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Envelope theorem. In mathematics and economics, the envelope theorem is a major result about the differentiability properties of the value function of a parameterized optimization problem. [1] As we change parameters of the objective, the envelope theorem shows that, in a certain sense, changes in the optimizer of the objective do not ...
Hotelling's lemma is a result in microeconomics that relates the supply of a good to the maximum profit of the producer. It was first shown by Harold Hotelling, and is widely used in the theory of the firm. Specifically, it states: The rate of an increase in maximized profits with respect to a price increase is equal to the net supply of the good.
Roy's identity (named after French economist René Roy) is a major result in microeconomics having applications in consumer choice and the theory of the firm. The lemma relates the ordinary (Marshallian) demand function to the derivatives of the indirect utility function. Specifically, denoting the indirect utility function as the Marshallian ...
Auction theory is a branch of applied economics that deals with how bidders act in auctions and researches how the features of auctions incentivise predictable outcomes. Auction theory is a tool used to inform the design of real-world auctions. Sellers use auction theory to raise higher revenues while allowing buyers to procure at a lower cost.
Shephard's lemma is a major result in microeconomics having applications in the theory of the firm and in consumer choice. [1] The lemma states that if indifference curves of the expenditure or cost function are convex, then the cost minimizing point of a given good ( ) with price is unique. The idea is that a consumer will buy a unique ideal ...
His 1979 paper, "On the Differentiability of the Value Function in Dynamic Economic Models," (co-authored its José Scheinkman) provided the foundation for dynamic programming in Economics. The paper used the envelope theorem to prove that the value function is differentiable when the objective is concave and differentiable.
F. Factor price equalization. Fisher separation theorem. Frisch–Waugh–Lovell theorem. Fundamental theorems of welfare economics.
Comparative statics is commonly used to study changes in supply and demand when analyzing a single market, and to study changes in monetary or fiscal policy when analyzing the whole economy. Comparative statics is a tool of analysis in microeconomics (including general equilibrium analysis) and macroeconomics.