notes_5 - Production Theory February 21, 2009 1 Production...

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Production Theory February 21, 2009 1 Production Production is the process of combining inputs to make outputs Technology: the technology of a firm refers to the method by which inputs are combined to produce the output Inputs: Labor, Physical Capital, Human Capital, Land. We assume the Technology is fixed; given the available technology the firm wants to produce the optimal quantity of output. Production Function: this is a function that tells us the maximum quantity of output a firm can produce over some period of time from each combination of inputs. q = F ( K,L ) The production function allows inputs to be combined in varying propor- tions, therefore outputs can be produced in many ways. This means that in order to produce the same output level ˜ q we could use more labor and less capital or vice versa. 1.1 Time: Short Run Vs. Long Run Often, the firm wants to adjust its level of production to the external en- vironment. To do so it has to adjust the level of the various inputs of production: however, some of these inputs cannot be modified immediately. Long Run is a time horizon long enough for a firm to vary all of its inputs Short Run is any time horizon during which at least one of the firm’s inputs cannot be varied. We distinguish between two different kinds of inputs 1
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1. Fixed Inputs: are the inputs whose quantity must remain constant, regardless of how much output is produced. 2. Variable Inputs: inputs whose usage can change as the level of out- put changes. 2 Production in the Short Run Total Product : is the maximum quantity of output that can be produced from a given combination of inputs. ( L, K ) = Q where Q denotes the Total Product (quantity) given a particular combination of labor L and capital K (which is fixed in the short run. I denote a fixed variable with an overline). How can I measure the variation in Total Product from a change in the variable inputs (fixed inputs simply don’t change in the Short Run)? Marginal Product of Labor (MPL) : it denotes the additional output produced when one or more worker is hired MPL = Δ Q Δ L = ∂F ( K,L ) ∂L ( you can compute the MPL by taking the ratio between the change in total product and the change in the number of workers employed ). We say that by increasing the number of workers you always increase the total Product: hence the MPL is always positive. But the additional increase in output changes according to the quantity of workers already hired. 1. For small numbers of workers, there is an Increasing Marginal Product of Labor : the marginal product of labor increases as more labor is hired. In this region (which is close to the origin of the axes) the Total Product curve is increasing at increasing rate (convex) 2. After a certain point, the production function exhibits Decreasing Marginal Product of Labor : the marginal product of labor de- creases as more labor is hired. In this region the curve is increasing at a decreasing rate (concave).
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This note was uploaded on 05/09/2009 for the course ECON 200 taught by Professor Junnie during the Spring '08 term at NYU.

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notes_5 - Production Theory February 21, 2009 1 Production...

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