《管理经济学》第五章

Returns to Scale and Returns to a Factor
Returns to scale measure output effect of increasing all inputs. Returns to a factor measure output effect of increasing one input.
Marginal Rate of Technical Substitution


The marginal rate of technical substitution (MRTS) is the amount of one input factor that must be substituted for one unit of another input factor to maintain a constant level of output. MRTS = ∂Y/∂X = Slope of an Isoquant The marginal rate of technical substitution usually diminishes as the amount of substitution increases. At the extremes, isoquants may even become positively sloped, indicating that the range over which input factors can be substituted for each other is limited.
Chapter 5 KEY CONCEPTS




production function discrete production function continuous production function returns to scale returns to a factor total product marginal product average product law of diminishing returns isoquant technical efficiency input substitution marginal rate of technical
Marginal Revenue Product and Optimal Employment





ridge lines marginal revenue product economic efficiency net marginal revenue isocost curve (or budget line) constant returns to scale expansion path increasing returns to scale decreasing returns to scale output elasticity power production function productivity growth labor productivity multifactor productivity

Input Combination Choice

Production Isoquants
Isoquant
denotes a curve that represents the different combinations of inputs that can be efficiently used to produce a given level of output. Technical efficiency is least-cost production of a target level of output.

Total, Marginal, and Average Product

Total Product
Total
product is total output.
Marginal Product
Marginal
product is the change in output caused by increasing input use. If MPX=∂Q/∂X> 0, total product is rising. If MPX=∂Q/∂X< 0, total product is falling (rare).
Marginal Rate of Technical Substitution

Rational Limits of Input Substitution

MPX<0 or MPY<0 are never observed, because this implies that output could be increased by using less of that resource. The rational limits of input substitution are where the isoquants become positively sloped. Ridge lines graphic bounds for positive marginal products. It is irrational to use any input combination outside these tangents (or ridge lines). Only for input combinations lying between the ridge lines will both inputs have positive marginal products. It is here and along the negatively sloped portion of the isoquant that optimal input combinations are found.
Representative Isoquants for Table 5.1
Input Combination Choice

Input Factor Substitution
Isoquant
shape shows input substitutability. C-shaped isoquants are common and imply imperfect substitutability.
Law of Diminishing Returns to a Factor


Illustration of Diminishing Returns to a Factor
Typically, increased specialization and better utilization of other factors in the production process allow factor productivity to grow. In practice it is very rare to see input combinations that exhibit increasing returns for any factor. With increasing returns to a factor, an industry would come to be dominated by one very large producer―and this is seldom the case. Input combinations in the range of diminishing returns are commonly observed.
Production Analysis and Compensation Policy
Chapter 5
Chapter 5 OVERVIEW



Production Functions Total, Marginal, and Average Product Law of Diminishing Returns to a Factor Input Combination Choice Marginal Revenue Product and Optimal Employment Optimal Combination of Multiple Inputs Optimal Levels of Multiple Inputs Returns to Scale Production Function Estimation Productivity Measurement
Marginal Revenue Product and Optimal Employment

Marginal Revenue Product
The
extra revenue obtained from using one more factor input to produce and sell additional units of output. Marginal revenue product of a factor is given by the factor’s marginal product multiplied by the marginal revenue of the product. MRPL= MPL x MRQ = ∂TR/∂L.
Isoquants for Inputs with Varying Degrees of Substitutability: (A) Electric Power Generation; (B) Bicycle Production
Isoquants for Inputs with Varying Degrees of Substitution: (C) Dress Production
Law of Diminishing Returns to a Factor

Diminishing Returns to a Factor Concept
The law of diminishing returns (the law of diminishing marginal returns) states that the marginal product of a variable factor must eventually decline as more of the variable factor is combined with other fixed resources.

Average product
APX=Q/wk.baidu.com.
Total, Marginal, and Average Product

Observations:
When
MP = 0, TP is at its maximum When MP > AP, AP is increasing When MP < AP, AP is decreasing When MP = AP, AP is at its maximum
Production Functions
Properties of Production Functions Production functions are determined by technology, equipment and input prices. Discrete production functions are lumpy. Continuous production functions employ inputs in small increments.