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- Key Takeaways A lump-sum distribution is an amount of money due that is paid all at once, as opposed to being paid in regular installments. Lump-sum distributions may be made from retirement plans, commissions earned, windfall earnings, or certain fixed-income investments. A lump-sum will typically be discounted to its net present value (NPV).
www.investopedia.com/terms/l/lumpsumdistribution.aspLump-Sum Distribution: What It is, How It Works - Investopedia
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一次总付 原则的结论表明：在增收 等额税收 的情况下，向个人所得增税留给消费者的效用比向单一商品增税留给消费者的效用更高，因为后者扭曲了消费者的 最优消费束 选择。. 但要注意到，一次总付原则的论证始终坚持除需要增税的商品外，其它商品价格不 ...
2021年10月4日 · I want to show mathematically that the lump sum principle does not apply to perfect complements. I was able to show it applied with a specific Cobb-Douglas utility function, but I am not sure how to show it does not apply with a perfect complements utility function: U(x, y) = Min{ax, by} U ( x, y) = M i n { a x, b y }
2020年10月9日 · Subscribed. 178. 8.9K views 3 years ago Microeconomic Theory 3: Utility Maximization and Expenditure Minimization. In this episode I introduce an important concept, known as Indirect Utility...
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Lump-sum principle Intertemporal consumption Suggested reading: Chapter 4 6. Demand Analysis (3 lectures) Income and substitution e⁄ect of price changes Demand elasticities Welfare analysis Suggested reading: Chapter 5, 6 7. Revealed Preference (2
- . Utility Maximization and Choice
- Chapter Utility Maximization and Choice
- An Initial Survey
- Budget constraint
- First-order conditions for a maximum
- Second-order conditions for a maximum
- Corner solutions
- = U (xÏ, x xn) ⋯
- First-order conditions
- ∂U~∂xj = pj
- MRS(xi for xj . ) = pj
- ∂U~∂xn
- Corner solutions
- L λpi a , then xi a ∂xi = ∂xi − < =
- Example .Ï Cobb-Douglas Demand Functions
- Numerical example. Suppose px Ï, py
- Ï = Example . CES Demand
- L ∂ ∂x L ∂ =
- y a .
- px
- y px a.
- U(x, y min (x, ) = y )
- + py
- Indirect Utility Function
- n x∗ =
- UÏ
- Case Ï: Cobb-Douglas.
- ae lump sum principle
- Case : Fixed proportions.
- I x∗
- I y∗
- Expenditure Minimization
- I V (px, py, I
- Properties of Expenditure Functions
- Engel’s law:
- E .Ï ae variability of budget shares
- E . Linear expenditure system
- U(x, y (x x α a (y y β a ) = − ) − )
- E .m CES utility
- = Ï K (px ~py
- E . ae almost ideal demand system (AIDS)
- + px +
- It can be shown that, for this function,
- c Vc a pcÏ
- + (E ~p )
. Income and Substitution Eòects E. Demand Relationships among Goods
Ming-Ching Luoh aa.Ï a. m. ais chapter examines the basic model of choice that economists use to explain individuals’ behavior. Individuals are assumed to behave as though they maximize utility subject to a budget constraint. To maximize utility, individuals will choose bundles of commodities for which the rate of trade-oò between any two goods (th...
Utility maximization: To maximize utility, given a ûxed ● amount of income to spend, an individual will buy those quantities of goods that exhaust his or her total income, and for which the psychic rate of trade-oò between any two goods (the MRS) is equal to the rate at which the goods can be traded one for the other in the marketplace.
Assume that the individual has I dollars to allocate between good x and good y. If px is the price of x and py is the price of y, then the individual is constrained by pxx I py y + ≤ ae slope of the constraint is px − py can be traded for x in the market. . ais slope shows how ● y Figure .Ï ae Individual’s Budget Constraints for Two Goods
Figure . A Graphical Demonstration of Utility Maximization ● C is a point of tangency between the budget constraint and the indiòerence curve. aerefore, at C we have slope of budget constraint px = − py = slope of indifference curve dy = dx WU=constant or px dy MRS x y py = − (of for dx W = U=constant )
ae tangency rule is necessary but not suõcient unless we assume that MRS is diminishing. If MRS is diminishing, then indiòerence curves are strictly convex. ae condition of tangency is both a necessary and suõcient condition for a maximum. If MRS is not diminishing, we must check second-order conditions to ensure that we are at a maximum. Figure .m...
