Question

Cobb-Douglas Preferences: Cobb-Douglas preferences on the consump-

tion set R2+ can be represented by a utility function of the form U (q1,q2) = Aq1αq2β,

where A > 0, α ∈ (0,1), and β ∈ (0,1) are fixed parameters.

1. If we assume that preferences are ordinal, explain why these precise

preferences are also represented by the utility function U(q ,q )=qγq1−γ,

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whereγ= α .Isγ∈(0,1)? (α+β)

2. If we assume that preferences are ordinal and restrict attention to the consumption set R2++, explain why these precise preferences are also represented by the utility function

U (q1, q2) = γ ln (q1) + (1 − γ) ln (q2) .

Why did we need to restrict the consumption set to R2++ for this part

of this question?

Answer 1