A consumer has monotonically increasing preferences. Her utility function is u(x), where x is a vector of consumed quantities of several goods (n goods in total). Utility levels may be positive or negative. For each of the following cases, determine whether the transformation of the utility function represents the same preferences as the function u. In what follows, the parameters a, b and c are all strictly positive. a) f(x) = a u(x) + b [u(x)]^2 . b) f(x) = a u(x) - b [u(x)]^2 . c) f(x) = u(x) + ?_{i=1}^2 x_i . d) f(x) = [u(x)]^2 + b u(x) + c.
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The reason is that the term b [u(x)]^2 introduces a non-linearity into the utility function. This means that the consumer's marginal rate of substitution between any two goods (the rate at which she is willing to give up one good to get more of another while Show more…
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