sketch)and identify his utility-maximizing pointJohn likes Coca-Cola. After consuming one Coke, John has a total utility of 10 utils. After two Cokes, he has a total utility of 25 utils. After three Cokes, he has a total utility of 50 utils. Does John show diminishing marginal utility for Coke or does he show increasing marginal utility for Coke? Suppose that John has $3 in his pocket. If Cokes cost $1 each and John is willing to spend one of his dollars on purchasing a first can of Coke, would he spend his second dollar on a Coke, too? What about the third dollar? If John’s marginal utility for Coke keeps on increasing no matter how many Cokes he drinks, would it be fair to say that he is addicted to Coke? *use tables and/or graphs if possible, please original workAmadea spends all her income on pizza,chocolate milk, and music streams. The price of pizza is $4 per slice and price ofchocolate milk $2 per bottle. At Amadea's current consumption level, her marginalutility for pizza is 50 units per slice and for music 100 units per stream. Assuming thatAmadea is a utility maximizer, how much is (a)her current marginal utility for a bottleof chocolate milk, and (b) the price of streams she buys. Show your work. [Hint: Ch 6:Utility-maximizing formula)
- Praxilla, who lived in ancient Greece, derivesutility from reading poems and from eating cucumbers.Praxilla gets 30 units of marginal utility from her firstpoem, 27 units of marginal utility from her secondpoem, 24 units of marginal utility from her third poem,and so on, with marginal utility declining by three unitsfor each additional poem. Praxilla gets six units ofmarginal utility for each of her first three cucumbersconsumed, five units of marginal utility for each of hernext three cucumbers consumed, four units of marginalutility for each of the following three cucumbersconsumed, and so on, with marginal utility declining byone for every three cucumbers consumed. A poem coststhree bronze coins but a cucumber costs only one bronzecoin. Praxilla has 18 bronze coins. Sketch Praxilla’sbudget set between poems and cucumbers, placingpoems on the vertical axis and cucumbers on thehorizontal axis. Start off with the choice of zero poemsand 18 cucumbers, and calculate the changes in…The table below shows the utility schedule for a consumer of candy bars. Candy Bars Consumed 0 1 2 3 4 5 6 7 Total Utility 0 5 9 12 14 15 15 13 Based on the data in the above table you can conclude that the Multiple Choice O total utility of 2 units is 4 utils. marginal utility of the fourth unit is 14 utils. marginal utility of the third unit is 4 utils. marginal utility of the sixth unit is O utils.Jill likes to consume coffee and cream in a very particular way: with every cup ofcoffee she always consumes two 0.5 oz. cream containers. Jill is a utility maximizer anddecides to spend her income is $120 per month on coffee and cream. If the price of eachcoffee cup is $2.50, and the price of each cream container is $0.25, she will consume______ cups of coffee and ______ cream containers per month.A) 48; 96.B) 96; 48.C) 240; 480D) 80; 40E) None of the above.
- Units of rice 1 2 3 4 5 6 7 8 O 50 utils O 53 utils O 28 utils Marginal Utility of rice O 25 utils 20 18 16 14 12 10 9 8 Units of raisins 1 2 3 4 5 6 7 If the consumer buys 2 units of rice and 2 units of raisins, the consumer's total utility will be O 4 utils 8 Marginal Utility of raisins 8 7 6 5 4 3 2 1At Annie's current level of consumption, let MUp denote Annie's marginal utility from an additional pound of pasta, and let MUb denote Annie's marginal utility from an additional loaf of bread. Thus, MUp/MUb represents the number of loaves of bread Annie has to give up in order to buy another pound of pasta. the number of loaves of bread Annie is willing to give up to have another pound of pasta. the number of pounds of pasta Annie has to give up in order to buy another loaf of bread. the number of pounds of pasta Annie is willing to give up to have another loaf of bread.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?