让数学走进生活——以《税率》教学为例

如何让数学网络教学真正有实效呢?笔者以教学《税率》一课谈谈体会。调动内需,主动请教。在教学《税率》的过程中,笔者首先放手请学生自学,让他们初步了解纳税的意义,知道税收的用途、应纳税额和税率的含义。通过自学,学生初步明白了"应纳税额÷各种收入=税率",但被销售额、营业额等名词绕晕了头,随后出现的已知税率和应纳税额求各种收入的问题、已知税率和各种收入求应纳税额的问题、商店营业额超过一定数额才交税的问题等,更让学生晕头转向。

China＇s Real Estate Tax Reform： Past, Present and Future

Since 1978, China＇s reform of real estate tax has made great strides with important milestones marked by the resumption of real estate tax collection on Chinese- funded enterprises and Chinese nationals. In the llth Five-Year Plan period （2006-2010）, the state administration completed the unification of tax rates for domestic and foreign- funded companies. However, the reform of real estate tax still requires many modifications during the 12th Five-Year Plan period （2011-2015）. The new plan should strive to streamline the tax system, adjust the tax base and tax rates, and delegate taxing authority.

A simplified differential game model for the optimal choice of tax rate

A classical problem on optimal choice of tax rate from the perspective of differential game approach is studied. Under some appropriate assumptions on the profit and utility functions, the open-loop Stackelberg equilibrium solution which is time- dependent is obtained. Result shows that 1) the optimal strategies derived from differential game and traditional unilateral optimal control approaches are different; 2) both marginal profit rate and the market rate of interest have great effect on the equilibrium solution; and 3) the government should think about the firm’s potential reaction when selecting tax rates and the timing of taxation.

Consequences of Tax Rate Decrease in Polish Tax System

After a transition from the central planning into a market economy, Poland was compelled to implement a new tax system. It was based on income taxes and turnover （especially value added） taxes. Primarily income taxes had high tax rates. In corporate tax the rate was proportional and at the beginning amounted to 40%. For natural persons the taxation had a progressive tendency. The tax rates amounted to 21%, 33% and 45% respectively with very low limits of income, which resulted in changing the rate. Since the beginning of 1991 and 1992 till now the tax rates have been decreased significantly. Now the tax rates amount to 18% and 32% respectively with high level of income, which results in changing the rate. The question arises whether such changes were really effective for the central budget. The article formulates and verifies a hypothesis assuming that lowering the rates was justified by the contemporary ＂fashion＂ rather than economic reasons. According to financial aspects, the impact of lower rates on the central budged will be examined.

China's Rising Labor Cost: Myths and Realities

This paper examines whether China＇s labor cost is too high and rising too fast from the five aspects of macro distribution, corporate cost structure, labor productivity, labor cost structure and international comparison, shedding light on the real causes of rising labor cost. On the basis of our analysis, we propose a few policy recommendations on China＇s macroeconomy and corporate development.

Substitution Marginal Rate and Its Usage in the Marginal Preference Calculation

The slope of indifference curve is known as a marginal rate of substitution （MRS）. MRS defining ratio always describes slope of indifferent curve, i.e. MRS matches the module of indifferent curves slope. Utility function U（Xl,X2） is used to calculate marginal rate of substitution （MRS）, because MRS gives the slope of appropriate indifference curve, it can be interpreted as a norm, in which costumer is ready to substitute good 1 by small amount of good 2. The word ＂marginal＂ in economic means ＂differential＂. Here we have partial differentiation, because in time of calculation of good l＇s marginal utility the amount of good 2 remains the same. We can calculate MRS in two ways using differential and function. In the first case consider change （akl,ak2） during which utility is unchanged. For the second method let the curve of indifference present by x2 （X1） function. The function shows how many of x2 is needed for each unit of xl to stay on this concrete curve of indifference. We obtain two equations for the term of MRS and budget constraint and two xl and x2 variables. To define the optimal choice of x1 and x2 as a function of the price and income, we need to solve those two equations. The problem of maximization can be solved by using differential.

