Parameter Constraints and the Concavity of v(t) = βt^α
For the function to represent convex preferences, it must be concave in . This is confirmed by checking its second derivative, . This derivative is negative because while , , and are all positive, the term is negative due to the constraint $0 < \alpha < 1$. The product of positive terms and one negative term results in a negative value, proving the function's concavity.
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Learn After
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