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Unformatted text preview: the Envelope Theorem, ∂π/∂α = pq * ( p,α ). But since π is convex in α , ∂π/∂α is nondecreasing in α . And since p > 0, q * ( p,α ) cannot decrease in α . (If π is C 2 , we have ≤ ∂ 2 π/∂α 2 = p∂q * ( p,α ) /∂α so that ∂q * ( p,α ) /∂α ≥ 0.) f ( x 1 , t ) f ( x 2 , t ) V ( t ) t V , f The Maximum of a Collection of Convex Functions is Convex V ( t ) = max x ∈ { x 1 , x 2 } f ( x , t )...
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 Spring '10
 schlee
 Microeconomics, Monotonic function, Convex function, α, ·

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