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The Cobb-Douglas Production Function - Admission/Application Essay Example

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In the paper “The Cobb-Douglas Production Function” the author depicted mathematically the production function. The production function shows how a certain amount of inputs would lead to a certain amount of output. The production function shows increasing, decreasing or constant returns…
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The Cobb-Douglas Production Function
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Download file to see previous pages The firm might vary the inputs such as labor and capital in order to increase the output but nevertheless, there is no certainty or rule which guarantees increasing returns to increase inputs or scale of operations. Thus costs might increase, decrease or remain constant given the ceteris paribus principle operates. Production and cost functions can be shown both mathematically and graphically.
Where, Q stands for quantity; f for the function of; X1 etc. for different inputs; and L and K for labor and capital respectively. The production function shows how a certain amount of inputs would lead to a certain amount of output while the corresponding cost function would show how the costs of those inputs would relate to the output. In other words, the latter function would depict different components of the total cost function such as average cost, marginal cost, fixed cost, variable cost, semi-variable cost and so on (Jehle and Reny, 2000).
In a simple hypothetical situation where the firm concerned produces a certain output of widgets during a certain period of time, the production function would show the different inputs of labor, capital, and land needed to produce the planned quantity of widgets, 100,000 widgets per week. Thus the equation would show,
100,000 widgets = f (45L and 8K). This is a functional relationship between inputs and output. In other words, it says quantity produced is a function of the variables. This relationship is what matters in a production function because all output decisions taken in conjunction with the firm’s current and predictable market share and sales are in conformance with the firm’s own profit expectations. Therefore it’s obvious that the production function necessarily incorporates input variables after a series of prior calculations on marginal and average costs. The subsequent calculations are determined by the expected profit margins.  ...Download file to see next pagesRead More
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