Relationship Among Reserve Ratio, Government Spending and Economic Growth

The relationship among reserve ration, government spending and economic growth was analyzed. A monetary endogenous growth model is well developed by taking into account the growth-enhancing effects of re- serve-augmenting seigniorage. If the government spends all the seigniorage revenue on the provision of a public input which has positive externality on the private sector’s production, some results to be utterly different from Bronx’s have been obtained: the economy has a unique saddle-balanced growth path, but it has nothing to do with reserve ratio. However, the higher reserve ratio, the faster speed of economic convergence.

Tax system＇s effect on income regulating distribution

Problems caused by the income distribution gap arises widespread attention in current theorists, sector and folk. Requiring adjustment of income distribution gap is growing from various aspects and this article attempts to investigate theoretical level of influence in government regulating income distribution gap, mainly involving the government and the blur, efficiency loss in market boundaries, the deficit effects and other aspects of government failure. We strive to prevent the possible deviations of goverrmaent in the implementation of the regulation, expect to deepen understanding and promote the practice for some benefit.

Choice and Simulation of Tax Rates in Resource Tax Reform

Resource tax reform will be done during China＇s 12m Five-Year Plan, but related research is still lacking. Here, we build a computable general equilibrium model （CGE） comprising the functional equations of production, consumption, income/expenditure and resources to analyze the resource tax rate. The model uses the valorem tax levy to simulate the impact of economic and resource systems with different resource tax rates, by referencing the expected rate ranges of China and developed countries. The results show that the impact is different for social, economic and resources of varying degrees. In the relatively stable period of economic development, we can select a tax rate of 5% to 7%; during higher economic development we can select an optional high level of resource tax; and in a fluctuating economy we can choose a lower tax level.

A STACKELBERG DIFFERENTIAL GAMES SOLUTION TO A PROBLEM OF OPTIMAL INTERTEMPORAL INVESTMENT AND TAX RATE DESIGN

Using the Stackelberg differential games(SDG) theory,we quantitatively study a problem of optimal intertemporal investment and tax rate design.Under some appropriate assumptions,the open-loop Stackelberg equilibrium solutions are obtained.Equilibrium solutions show that:1.The optimal strategies derived from differential game and unilateral optimal control approaches are different;2.It is not always the best strategy for the government to use a constant tax rate over the whole time period;3.The admissible size of tax rate adjustment may have great effect on the government's optimal strategy;4.SDG approach has no significant effect on the firm's optimal investment strategy.

Predicted Modulated Differential Rates for Direct WIMP Searches at Low Energy Transfers

The differential event rate for direct detection of dark matter,both the time averaged and the modulated one due to the motion of the Earth,are discussed.The calculations focus on relatively light cold dark matter candidates (WIMP) and low energy transfers.It is shown that for sufficiently light WIMPs the extraction of relatively large nucleon cross sections is possible.Furthermore for some WIMP masses the modulation amplitude may change sign,meaning that,in such a case,the maximum rate may occur six months later than naively expected.This effect can be exploited to yield information about the mass of the dark matter candidate,if and when the observation of the modulation of the event rate is established.

Heavy tails of a Lévy process and its maximum over a random time interval

Let {Xt,t ≥ 0} be a Levy process with Levy measure v on （-∞,∞）, and let τ be a nonnegative random variable independent of {Xt,t ≥ 0}. We are interested in the tail probabilities of Xτ and X（τ） = sup0≤t≤τ Xt. For various cases, under the assumption that either the Levy measure v or the random variable T has a heavy right tail we prove that both Pr（XT 〉 x） and Pr（X（τ） 〉 x） are asymptotic to ETv（（x, ∞）） ＋ Pτ（τ 〉 x/（0 V EX1）） as x → ∞, where Pr（τ 〉 x/x） = 0 by convention.