Consider a consumer with income M who can buy two products, good 1 and good 2...
Consider a consumer with income M who can buy two products, good 1 and good 2 for prices p1 and p2. If the consumer has Cobb-Douglas utility, show that her preferences are homothetic.
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Consider a consumer with income M who can buy two products, good
1 and good 2...
Consider an exchange economy with two consumers, A and B, who can consume only two goods....
Consider an exchange economy with two consumers, A and B, who can consume only two goods. Suppose consumers’ preferences are represented by a Cobb- Douglas utility function of the form u(x1i,x2i) = x1ix2i (here i is for consumer A or B) for a consumption bundle of two goods (x1i,x2i). The consumers have endowments eA = (e1A;e2A) = (4;1) and eB = (e1B;e2B) = (1;4). The price of good 1 is p1 and the price of good 2 is p2. You...
α1-α Given prices (P1 and p2) and income (Y), we know from lecture that if preferences...
α1-α Given prices (P1 and p2) and income (Y), we know from lecture that if preferences can be represented by the Cobb-Douglas utility function u (q1,22 for 0< α< 1, then the demand for goods 1 and 2 are (1-a)Y P2 q1-- and q2 = P1 We also know that any monotonic transformation of utility represents the same preferences. Consider the monotonic transformation v (q1.q2,-In(u (442),-InG In q192 qq As was shown in lecture, by the rules of logarithms this...
A consumer has preferences represented by the utility function: u(21,12)=x2? Market prices are p1 = 2...
A consumer has preferences represented by the utility function: u(21,12)=x2? Market prices are p1 = 2 and P2 = 5. The consumer has an income m = 13. Find an expression for the consumer's demand for good 1,21 (P1). 39p1
2- Lisa's preference between good X and a composite good of everything else (Z) can be...
2- Lisa's preference between good X and a composite good of everything else (Z) can be shown by a Cobb-Douglas function as below U(X,Z) = xaz1-a where 0 < a < 1. We can show that the marginal utility of each good is 1-a MUx = a (5)" MU; = (1 –a) (?) a. *Assume a = 0.25 and use an X-Z graph. Sketch the indifference curves which pass through combinations (2,3) and (4,6). A combination (x,z) is a bundle...
A consumer uses his income I for the consumption of two goods ?1 and ?2. He maximises utility at given product prices ?1...
A consumer uses his income I for the consumption of two goods ?1 and ?2. He maximises utility at given product prices ?1, ?2. His preferences with respect to both products can be described by an ordinal utility function ?(?1,?2), which exhibits a decreasing marginal rate of substitution (normal preferences). Please indicate whether the following statements are right or wrong in this context. If a statement is wrong, then describe briefly what is wrong (one sentence). a) A double value...
Eugenia can consume two goods, good 1 and good 2 where xi and Xz denote the...
Eugenia can consume two goods, good 1 and good 2 where xi and Xz denote the quantity consumed of each good. These goods sell at prices P. and P2, respectively. Eugenia's income is I and her preferences are given by: U(x1, x2) = x2x2 a) Are goods 1 and 2 perfect complements, perfect substitutes or imperfect substitutes to Eugenia? Explain. b) Derive Eugenia's demand functions for the two goods. c) Assume that p1 = P2 = $5 and 7 =...
7. Suppose you know that a demand function of consumer for good 1 is p-, where...
7. Suppose you know that a demand function of consumer for good 1 is p-, where pi is price of the good and xi is the quantity consumed. You know that the consumer can buy only good 1 or good 2. Her income is $2000 and the price of good 2 is P2 〉 0. (a) Find an utility function that represents the preferences of this consumer (b) Given the above utility function derive demand for good 2. (c) Suppose...
A consumer has income M, and faces prices (for goods 1 and 2) p1 and p2....