Individuals may maximize utility by choosing to consume only one of the goods. At the optimal point, in Figure . , the budget constraint E, is atter than the indiòerence curve. ae rate at which x can be traded for y in the market is lower than the MRS. Figure . Corner Solution for Utility Maximization ae n-Good Case ae individual’s objective is to ...
subject to the budget constraint I pÏxÏ = + p x pnxn. + ⋯ + ae Lagrangian expression is U(xÏ, x , , xn) ++ λ (I − pÏxÏ − p x = ⋯ − ⋯ − pnxn)
First-order conditions for an interior maximum (n Ï + equations) ∂ L ∂xÏ ∂U λpÏ a = ∂xÏ − = ∂x L ∂ = ∂U λp a ∂x − = ∂ ⋯ L ∂xn ∂ L ∂λ ∂U λpn a = ∂xn − = = I pÏxÏ p x a − − − ⋯ − pnxn = Implications of ûrst-order conditions For any two goods, xi and xj, we have
It has been shown that the ratio of the marginal utilities of ● two goods along an indiòerence curve is equal to the marginal rate of substitution between them, the conditions for an optimal allocation of income become pi
ais is exactly the result derived earlier. Interpreting the Lagrange multiplier
= ⋯ = pn λ is the marginal utility of an extra dollar of consumption expenditure. Or, the marginal utility of “income." Another way to rewrite the necessary condition ● ∂U pi ~∂xi = λ for every i. At the margin, the price of a good represents the consumer’s evaluation of the utility of the last unit consumed. ae price of a goods also represents how...
When corner solutions arise, the ûrst-order conditions must ● be modiûed as ∂ ∂U L ∂xi = ∂xi − λpi≤ a (i Ï, = ⋯ , n , ) and if ∂ ∂U
ais means that ∂U pi ~∂xi . λ In other words, any goods whose price(pi) exceeds its marginal value to the consumer will not be purchased (xi a ). =
ae Cobb-Douglas utility function is given by ● U(x, y xα yβ ) = where, for simplicity, we assume α β Ï. + = ae Lagrangian expression ● xα yβ λ (I pxx py y L = + − − ) yields the ûrst-order conditios ∂x L ∂ = ∂y L ∂ = αxα−Ïyβ a − λpx = βxα yβ−Ï λpy a − = ∂λ L ∂ = I pxx a − py y − = Taking the ratio of the ûrst two terms shows that ● αy px βx = py or...
= = that α β a . , then = = , I Ê. Suppose also = x∗ = αI a . I a . Ê () , px = px = Ï = y∗ = βI a . I a . Ê () Ï, py = py = = and at these optimal choices, U = λ = x a . a. a . y = ( ) αxα−Ïyβ a . px = a. Ï , () = − a . Ïa . ( ) ( ) a.
aree speciûc examples of the CES function to illustrate ● cases in which budget shares are responsive to relative prices. Case Ï: δ= a . . In this case, σ Ï Ï δ = ~(− ) = , utility function is U(x, y x a . y a . ) = + Setting up the Lagrangian expression a . pxx py y a . y λ (I + − L = − ) yields the following ûrst-order conditions for a maximum:
∂y = a. a . x− λpx a , − = a . a . y− λpy a , − = ∂λ L ∂ = I − pxx py −
= Division of the ûrst two equations shows that y a .
x = py py y = pyx px py pxx = px py Substituting this into the budget constraint, we have pxx py y pxx pxx = px I py = and x∗ = px[ Ï I , y∗ (px~py)] = py[ Ï + (py~px)] ae share of income spent on good ● x depends on the price ratio px ~py. ae higher is the relative price of x, the smaller will be the share of income spent on x. Case : δ=-Ï. In t...
