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## 经济代写|Economics代考微观经济学代写|The Standard Commodity as the ‘average’ Commodity Marx Was Looking For

When explaining the reasoning that brought Marx to conclude that $r=S /(C+V)$ in labour values, I argued that he was looking for a commodity of ‘average’ organic composition, for which there was no need to change its price relative to the value of its means of production when passing from prices proportional to labour values to prices associated with a uniform rate of profit. For such a commodity, the rate of profit would be correctly determined even when evaluating its product and its advanced capital at labour values. Marx was wrong in believing that the social product was such a commodity; but such a commodity does exist. It was discovered by Sraffa, and it is called the Standard commodity.

Here its illustration will be limited to the two-goods corn-iron economy, a more complete treatment will be offered in Chap. 2. Assume advanced wages, and define subsistence-inclusive technical coefficients $c_{i j}$ ( $i$ input, $j$ output) as follows: if the average real wage rate physically specified consists of the vector $\left(z_{1}\right.$, $\left.z_{2}\right)$, then
$$c_{i j} \equiv a_{i j}+z_{i} a_{L j,}, \quad i, j=1,2 .$$
For example, if to produce one unit of corn (good 1 ) one needs $0.2$ units of corn as seed, $0.1$ units of iron and $0.8$ units of labour, and if the real wage rate consists of $0.5$ units of corn and $0.2$ units of iron, then $c_{11}=0.2+0.5 \cdot 0.8=0.6$, and $c_{21}=0.1+0.2 \cdot 0.8=0.26$. Of course, for the economy to be able to produce a surplus, it must be $c_{11}<1$ and $c_{22}<1$.

Then the price equations can be written without any explicit appearance of labour quantities, by using the technical coefficients $c_{i j}$. The reader can easily check that Eqs. (1.2)-(1.3), once the real wage is specified by Eq. (1.4), are equivalent to the following ones:
\begin{aligned} &p_{1}=(1+r)\left(c_{11} p_{1}+c_{21} p_{2}\right) \ &p_{2}=(1+r)\left(c_{12} p_{1}+c_{22} p_{2}\right) \end{aligned}
The solution of these price equations is independent of the dimensions of industries as long as technical coefficients remain unaltered. I et us then imagine, $\mathrm{~ a ̀ s ~ a ̈ ~ m e e n ̃ a ̄ l ~ e x ̄ p e r r i n ̄ e n n t , ~ t o ̄ ~ a ̄ l t e ̄ r ~ t h e ̄ ~ r e ̈ l a ̄ t i v e e ~ đ i m}$ such a way as to reach the proportions necessary for maximum potential growth of both industries at a common rate. To such an end, with $x_{1}$ the quantity produced of corn and $x_{2}$ the quantity produced of iron, define the rate of physical surplus of commodity $i=1,2$ as
$$\sigma_{i} \equiv\left(x_{i}-\left(c_{i 1} x_{1}+c_{i 2} x_{2}\right)\right) /\left(c_{i 1} x_{1}+c_{i 2} x_{2}\right) .$$

## 经济代写|Economics代考微观经济学代写|Quantities

Differently from Ricardo, Marx did not accept Say’s $L a w$, the thesis that aggregate demand is never inferior to aggregate supply, nor was he alone in so doing among the classical economists.

The impossibility of ‘general gluts’, i.e. of generalized overproduction of commodities relative to demand, was strongly argued by Jean-Baptiste Say, a French economist contemporary of Ricardo, hence the name. Say was mainly concerned with denying that a continuous growth of production would hit against the limits of a given demand for commodities; he argued that one half of the social product necessarily buys the other half, clearly meaning by this that production produces the incomes which are then spent to buy the produced goods, so more production increases purchasing power in step with the increase in production; he concluded that there can be a glut in the markets of particular commodities if the composition of production is not well adapted to the composition of demand, but not an overall lack of purchasing power. Ricardo accepted Say’s argument but reformulated it in a clearer way. On the basis of Adam Smith’s argument that nobody will be so fool as to leave some of his income idle when he can employ it for a positive return, he stated that the value of production is distributed as gross income, and what of this income is not spent on consumption is, directly or indirectly (by lending it to others), invested in production; thus saving decisions are investment decisions, and aggregate expenditure is necessarily equal to the aggregate value of production because equal to aggregate gross incomes. Therefore except in cases of extreme perturbation of economic activity (such as the sudden cessation of a big war, which requires an enormous reorientation of economic activity; or a crazy decree suddenly suspending all banking operations), according to Ricardo general overproduction is impossible: there can only be overproduction in some industries, to which there will correspond underproduction in other industries.

The Ricardian theory of growth deriving from Say’s Law is simple: capital accumulation does not meet obstacles from the demand side; the aggregate level of production is tendentially the one associated with the normal utilization of the existing productive capacity created by earlier accumulation; what is not consumed is invested. ${ }^{64}$ Savings originate nearly exclusively from profits, because the workers are too poor to save, and the landlords are spendthrifts. Thus the share of savings in aggregate income depends on the share of profits: a higher profit rate entails a higher growth rate. If accumulation entails the extension of cultivation to less and less fertile land, since wages cannot fall below subsistence, the rate of profit will slowly decrease. Ricardo concludes that the rate of profit will tend to rise, remain constant or decline secularly, depending on whether its tendential decrease will be more than compensated, just compensated, or less than compensated, by the increase in the productivity of labour in agriculture due to technical progress.

## 经济代写|Economics代考微观经济学代写|The Standard Commodity as the ‘average’ Commodity Marx Was Looking For

$$c_{i j} \equiv a_{i j}+z_{i} a_{L j,}, \quad i, j=1,2 .$$

$$p_{1}=(1+r)\left(c_{11} p_{1}+c_{21} p_{2}\right) \quad p_{2}=(1+r)\left(c_{12} p_{1}+c_{22} p_{2}\right)$$

às ä meeñāl ex̄perrinennt, tō āltēr thē rëlātivee Dim以达到两个行业以共同速度实现最大潜在增长所需的比例。为此，与 $x_{1}$ 玉米的 产量和 $x_{2}$ 铁的生产量，定义商品的实物剩余率 $i=1,2$ 作为
$$\sigma_{i} \equiv\left(x_{i}-\left(c_{i 1} x_{1}+c_{i 2} x_{2}\right)\right) /\left(c_{i 1} x_{1}+c_{i 2} x_{2}\right)$$

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MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。

assignmentutor™您的专属作业导师
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