# 经济代写|Microeconomics代考微观经济学代写|ECON110

#### Doug I. Jones

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## 经济代写|Microeconomics代考微观经济学代写|The Indirect Factor Substitution Mechanism

What difference does it make to introduce consumer choice into the analysis? If as done up to here-one assumes no savings, only one product, and a rigid supply both of labour and of land, consumer choice has no role in the determination of equilibrium, nor in the arguments supporting a tendency toward it. The gravitation toward equilibrium relies only on technical substitutability.

Consumer choice among different consumption goods is important in the marginal approach because it is argued to entail a reason, for decreasing demand curves for factors, alternative or additional to technical substitutability among factors. It activates-the argument goes-an indirect factor substitution mechanism which can generate decreasing demand curves for factors even in the absence of technical substitutability, or adds its action to that of technical substitutability making demand for a factor more sensitive to changes of its rental, which increases the plausibility of the theory as will be explained in the next section.
Being based on consumer choice this mechanism needs at least two consumption goods. So let us assume that there are two consumption goods, corn (good 1) and meat (good 2), produced by labour and land in separate industries. In order to examine the working of this factor substitution mechanism in isolation, assume zero technical factor substitutability: in the production of each good only one method of production is known, characterized by given technical coefficients and therefore by a fixed $L T$ ratio, that differs as between the two industries. Let these technical coefficients be $a_{L 1}, a_{T 1}$ in the corn industry and $a_{L 2}, a_{T 2}$ in the meat industry. Assume $a_{L 1} / a_{T 1}>a_{L 2} / a_{T 2}$, i.e. the corn industry employs more labour per unit of land than the meat industry: corn is the more labour-intensive good.

## 经济代写|Microeconomics代考微观经济学代写|The Simultaneous Operation of Both Substitution

I have examined the direct factor substitution mechanism and the indirect factor substitution mechanism separately so as to highlight their functioning as clearly as possible. But generally, the marginal approach argues, in a real economy both factor substitution mechanisms will be simultaneously at work. Their joint operation renders the aggregate demand for each factor more responsive to changes in its rental than if only one mechanism was active; in the economic jargon, each factor demand curve is more elastic.

The notion of elasticity of a function is a useful one in economics, and so I dedicate some space now to introducing it for newcomers to economics.

Let $y=f(x)$ be a continuous function of one variable. If $x$ changes from $x^{\prime}$ to $x^{\prime \prime}=x^{\prime}+\Delta x$, then $y$ changes from $y^{\prime}=f\left(x^{\prime}\right)$ to $y^{\prime \prime}=f\left(x^{\prime \prime}\right)=y^{\prime}+\Delta y$. The interval elasticity of $f(x)$ is defined as the proportional (or percentage) variation of $y$ divided by the proportional or percentage variation of $x$ that causes it, i.e.
$\frac{\Delta y / y}{\Delta x / x}$, sometimes represented as $\frac{\% \Delta y}{\% \Delta x}$.
If $f(x)$ is differentiable and we consider smaller and smaller variations of $x$, tending in the limit to an infinitesimal variation $d x$, the variation of $y$ tends to $d y=f^{\prime}(x) \cdot d x$, and the value of the interval elasticity tends in the limit to the point elasticity which is, for differentiable functions, what economists intend by elasticity:
$$\varepsilon=(d y / y) /(d x / x)=(d y / d x) \cdot x / y=f^{\prime}(x) \cdot x / f(x) .$$
In intuitive approximate terms, the elasticity measures the percentage variation of the dependent variable $y=f(x)$ caused by a $1 \%$ increase in the independent variable $x$. An elasticity greater than 1 in absolute value tells us that $y$ varies percentwise more than $x$. When both $x$ and $y$ are positive-the usual case in economics-the sign of the elasticity is the same as the sign of $d y / d x$, so an elasticity equal to $-2$ tells us that $y$ decreases by $2 \%$ if $x$ increases by $1 \% .^{21}$ The elasticity of a decreasing demand function is a negative number, but careful!, most economists have come into the habit of calling elasticity of a demand function the absolute value of this negative elasticity; so when an economist says that a demand function has elasticity 1 , he means that a $1 \%$ increase in price causes a $1 \%$ decrease in demand, and when he says a demand function has become more elastic, he means the absolute value of that elasticity has increased.

# 微观经济学代考

## 经济代写|Microeconomics代考微观经济学代写|The Simultaneous Operation of Both Substitution

$$\varepsilon=(d y / y) /(d x / x)=(d y / d x) \cdot x / y=f^{\prime}(x) \cdot x / f(x) .$$

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