Consider the classic consumer's choice problem of an individual who is allocating Ý dollars of wealth amongst two goods. Let c1 denote the amount of good 1 that the individual would like to consume at a price of P per unit and c2 denote the amount of good 2 that the individual would like to consume at a price of P2 per unit. The individual's utility is defined over the consumption of these two goods (only). Suppose we allow the individual's happiness to be measured by a utility function u(c1, c2) which is increasing and strictly concave in both goods while also satisfying the Inada condition, limcı→0 du(cı,c2) = limcı→0 du(c1,c2) dc2 = ∞. %3D dci The Inada conditions simply say that the slope of the utility function becomes vertical in the direction of the good that has its consumption level go to zero. By assuming increasing and strictly concave utility in both directions, we are assuming that the shape of the utility function is such that, holding constant the amount of one good, as the

Consider the classic consumer's choice problem of an individual who is allocating Ý dollars of wealth amongst two goods. Let c1 denote the amount of good 1 that the individual would like to consume at a price of P per unit and c2 denote the amount of good 2 that the individual would like to consume at a price of P2 per unit. The individual's utility is defined over the consumption of these two goods (only). Suppose we allow the individual's happiness to be measured by a utility function u(c1, c2) which is increasing and strictly concave in both goods while also satisfying the Inada condition, limcı→0 du(cı,c2) = limcı→0 du(c1,c2) dc2 = ∞. %3D dci The Inada conditions simply say that the slope of the utility function becomes vertical in the direction of the good that has its consumption level go to zero. By assuming increasing and strictly concave utility in both directions, we are assuming that the shape of the utility function is such that, holding constant the amount of one good, as the

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter3: Preferences And Utility

Section: Chapter Questions

Problem 3.15P

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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…
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? 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 work