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Calculate the formula for mrs

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Consider the following ?ve utility functions and assume that α and β are positive real numbers:

1. uA(x1,x2) = xα 1 xβ 2

2. uB(x1,x2) = αx1 + βx2

3. uC(x1,x2) = αx1 + β ln x2

4. uD(x1,x2) = (α/β)ln x1 + ln x2

5. uE(x1,x2) = -α ln x1 -β lnx2

(4.30)

(a) Calculate the formula for MRS for each of these utility functions.

(b) Which utility functions represent tastes that have linear indi?erence curves?

(c) Which of these utility functions represent the same underlying tastes?

(d) Which of these utility functions represent tastes that do not satisfy the monotonicity assumption?

(e) Which of these utility functions represent tastes that do not satisfy the convexity assumption?

(f) Which of these utility functions represent tastes that are not rational (i.e. that do not satisfy the completeness and transitivity assumptions)?

(g) Which of these utility functions represent tastes that are not continuous?

(h) Consider the following statement: "Bene?ts from trade emerge because we have di?erent tastes. If individuals had the same tastes, they would not be able to bene?t from trading with one another." Is this statement ever true, and if so, are there any tastes represented by the utility functions in this problem for which the statement is true?

Reference no: EM132440668

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