Please show full working Consider the following utility functions: U(x_1,x_2) =

Question

Please show full working

Consider the following utility functions: U(x_1,x_2) = 7x_1x_2 + 11x^3_2 For all of the above, X_1 Greaterthanorequalto 0, x_2 Greaterthanorequalto 0, since they are quantities. Is V(x_1,x_2) a positive monotonie transformation of U(x_1,x_2)? Show that this is the case. Is W(x_1,x_2) a positive monotonie transformation of U(x_1,x_2)? Show that this is the case. Explain why D(x_1, x_2) is not a positive monotonie transformation of A(X_1, x_2), even though b(x_1,x_2) and C(x_1,x_2) are.

Explanation / Answer

A monotonic transformation is way of transforming one set of numbers in to another set of numbers so that the rank order of the original set of numbers is preserved.

a)

Yes, the function V(x1,x2) is a monotonic transformation of the utility function U(x1,x2) since the orginal bundle of preferneces fo the original utility function is preserved as it is.

b)

In case of a positive monotonic transformation, the MRS of both the utility functions remain the same.

In thie given case, MRS (U) = 7x2/7x1+33x22

MRS(W) will not be equal to MRS(U)

Hence, it is not positive transformation.

c)

In case of a positive monotonic transformation, the MRS of both the utility functions remain the same.

In thie given case, MRS (A) = x2/x1

MRS(D) = x2/x1

Thus, D(x1,x2) is a positive monotonic transformation of A(x1,x2)

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