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Let be the state at time .For a decision that begins at time 0, we take as given the initial state .At any time, the set of possible actions depends on the current state; we express this as (), where a particular action represents particular values for one or more control variables, and () is the set of actions available to be taken at state .
The actuarial present value (APV) is the expected value of the present value of a contingent cash flow stream (i.e. a series of payments which may or may not be made). Actuarial present values are typically calculated for the benefit-payment or series of payments associated with life insurance and life annuities .
For proportional transaction costs the problem was solved by Davis and Norman in 1990. [6] It is one of the few cases of stochastic singular control where the solution is known. For a graphical representation, the amount invested in each of the two assets can be plotted on the x - and y -axes; three diagonal lines through the origin can be ...
As any universal Turing machine can do what any other Turing machine can, a central calculator in principle has no advantage over a system of dispersed calculators, i.e. a market, or vice versa. [25] In some economic models, finding an equilibrium is hard, and finding an Arrow–Debreu equilibrium is PPAD-complete. If the market can find an ...
Walras's law is a consequence of finite budgets. If a consumer spends more on good A then they must spend and therefore demand less of good B, reducing B's price. The sum of the values of excess demands across all markets must equal zero, whether or not the economy is in a general equilibrium.
Estimates for the value of a life are used to compare the life-saving and risk-reduction benefits of new policies, regulations, and projects against a variety of other factors, [2] often using a cost-benefit analysis. [3] Estimates for the statistical value of life are published and used in practice by various government agencies.
Assessing whether increased maintenance costs will economically change the useful life of an asset. [10] Calculating how much should be invested in an asset in order to achieve a desired result (i.e., purchasing a storage tank with a 20-year life, as opposed to one with a 5-year life, in order to achieve a similar EAC). [11]
an income effect: the purchasing power of a consumer increases as a result of a price decrease, so the consumer can now purchase other products or more of the same product, depending on whether the product(s) is a normal good or an inferior good. The Slutsky equation decomposes the change in demand for good i in response to a change in the ...