Explain the marginal rate of substitution and the reasons for its decreasing

What is the marginal rate of substitutionThe substitution rate is that when you add one unit of a certain good, you have to give up the quantity of another good.

In general, because there are more commodities, the increment of human satisfaction decreases for each additional unit.

Here's a mathematical reasoningFor example, if the quantity of commodity A increases by 100 as the quantity of commodity A goes from 0 to 1, and as the quantity of commodity A increases from 99 to 100, the satisfaction may only increase by 1, and the satisfaction function fa(x) of commodity A is an increasing function.

f a(x) is a decreasing function.

and f a(x) 0

The same goes for existing product B

fb(y) is an increasing function, and fb(y) is a subtraction function, and the existing combination of a and b commodities is a subtraction.

In the case of c, c is a constant, and c=fa(x)+fb(y) is the substitution of a for b in the same case of satisfaction.

fb（y）=cfa（x）fb′(y)=fa (x) 0 because fb(y) is a monotonic function.

So its inverse function y=f -1(y) (I don't know how to play by the computer) monotonicity.

Same. Since fb (y) = -fa (x) 0, y = f( -1) (y) 0

So the marginal rate of substitution of A for B decreases.

Math pushes to this, typing is too annoying, so click to the point to ask us.

The law of diminishing marginal substitution rate of commodities refers to the gradual decrease in the consumption of another commodity that consumers are willing to give up while increasing the consumption of one unit of the commodity under the condition of keeping the utility level unchanged, that is, with the increase of the quantity of one commodity, the marginal substitution rate of another commodity decreases.

The marginal rate of substitution of a good reflects the quantity of another good that consumers are willing to give up in order to get one unit of a good at the same level of utility, that is, the relative valuation of the degree of consumer preference for the two goods. However, as the consumption of a good increases or decreases, its scarcity changes, and the consumer's preference for an additional unit of the good also changes, so the marginal substitution rate of the good is related to the consumption of the two goods consumed by the consumer. Moreover, as the consumption of one commodity increases, the marginal substitution rate of that commodity for another commodity becomes smaller and smaller.

This characteristic is summarized as the law of diminishing marginal substitution rate.

It can be seen that the existence of the law of diminishing marginal substitution rate is due to the law of diminishing marginal utility. This is essentially the root cause of the typical indifference curve convex to the origin.

The marginal rate of substitution (MRS) refers to the amount of consumption of another good that consumers need to give up to increase the consumption of one unit of a certain article under the premise that two goods can be replaced at a certain rate (i.e., on the same indifference curve) under the premise of maintaining the same degree of satisfaction (i.e., on the same indifference curve). The marginal substitution rate can be graphically represented by the slope of the line connecting two points on an indifference curve.

Reasons for decline: As the quantity of a good consumed gradually increases, the consumer's desire to get more of that good decreases, so that he is willing to give up less and less of another good in order to get an extra unit of this good.

Mainly because of the law of diminishing marginal returns.

is working. Production technology for any kind of product.

All require an appropriate proportion of inputs between the elements, suggesting that substitution between elements is limited. To put it simply, taking the input of labor and capital as an example, in the case of a small amount of labor input and a large amount of capital input, it is easy to reduce some of the capital input by increasing the amount of labor input to maintain the original level of output, that is, it is very easy for labor to replace capital, but it will be very difficult to use labor to replace capital with labor when the amount of labor input increases to a considerable amount and the amount of capital input decreases to a very small amount. On the same isoproduction line, the marginal output of labor as labor continues to replace capital.

It will gradually decrease, while the marginal output of capital will gradually increase.

Extended data: Under the condition of constant output, in the substitution process of increasing labor input and decreasing capital input, the law of diminishing marginal technology substitution rate is decreasing. The isoyield curve generally has the characteristics of convex origin, which is determined by the law of diminishing marginal technology substitution rate.

Because, from the definition formula of the marginal technology substitution rate, it can be seen that the marginal technology substitution rate at a certain point on the equal yield curve is the absolute value of the slope of the equal yield curve at that point.

