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
Homework Answers
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A consumer has income M, and faces prices (for goods 1 and 2) p1
and p2....
The individual has a utility function of u(x1, x2) = min (4x1, 5x2) and faces prices...
The individual has a utility function of u(x1, x2) = min (4x1, 5x2) and faces prices p1=2 and p2=1. We know they consume 20 units of x2 and spend all their income. What is the demand function for x1?
Suppose that a consumer has a utility function given by u(x1, x2) = 2x1 + x2. Initially the consumer faces prices (2, 2) and has income 24. i. Graph the budget constraint and indifference curves. Find...
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4. Suppose U(x1, x2) = 2lnx1 + 3lnx2 and P1 = 4, P2 = 1, and...
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Q2 For each of the following utility functions, derive the consumer's Marshallian demand functions, 21(P1, P2,...
Q2 For each of the following utility functions, derive the consumer's Marshallian demand functions, 21(P1, P2, B) and x (P1, P2, B), and calculate 11 (income elasticity of good 1), €1 (own-price elasticity of good 1), and €12 (cross-price elasticity). a U(x1, x2) = 21 b U(x1, x2) = 2.925-a for a € (0,1) CU(21, 12) = ln(21) + x2 where B > P2.
2. Jane's utility function has the following form: U (1,y) = 3x2 +2.ry The prices of...
2. Jane's utility function has the following form: U (1,y) = 3x2 +2.ry The prices of cand y are p, and Py respectively. Jane's income is I. (a) Find the Marshallian demands for and y and the indirect utility function. (b) Without solving the cost minimization problem, recover the Hicksian de mands for x and y and the expenditure function from the Marshallian demands and the indirect utility function. (c) Write down the Slutsky equation determining the effect of a...
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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...
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