Lecture 01-2005 - Basic Notions of Production Functions...

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1 Basic Notions of Production Functions Lecture I I. Overview of the Production Function A. The production function is a technical relationship depicting the technical transformation of inputs into outputs. 1. The production function in and of itself is devoid of economic content. 2. In the development of production functions, we are interested in certain characteristics that make it possible to construct economic models based on optimizing behavior. B. One way to write the production function is as a function map: : nm f RR + + which states that the production function ( f ) is a function that maps n inputs into m outputs. By convention, we are only interested in positive input bundles that yield positive output bundles. C. The first lecture will focus on the production function as a continuous function as students have probably seen it in previous courses. The next lecture will develop the concept of the production function more rigorously. II. One Product, One-Variable Factor Relationships A. A commonly used form of the production function is the “closed form” representation where the total physical product is depicted as a function of a vector of inputs. ( ) yfx = where y is the scalar (single) output and x is a vector (multiple) inputs. B. Focusing for a moment on the single output case, we could simplify the above representation to: ( ) 12 yf x x = or we are interested in examining the relationship between 1 x and y given that all the other factors of production are held constant. Using this relationship, we want to identify three primary relationships: 1. Total physical product –which is the original production function. 2. Average physical product –defined as the average output per unit of input. Mathematically, ( ) f x y APP x x == 3. Marginal physical product –defined as the rate of change in total physical product at a specific input level. Mathematically, ( ) ( ) () dTPP df x dy MPP f x dx dx dx = =
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AEB 6184 – Production Economics Lecture I Professor Charles B. Moss Fall 2005 2 C. Given these notions of a production function, we can introduce the classical shape of the production function: 0 20 40 60 80 100 120 140 160 180 0 20 40 60 80 100 120 140 160 180 Nitrogen (lbs./acre) Corn (bu./acre) High Yield Function Average Yield Function Low Yield Function This set of production functions are taken from Moss and Schmitz “Investing in Precision Agriculture”.
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Lecture 01-2005 - Basic Notions of Production Functions...

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