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Convexity is a geometric property with a variety of applications in economics. [1] Informally, an economic phenomenon is convex when "intermediates (or combinations) are better than extremes". For example, an economic agent with convex preferences prefers combinations of goods over having a lot of any one sort of good; this represents a kind of ...
This equation is a rearrangement of the definition of velocity: :=. As such, without the introduction of any assumptions, it is a tautology . The quantity theory of money adds assumptions about the money supply, the price level, and the effect of interest rates on velocity to create a theory about the causes of inflation and the effects of ...
In economics the production set is a construct representing the possible inputs and outputs to a production process. A production vector represents a process as a vector containing an entry for every commodity in the economy. Outputs are represented by positive entries giving the quantities produced and inputs by negative entries giving the ...
Theorem — Let be a positive integer. If : {: =,, >} is a set-valued function with closed graph that satisfies Walras's law, then there exists an economy with households indexed by , with no producers ("pure exchange economy"), and household endowments {} such that each household satisfies all assumptions in the "Assumptions" section except the "strict convexity" assumption, and is the excess ...
Mathematical economics is the application of mathematical methods to represent theories and analyze problems in economics.Often, these applied methods are beyond simple geometry, and may include differential and integral calculus, difference and differential equations, matrix algebra, mathematical programming, or other computational methods.
This is a corner solution as the highest possible IC (IC 2) intersects the budget line at one of the intercepts (x-intercept). [1] In mathematics and economics, a corner solution is a special solution to an agent's maximization problem in which the quantity of one of the arguments in the maximized function is zero. In non-technical terms, a ...
In mathematical economics, the Arrow–Debreu model is a theoretical general equilibrium model. It posits that under certain economic assumptions (convex preferences, perfect competition, and demand independence), there must be a set of prices such that aggregate supplies will equal aggregate demands for every commodity in the economy.
The equation demonstrates that the change in the demand for a good caused by a price change is the result of two effects: a substitution effect : when the price of a good change, as it becomes relatively cheaper, consumer consumption could hypothetically remain unchanged.