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However, there is no hard and fast definition as to what is classified as "long" or "short" and mostly relies on the economic perspective being taken. Marshall's original introduction of long-run and short-run economics reflected the 'long-period method' that was a common analysis used by classical political economists.
The maximum theorem provides conditions for the continuity of an optimized function and the set of its maximizers with respect to its parameters. The statement was first proven by Claude Berge in 1959. [1] The theorem is primarily used in mathematical economics and optimal control.
The law of diminishing returns is a fundamental principle of both micro and macro economics and it plays a central role in production theory. [ 5 ] The concept of diminishing returns can be explained by considering other theories such as the concept of exponential growth . [ 6 ]
Graphically, the iso-profit line must be tangent to the production function. [1] The vertical intercept of the iso-profit line measures the level of profit that Robinson Crusoe's firm will make. This level of profit, Π, has the ability to purchase Π dollars worth of coconuts. Since Price Coconuts is $1.00, Π number of coconuts can be purchased.
In statistics, ordinary least squares (OLS) is a type of linear least squares method for choosing the unknown parameters in a linear regression model (with fixed level-one [clarification needed] effects of a linear function of a set of explanatory variables) by the principle of least squares: minimizing the sum of the squares of the differences between the observed dependent variable (values ...
The theory entails that there is a limit to how much one factor can be substituted for another. When production reaches a point where substitution between the factors becomes impossible (MP LK), the isoquant becomes positively sloping. No rational entrepreneur will operate at a point outside the ridge lines (Region of Economic Nonsense). [1]
The definition of global minimum point also proceeds similarly. If the domain X is a metric space, then f is said to have a local (or relative) maximum point at the point x ∗, if there exists some ε > 0 such that f(x ∗) ≥ f(x) for all x in X within distance ε of x ∗.
A simple example of such a problem is to find the curve of shortest length connecting two points. If there are no constraints, the solution is a straight line between the points. However, if the curve is constrained to lie on a surface in space, then the solution is less obvious, and possibly many solutions may exist.