Solve the optimal combination of factors of production in economics

Derivative of mp)l=q = 20-12l (with k as a constant), the same is true (mp)k = 50-4k (with l as a constant).

Establish the equation: 660 = 15l + 30k, (20-12l) 15 = (50-4k) 30

solution, l = 3 k = 41 2 =

The formulas of these two equations can be reasoned by yourself according to the above listed, I will not fight, I hope it can help you.

In the actual production and operation decision-making, the optimal combination of factors is specifically manifested in the following two situations:

First, under the condition of a given cost, the combination of factors with the largest output (technical efficiency of production); The second is the combination of factors with the lowest cost (economic efficiency of production) under the given conditions of output.

The analysis of this optimal combination is very similar to the analysis of consumer equilibrium. We first get a set of production isoyield lines (combinations of different production factors for the same output); Then, through the manufacturer's cost equation, the equivalent cost line, that is, the production budget constraint line, is obtained.

At the tangent of the equicost line and the isoyield line, the equilibrium point of production is obtained, and the combination of factors at this point is called the optimal factor production factor combination, which refers to the combination of factors that maximize the output under the condition of a given cost, or the combination of factors that minimize the cost under the condition of a given output.

The conditions that can satisfy the optimal combination of factor inputs are:

The optimal combination of factor inputs occurs at the tangent of the isoyield curve and the isocost line, that is, the tangent of the isoyield curve is required.

The slope is equal to the slope of the isocost line.

One. The combination of factors with the largest output when the cost is given The equivalent output curve of the enterprise and the corresponding equivalent cost line are drawn in the same plane coordinate system.

, it is possible to determine the optimal combination of factors for the enterprise to achieve maximum output at a given cost. When the isoyield curve and the isocost line are tangent, the tangent point is allocated.

That is, the average cultivation and balance point of production.

Two. The combination of factors with the lowest cost when the output is given If the producer strives for the lowest cost under the given output conditions, then how should the optimal combination of labor input and capital input be chosen? Similarly, by drawing the equivalent output curve and the corresponding equivalent cost line in the same plane coordinate system, we can determine the optimal combination point of the factors at which the enterprise achieves the minimum cost under the given output, that is, the producer equilibrium point.

1. The optimal conditions for maximizing the output at a given cost:

Since the marginal technology substitution rate reflects the substitution ratio of the two factors in production, and the proportion of the factors reflects the substitution ratio of the two factors in the purchase, as long as the two are not equal, the manufacturer can always increase the total output by re-selecting the combination of factors under the condition of constant cost.

At the equilibrium point of production, there is: mrtslk=w r.It indicates:

In order to achieve the maximum output under the given cost conditions, the manufacturer must choose the optimal combination of production factors, so that the marginal technology substitution rate of the two factors is equal to the proportion of the two factors. This is the principle of optimal combination of the two factors of production.

Therefore, the above equation can be written as: mrtslk=mpl mpk=w r, and further can be: mpl w=mpk r.

It shows that manufacturers can continuously adjust the amount of input of more than two factors, so that the marginal output obtained by the last unit of cost expenditure is equal no matter which factor of production is used to purchase, so as to achieve the maximum output under the given cost condition.

2. The optimal condition for cost minimization under a given output:

In order to achieve the minimum cost under the given conditions, the manufacturer should continuously adjust the input amount of the two factors so that the marginal output of the last unit of cost expenditure spent on each factor is equal. This is the principle of optimal combination of two elements for manufacturers to achieve the minimum cost under the condition of a given output, which is the same as the principle of the optimal combination of the two elements for the manufacturer to produce the maximum output under the condition of a given cost.

When the producer's output target is set, the producer can determine the combination of production factors that can bring the maximum output under the given output target by finding the equivalent cost line tangent to the output line and determining the cut-off point.

Factor of production. The optimal combination of is the tangent point of the isoyield curve and the equivalence equation.

The optimal combination of production factors refers to the input combination of production factors that maximize output at a given cost or minimize the cost under a given output. In the case of changes in the input of various factors of production, the production technology of the manufacturer.

This can be represented by an isoyield curve.

The relationship between the cost of the firm and the input of production factors can be expressed by the equivalent cost equation. Therefore, the optimal combination of production factors is represented by the tangent point of the equal output curve and the equivalent cost equation. Under the condition that the cost is given, the conditions that need to be met for the input of production factors are:

rtsl,k =rl/rk，rl+rk=c。

Or under the condition of a given output, the conditions that need to be met for the input of production factors are: RTSL, K = RL Rk, F(L, K) = Y. These conditions show that whether the output is the largest at a given cost or the smallest under a given output, the firm seeking the optimal combination of production factors will choose the quantity of production factors in the marginal output that can be produced by the factors purchased at unit cost.

Equal points. <>

The tangent point of the constant yield curve and the equal cost curve --elliott

Summary. Hello, the combination of factors that minimize costs and maximize benefits is the optimal combination. Derivative of mp)l=q = 20-12l (with k as a constant), the same is true (mp)k = 50-4k (with l as a constant).

Establish the equation: 660 = 15l + 30k, (20-12l) 15 = (50-4k) 30

solution, l = 3 k = 41 2 =

The formulas of these two equations are based on the above list of reasoning.

Economics, which deals with the optimal combination of factors of production that manufacturers put in.

Please wait patiently for three minutes, we are sorting it out, and we will answer you immediately, and please don't end the consultation.

Hello, the combination of factors that minimize costs and maximize benefits is the optimal combination. The derivative of (mp)l=q=20-12l (with mu feng old k as a constant), and the same way (mp)k=50-4k (with l as the constant base) to establish the equation: 660=15l+30k, (20-12l) 15=(50-4k) 30 solution, and the rapid rise l= 3 k=41 2=The formulas of these two equations can be reasoned according to the above list.

Answer]: When analyzing the reasonable input of a variable factor, the production process can be divided into three stages: average output increase, average output decrease and marginal output negative according to the change in output.

In the first stage, the variable factor input is increased to the maximum average output. At this stage, both the total output and the average output are increasing, so rational producers will not choose to reduce the amount of labor input in this later stage, and Lihui will continue to increase the amount of labor input.

In the second stage, the average yield begins to decline to zero marginal yield. At this stage, both the average and marginal yields are decreasing, but the total output is increasing and reaching a maximum.

In the third stage, the total output begins to decline, and the marginal output is negative. At this stage, the total output begins to decline, so the rational producer will choose to increase the amount of labor input at this stage, but will reduce the amount of labor input.

To sum up, rational producers do not choose the first and third stages of production, but inevitably choose to organize production in the second stage, that is, only the second stage is a reasonable area for variable factor input. But in this region, how much variable factors producers put in and how much they can produce must be determined in conjunction with the cost function.

Kiss. Hello, I am glad to answer the question of leakage width for you: has the producer reached equilibrium at the optimal combination of production factors, and the optimal combination of production factors The producer reached equilibrium at the tangent point of the equal output curve and the equal cost curve, and the equilibrium point:

mrtslk = w/r;It shows that in order to achieve the maximum output of the mid-stage search under the condition of fixed cost, it is necessary to select the optimal combination of production factors, so that the marginal technology substitution rate of the two factors is equal to the ratio of the two factors.