Consider the classic consumer's choice problem of an individual who is allocatingY dollars of wealth amongst two goods. Let c1 denote the amount of good 1 that theindividual would like to consume at a price of Pı per unit and c2 denote the amountof good 2 that the individual would like to consume at a price of P2 per unit. Theindividual's utility is defined over the consumption of these two goods (only). Supposewe allow the individual's happiness to be measured by a utility function u(c1, c2) whichis increasing and strictly concave in both goods while also satisfying the Inada condition,limcı→0du(c1,c2)= limc1→0du(c1,c2)dc2= 0.The Inada conditions simply say that the slope of the utility function becomes verticalin the direction of the good that has its consumption level go to zero. By assumingincreasing and strictly concave utility in both directions, we are assuming that the shapeof the utility function is such that, holding constant the amount of one good, as theindividual consumes more of the other good, they are happier but each additional unitof consumption yields less extra happiness than the previous unit (diminishing marginalutility of consumption). These assumptions imply that the first-order partial derivativeof the utility function with respect to good one, u1(C1, C2)du(c1,c2) and good two,acidu(c1,c2)u2(C1, C2)U1(C1, C2) remains positive but gets smaller. Similarly, holding c constant, ifU2(C1, C2) remains positive but gets smaller.Ci increases,increases,exist and are positive. Moreover, holding C2 constant,ifdc2C2 1. Let the budget constraint faced by the individual be PiC1 + P2c2 =Y. In words,interpret the meaning of the mathematical budget constraint.2. The individual's problem is to choose the consumption bundle (cı, c2) optimally.Specifically,max {u(с1, С2)}C1,C2subject to (cı, c2) satisfying the budget constraint, Pic1 + P2c2 = Y. Using theMethod of Lagrange, let A be the Lagrange multiplier on the budget constraint.The the Lagrangean function can be written asL(c1, C2, A) = u(c1, c2) + A (Y – P.c1 – P,c2).-Take the first order-derivative of the Lagrangean function with respect to c1, c2 andA. Set each of them equal to zero in order provide the equations that can be usedto identify the Lagrangean function's "critical points".

Consider the classic consumer's choice problem of an individual who is allocating Y dollars of wealth amongst two goods. Let c, denote the amount of good 1 that the ndividual 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 ndividual'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(Cı, c2) which s increasing and strictly concave in both goods while also satisfying the Inada condition, Limcı→0 du(c1,c2) limcı→0 du(c1,c2) = 0. The Inada conditions simply say that the slope of the utility function becomes vertical n the direction of the good that has its consumption level go to zero. By assuming ncreasing and strictly concave utility in both directions, we are assuming that the shape

Consider the classic consumer's choice problem of an individual who is allocating Y dollars of wealth amongst two goods. Let c, denote the amount of good 1 that the ndividual 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 ndividual'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(Cı, c2) which s increasing and strictly concave in both goods while also satisfying the Inada condition, Limcı→0 du(c1,c2) limcı→0 du(c1,c2) = 0. The Inada conditions simply say that the slope of the utility function becomes vertical n the direction of the good that has its consumption level go to zero. By assuming ncreasing and strictly concave utility in both directions, we are assuming that the shape

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Andrea has a budget of £21 to spend on toothbrushes and tooth paste. He does not receive any utility from owning a toothbrush, but for the consumption of every tube of tooth paste he gains a utility of 2 utils – but only if he owns a tooth brush. Without a tooth brush, Andrea gains no utility from consuming tooth paste. In addition, after consuming 10 tubes of tooth paste, a toothbrush needs to be replaced, i.e., Andrea needs to buy a new one. The current price of tooth brushes on the market is £5 and the current price for tooth paste is £1 per tube. Assume that Andrea aims to maximise consumer surplus. wwwwwww a) In a graph, draw total utility as a function of number of toothpaste tubes, assuming that Andrea buys 1 tooth brush. b) How many tubes will Andrea buy if he wants to maximise consumer surplus, assuming that Andrea can buy any amount of tooth brushes? What is Andrea's total consumer surplus? c) How many tubes will he buy if the current price is £0.50 per tube? d) Find Andrea's…
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12 There are two goods and John's preferences can be represented by u: R²0 R given by u(x) = x₁³x2³. His income and price of the two goods are given by (M, P1, 20 P2) = (12, 1, 2). Which 2 of the following 8 options are false: In John's optimal bundle, he consumes the same amount of good 1 as good 2. If we change John's utility function to u(x) = x + then John's optimal bundle remains unchanged. At John's optimal bundle, the slope of the budget constraint equals the slope of the indifference curve. In John's optimal bundle, he spends the same amount on good 1 as good 2. John's preferences satisfy local non-satiation. At John's optimal bundle, his bang per buck of good 1 equals his bang per buck of good If we change John's utility function to u(x) = In (17 +x₁x₂) then John's optimal bundle remains unchanged. If we change the budget set to (M, P1, P2) = (24, 2, 4) then John's optimal bundle remains unchanged.
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The table shows the total utility data for products S and T. Assume that the prices of S and T are $3 and $5, respectively, and that consumer income is $22. Total Utility 12 27 39 48 51 Units of S 1 2 3 4 5 Multiple Choice If the price of T decreases from $5 to $3, while the price of S and the consumer's income stay the same, then the utility-maximizing combination is such that the quantity of T increases from 2 to 4. Units of T 1 2 3 4 5 Total Utility 20 35 45 50 52 decreases from 4 to 3. stays the same at 2, but the consumer has $1 remaining. increases from 2 to 3, but the consumer has $1 remaining.
Part A . Consider an economy with the following features. • There are 100 identical consumers that derive utility from consuming three different goods: software, computers, and good m. • Each consumer decision utility function is given by U (c, 8) = 4c¹/48¹/4+m, where e denotes the amount of computers that she consumes, s denotes the amount of software that she consumes, and m denotes the amount of good m that she consumes. cand s must be non-negative, but m can take any real value. • Computers are produced by 20 identical competitive firms with a total cost function given by 10c². • Software is produced by 40 identical competitive firms with a total cost function given by 20s². . QUESTION 1: What are the equilibrium prices for software and comput- ers in equilibrium? Part B • Suppose that there is a positive technology shock in the software industry so that that the new cost function of the software firms becomes 10s². Let C and S denote, respectively, the aggregate level of…
John’s preferences for apples (A) and berries (B) are represented by U(A,B)= A+2B . Apples cost £2 and berries £1. Given that John’s monthly income is £30 answer the following questions: What type of goods are apples and berries for John? What is the proportion to which John is willing to exchange apples for berries? Illustrate and solve graphically John’s utility maximization problem. If his income increases every month by £10, how will John’s consumption choice be affected? Illustrate graphically the income expansion path and the Engel curve for each good. How will an increase in the price of berries to £6 affect John’s optimal consumption choice? (John’s income is £30) Graph John’s demand curve for each good. Assume that John wins a voucher of £20, redeemable only in apples. How would this affect John’s utility? (Assume that prices and income are as described initially) Assume that John is presented with two options: an apple voucher of £20 or just £6 to spend on any good he wants.…
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