MICROECONOMICS: Theory & Applications Chapter 7: Production By Edgar K. Browning & Mark A. Zupan John Wiley & Sons, Inc. 11th Edition, Copyright 2012 PowerPoint prepared by Della L. Sue, Marist College

Learning Objectives Establish the relationship between inputs and output. Distinguish between variable and fixed inputs. Define total, average, and marginal product. Understand the Law of Diminishing Marginal Returns. (continued) Copyright 2012 John Wiley & Sons, Inc.

Learning Objectives (continued) Investigate the ability of a firm to vary its output in the long run when all inputs are variable. Explore returns to scale: how a firm’s output response is affected by a proportionate change in all inputs. Describe how production relationships can be estimated and some difference potential functional forms for those relationships. Copyright 2012 John Wiley & Sons, Inc.

Relating Output to Inputs Factors of production – inputs or ingredients mixed together by a firm through its technology to produce output Production function – a relationship between inputs and output that identifies the maximum output that can be produced per time period by each specific combination of inputs Q = f(L,K) Technologically efficient – a condition in which the firm produces the maximum output from any given combination of labor and capital inputs Copyright 2012 John Wiley & Sons, Inc.

Production When Only One Input is Variable: The Short Run Fixed inputs - resources a firm cannot feasibly vary over the time period involved Total product - the total output of the firm Average product - the total output divided by the amount of the input used to produce that output Marginal product - the change in total output that results from a one-unit change in the amount of an input, holding the quantities of other inputs constant Copyright 2012 John Wiley & Sons, Inc.

Table 7.1 Copyright 2012 John Wiley & Sons, Inc.

Figure 7.1 - Total, Average, and Marginal Product Curves Copyright 2012 John Wiley & Sons, Inc.

The Relationship Between Average and Marginal Product Curves When the marginal product is greater than average product, average product must be increasing. When the marginal product is less than average product, average product must be decreasing. When the marginal and average products are equal, average product is at a maximum. Copyright 2012 John Wiley & Sons, Inc.

The Geometry of Product Curves Average product of labor (at a point) slope of a straight line from the origin to that point on the total product curve Marginal product of labor (at a point): change in total product with a small change in the use of an input slope of the total product curve at that point steeper total product curve => output rises faster as more input is used => larger marginal product Copyright 2012 John Wiley & Sons, Inc.

Figure 7.2 – Deriving Average and Marginal Product Copyright 2012 John Wiley & Sons, Inc.

The Law of Diminishing Marginal Returns A relationship between output and input that holds that as the amount of some input is increased in equal increments, while technology and other inputs are held constant, the resulting increments in output will decrease in magnitude Copyright 2012 John Wiley & Sons, Inc.

Production When All Inputs Are Variable: The Long Run Short run – a period of time in which changing the employment levels of some inputs is impractical Long run – a period of time in which the firm can vary all its inputs Variable inputs – all inputs in the long run Copyright 2012 John Wiley & Sons, Inc.

Production Isoquants Isoquant – a curve that shows all the combinations of inputs that, when used in a technologically efficient way, will produce a certain level of output Characteristics: Isoquants must slope downward as long as both input are productive (I.e., marginal products > 0) Isoquants lying farther to the northeast identify greater levels of output Two isoquants can never intersect. Isoquants will generally be convex to the origin. Copyright 2012 John Wiley & Sons, Inc.

Marginal Rate of Technical Substitution (MRTS) The amount by which one input can be reduced without changing output when there is a small (unit) increase in the amount of another input When the MRTS diminishes along an isoquant, the isoquant is convex. Copyright 2012 John Wiley & Sons, Inc.

Figure 7.3 - Production Isoquants Copyright 2012 John Wiley & Sons, Inc.

MRTS and the Marginal Products of Inputs MRTSLK = (-) ΔK/ΔL = MPL/MPK Copyright 2012 John Wiley & Sons, Inc.

MRTS and the Marginal Products of Inputs (Derivation) Copyright 2012 John Wiley & Sons, Inc.

Figure 7.4 - Isoquants Relating Gasoline and Commuting Time Copyright 2012 John Wiley & Sons, Inc.

Returns to Scale Constant returns to scale – a situation in which a proportional increase in all inputs increases output in the same proportion Increasing returns to scale – a situation in which output increases in greater proportion than input use Decreasing returns to scale – a situation in which output increases less than proportionally to input use Copyright 2012 John Wiley & Sons, Inc.

Factors Giving Rise to Increasing Returns Specialization and division of labor within the firm “Volume” capacity increases faster than “area” dimensions (arithmetic relationship) Available of techniques that are unique to large-scale operation Copyright 2012 John Wiley & Sons, Inc.

Factors Giving Rise to Decreasing Returns Inefficiency of managing large operations: Coordination and control become difficult Loss or distortion of information Complexity of communication channels More time is required to make and implement decisions Copyright 2012 John Wiley & Sons, Inc.

Figure 7.5 - Returns to Scale Copyright 2012 John Wiley & Sons, Inc.

Functional Forms and Empirical Estimation of Production Functions Linear Q = a + bL + cK Multiplicative Cobb-Douglas production function: Q = aLbKc Empirical Estimation Techniques Survey Experimentation Regression analysis Copyright 2012 John Wiley & Sons, Inc.

Linear Forms of Production Functions Copyright 2012 John Wiley & Sons, Inc.

Multiplicative Forms of Production Functions: Cobb-Douglas as an Example Copyright 2012 John Wiley & Sons, Inc.

Exponents and Cobb-Douglas Production Functions b + c > 1 increasing returns to scale b + c = 1 constant returns to scale b + c < 1 decreasing returns to scale Copyright 2012 John Wiley & Sons, Inc.

The Mathematics behind Production Theory: The Marginal-Average Product Relationship (continued) Copyright 2012 John Wiley & Sons, Inc.

Marginal-Average Product Relationship The Mathematics behind Production Theory: The Marginal-Average Product Relationship Marginal-Average Product Relationship Whenever MPL>APL, APL is increasing. Whenever MPL<APL, APL is decreasing. Whenever MPL=APL, APL is at a maximum. Copyright 2012 John Wiley & Sons, Inc.

The Mathematics behind Production Theory: MRTS and the Ratio of Inputs’ Marginal Products (continued) Copyright 2012 John Wiley & Sons, Inc.

MRTS equals the ratio of marginal products. The Mathematics behind Production Theory: MRTS and the Ratio of Inputs’ Marginal Products Summary Marginal product measures the additional output produced when only one input is varied and other inputs are held constant. The slope of an isoquant (dK/dL), equals (minus) the ratio of the marginal products of the inputs. MRTS equals the ratio of marginal products. Copyright 2012 John Wiley & Sons, Inc.

Cobb-Douglas production function (example): The Mathematics behind Production Theory: Some Additional Properties of Constant Returns to Scale Production Functions “Linear Homogeneous Function” – a production function that exhibits constant returns to scale Cobb-Douglas production function (example): where 0<α<1 (continued) Copyright 2012 John Wiley & Sons, Inc.

The Mathematics behind Production Theory: Some Additional Properties of Constant Returns to Scale Production Functions Properties: Marginal product of each input depends only on the proportion in which inputs are used (K/L) MRTS depends only on the proportion in which inputs are used (K/L) Copyright 2012 John Wiley & Sons, Inc.

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