In mathematical economics, Topkis's theorem is a result that is useful for establishing comparative statics. The theorem allows researchers to understand how the optimal value for a choice variable changes when a feature of the environment changes. The result states that if f is supermodular in (x,θ), and D is a lattice, then is nondecreasing in θ. The result is especially helpful for establishing comparative static results when the objective function is not differentiable.
Read more about Topkis's Theorem: An Example, Notes and References
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“To insure the adoration of a theorem for any length of time, faith is not enough, a police force is needed as well.”
—Albert Camus (1913–1960)