= x py Substituting into the budget constraints, we have pxx + py px a. x I py = x∗ = px py (px ~py a . ) I = px Ï (py ~px a . [ + ) ] x∗ = y∗ = px Ï [ (py ~px a . ) ] py Ï (px ~py a . [ + ) ] aese demand functions are less price responsive than the Cobb-Douglas function in two ways. ae share of income spent on good x, pxx ~I Ï Ï (py~px) a . ,...
A utility-maximizing person will choose only combinations of the two goods for which x = the budget constraint: y. Substituting this condition into pxx py y pxx py (px a . = + = + = + py)x. Hence
In this case, the share of a person’s budget devoted to good x ● rises rapidly as the price of x increases because x and y must be consumed in ûxed proportions. pxx∗ Ï
Examples .Ï and . illustrates that it is o en possible to manipulate ûrst-order conditions to solve for optimal values of xÏ, x , , xn. ⋯ aese optimal values in general will depend on the prices of all the goods and on the individual’s income. aat is, Ï x∗ = x∗ = ⋮
xÏ(pÏ, p , , pn, I , ⋯ ) x(pÏ, p , , pn, I , ⋯ ) xn(pÏ,p , , . ⋯ pn, I ) We can use the optimal values of the x’s to ûnd the indirect ● utility function. maximum utility = U[x∗ Ï (pÏ, , pn, I , x∗ (pÏ, , pn, I , , , ⋯ ) ⋯ ) x∗ n(pÏ, I ⋯ ⋯ pn, )] V = (pÏ, p , , pn, I . ⋯ ) ae indirect utility function is an example of a value ● function. ae optimal ...
> Example .m Indirect Utility and the Lump Sum Principle
where p is an index of prices deûned by ln p aa aÏ ln a ln a . bÏ ln = + Px py
where p is an index of prices deûned by ln p aa aÏ ln a ln a . bÏ ln = + Px py
where p is an index of prices deûned by ln p aa aÏ ln a ln a . bÏ ln = + Px py
where p is an index of prices deûned by ln p aa aÏ ln a ln a . bÏ ln = + Px py
where p is an index of prices deûned by ln p aa aÏ ln a ln a . bÏ ln = + Px py
where p is an index of prices deûned by ln p aa aÏ ln a ln a . bÏ ln = + Px py
where p is an index of prices deûned by ln p aa aÏ ln a ln a . bÏ ln = + Px py
where p is an index of prices deûned by ln p aa aÏ ln a ln a . bÏ ln = + Px py
where p is an index of prices deûned by ln p aa aÏ ln a ln a . bÏ ln = + Px py
where p is an index of prices deûned by ln p aa aÏ ln a ln a . bÏ ln = + Px py
where p is an index of prices deûned by ln p aa aÏ ln a ln a . bÏ ln = + Px py
where p is an index of prices deûned by ln p aa aÏ ln a ln a . bÏ ln = + Px py
where p is an index of prices deûned by ln p aa aÏ ln a ln a . bÏ ln = + Px py
where p is an index of prices deûned by ln p aa aÏ ln a ln a . bÏ ln = + Px py
where p is an index of prices deûned by ln p aa aÏ ln a ln a . bÏ ln = + Px py
where p is an index of prices deûned by ln p aa aÏ ln a ln a . bÏ ln = + Px py
where p is an index of prices deûned by ln p aa aÏ ln a ln a . bÏ ln = + Px py
where p is an index of prices deûned by ln p aa aÏ ln a ln a . bÏ ln = + Px py
where p is an index of prices deûned by ln p aa aÏ ln a ln a . bÏ ln = + Px py
A lump-sum tax is a special way of taxation, based on a fixed amount, rather than on the real circumstance of the taxed entity. [1] . In this, the entity cannot do anything to change their liability. [2] In contrast with a per unit tax, lump-sum tax does not increase in size as the output increases. [3] Description.
an amount of money that is paid in one large amount on one occasion. 一次性支付的金額，一整筆款項. Her divorce settlement included a lump sum of $2 million. 她的離婚協議包括一次性補償200萬美元。 (lump sum在劍橋英語-中文（繁體）詞典的翻譯 © Cambridge University Press) lump sum的 例句.