A consumer has income M, and faces prices (for goods 1 and 2) p1 and p2. For each of the following utility functions, graphically show the following: (i) the Slutsky substitution and income e⁄ects when p1 decreases. (ii) the Hicks substitution and income e⁄ects when p1 decreases. (iii) the Marshallian and Hicksian demand curves for good 1: (a) perfect complements: U(x1 , x2) = min {4x1, 5x2} (b) quasi-linear: U(x1 , x2) = x^2/3 1 + x2
number 1 please Problem 2. Consider a consumer has Cobb-Douglas preferences over two goods 21 and...
number 1 please
Problem 2. Consider a consumer has Cobb-Douglas preferences over two goods 21 and 22, given by u (21, 22) = 7 ln 21 + In 22. Let pı = 5 and p2 = 3 be the prices of the two goods, and suppose the agent has income I = 20. Suppose there is rationing of goods, so that in addition to paying for goods, the agent must have the appropriate number of coupons. Suppose, the agent begins...
= 1/ 23/2. If the prices for goods 1 and 2 are, and respectively, and income is M, what is the Consider a consumer wit...
= 1/ 23/2. If the prices for goods 1 and 2 are, and respectively, and income is M, what is the Consider a consumer with a utility function consumer's optimal consumption of good 1? x1 = M/(3p2) xi = M/(482) xi = 3M/(4px) x1 = 4Mp1/(P2) None of the above Consider a consumer with a utility function y = 1/2/3/2. If the prices for goods 1 and 2 are 2 and 4 respectively, and income is 40, what is the...
α1-α Given prices (P1 and p2) and income (Y), we know from lecture that if preferences can be represented by the Cobb-Douglas utility function u (q1,22 for 0< α< 1, then the demand for goods 1 and 2 are (1-a)Y P2 q1-- and q2 = P1 We also know that any monotonic transformation of utility represents the same preferences. Consider the monotonic transformation v (q1.q2,-In(u (442),-InG In q192 qq As was shown in lecture, by the rules of logarithms this...
A consumer has preferences represented by the utility function: u(21,12)=x2? Market prices are p1 = 2 and P2 = 5. The consumer has an income m = 13. Find an expression for the consumer's demand for good 1,21 (P1). 39p1
2- Lisa's preference between good X and a composite good of everything else (Z) can be shown by a Cobb-Douglas function as below U(X,Z) = xaz1-a where 0 < a < 1. We can show that the marginal utility of each good is 1-a MUx = a (5)" MU; = (1 –a) (?) a. *Assume a = 0.25 and use an X-Z graph. Sketch the indifference curves which pass through combinations (2,3) and (4,6). A combination (x,z) is a bundle...
Eugenia can consume two goods, good 1 and good 2 where xi and Xz denote the quantity consumed of each good. These goods sell at prices P. and P2, respectively. Eugenia's income is I and her preferences are given by: U(x1, x2) = x2x2 a) Are goods 1 and 2 perfect complements, perfect substitutes or imperfect substitutes to Eugenia? Explain. b) Derive Eugenia's demand functions for the two goods. c) Assume that p1 = P2 = $5 and 7 =...
7. Suppose you know that a demand function of consumer for good 1 is p-, where pi is price of the good and xi is the quantity consumed. You know that the consumer can buy only good 1 or good 2. Her income is $2000 and the price of good 2 is P2 〉 0. (a) Find an utility function that represents the preferences of this consumer (b) Given the above utility function derive demand for good 2. (c) Suppose...
number 1 please
Problem 2. Consider a consumer has Cobb-Douglas preferences over two goods 21 and 22, given by u (21, 22) = 7 ln 21 + In 22. Let pı = 5 and p2 = 3 be the prices of the two goods, and suppose the agent has income I = 20. Suppose there is rationing of goods, so that in addition to paying for goods, the agent must have the appropriate number of coupons. Suppose, the agent begins...
= 1/ 23/2. If the prices for goods 1 and 2 are, and respectively, and income is M, what is the Consider a consumer with a utility function consumer's optimal consumption of good 1? x1 = M/(3p2) xi = M/(482) xi = 3M/(4px) x1 = 4Mp1/(P2) None of the above Consider a consumer with a utility function y = 1/2/3/2. If the prices for goods 1 and 2 are 2 and 4 respectively, and income is 40, what is the...
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