And since the marginal technology substitution rate is decreasing, the absolute value of the slope of the isoyield curve is decreasing, that is, the isoyield curve is convex to the origin.

The law of diminishing marginal technology substitution rate is: under the condition of keeping the output unchanged, with the production factors.

With the increase of quantity, the number of other elements replaced by each unit of the element gradually decreases, that is, the marginal technical substitution rate of one element for another element decreases with the increase of this element. The reason for the diminishing rate of marginal technological substitution is that, as the amount of labor input increases, the marginal output increased by each additional unit of labor becomes smaller and smaller, and the amount of capital it replaces becomes smaller and smaller; At the same time, as labor substitutes, the amount of capital input becomes smaller and smaller, and its marginal output becomes larger and larger, so that it is less likely to be replaced by labor.

Therefore, the marginal rate of technological substitution of labor for capital decreases with the increase in the amount of labor input.

Ahem: Should you be a big baby?

The law of diminishing marginal returns.

It refers to the addition of a certain factor of production in the short-term production process, under the premise that the implicit conditions for dismantling remain unchanged (such as the technical level remains unchanged).

When the input quantity of the factor of production increases to a certain extent, the increase in output brought about by the increase of one unit of the factor is decreasing, and the law of diminishing marginal returns is conditional on the fact that the level of technology and the input quantity of other factors of production remain unchanged. In addition, the marginal output is only when the variable input is increased to a certain extent.

before decreasing. Law of diminishing marginal utility.

It refers to a decreasing trend in a certain period of time, under the condition that the consumption of other goods remains unchanged, as people's consumption of a certain commodity (or service) increases, the increase in the degree of satisfaction obtained from the unit increment of consumption of the commodity (or service) shows a decreasing trend.

From the explanation of the two laws, I think the most obvious connection is that the two laws are reacting, and under one condition, quantitative change will cause qualitative change. Moreover, from a certain point of view, the law of diminishing marginal efficiency of jujube can be regarded as a special case of diminishing marginal returns. If the income obtained from the consumption of goods is regarded as an input-output, then the law of diminishing marginal utility can be rationalized in this way: when your input (i.e., total consumption) is increasing and other conditions remain unchanged, when your input exceeds a critical value, your output is marginally decreasing (that is, the utility of goods is diminishing).

The diminishing marginal rate of substitution of technology is based on the law of diminishing marginal returns.

Diminishing marginal returns are properties of a short-term production function or a production function of a variable factor of production; The diminishing marginal rate of technological substitution reflects the nature of the production function of the two variable factors of production.

The law of diminishing marginal technological substitution rate refers to the decreasing rate of marginal technological substitution, when the input of one factor of production is constantly increasing, the quantity of another factor of production that can be replaced by each unit of this factor of production decreases, that is, the marginal technological substitution rate of one factor to another factor decreases with the increase of this factor. The main reason for the diminishing marginal rate of technological substitution is that the production technology of any kind of product requires an appropriate proportion of factor inputs, which makes the substitution between factors limited.

The law of diminishing marginal returns refers to the fact that, under the condition that the technical level remains unchanged, in the process of continuously increasing a variable factor of production to one or several other factors of production with the same quantity, when the input of such variable factors of production is less than a certain value, the marginal output brought about by increasing the input of the factor of production is incremental, and when the input of such variable factors increases continuously and by the same amount exceeds this specific value, the marginal output brought about by increasing the input of the factor is decreasing. The reason for the establishment of the law of diminishing marginal returns is that for the short-term production of any product, there is an optimal quantitative combination between variable factor input and fixed factor input, and with the gradual increase of variable factor input, the amount of production factor input gradually approaches the optimal combination ratio, and the corresponding marginal output of variable factor shows an increasing trend. Once the input of production factors reaches the optimal combination ratio, the marginal output of variable factors reaches the maximum.

After this, as the input of variable factors continues to increase, the input of production factors deviates more and more from the optimal combination ratio, and the marginal output of the corresponding variable factors shows a decreasing trend.