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Assume we have monotonicity. To determine whether preferences are consistent wit

ID: 1147375 • Letter: A

Question

Assume we have monotonicity. To determine whether preferences are consistent with the hypothesis of diminishing marginal rates of substitution (MRS), we examine what happens to the absolute value of the MRS  as we move to the south-east along an indifference curve (increasing x1 and decreasing x2. If the absolute value of the MRS falls, then the consumer's preferences are consistent with diminishing MRS.

Suppose a consumer's preferences over x1 and x2 can be represented by the utility function U(x1,x2) = 9(x1)1/3 + x2. Are these preferences consistent with the hypothesis of diminishing MRS?  

consistent with diminishing marginal rate of substitution.

not consistent with a utility function.

consistent with increasing marginal rate of substitution.

consistent with constant marginal rate of substitution.

a.

consistent with diminishing marginal rate of substitution.

b.

not consistent with a utility function.

c.

consistent with increasing marginal rate of substitution.

d.

consistent with constant marginal rate of substitution.

Explanation / Answer

MRS=(MU1/MU2)

MU1=dU/dx1

MU1=3x1^2/3

MU2=du/dx2

MU2=1

Therefore, MRS=(3X1^2/3)/1

If x1 is increasef x1^2/3 will be increased. Therefore option c is correct.