An Example of a Production Function

This Demonstration considers a production function f(K,L)=((600 (K^2)(L^2)-(K^3)(L^3))/1000000), where K and L are the capital and labor inputs. Both inputs are variable in the long run. In the short run K is fixed.

On the right, the long-run representations are shown using 3D and isoquant curves. On the left, the short-run curves of total production (top) and the marginal and average product (bottom) are shown (mouse over to distinguish the curves). The horizontal line in the contour plot and the vertical plane in the 3D plot show the relation between the short and long run. It is easy to see the short-run production function as the intersection of the 3D surface of long-run production and the vertical plane determined by the fixed short run K.

Also, the geometric relationship between the three short-run curves is illustrated on the left. In particular, you can see the coincidence point of average and marginal product curves at the top left.

THINGS TO TRY

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DETAILS

Additional information on this topic can be found in:

W. Nicholson, Microeconomic Theory: Basic Principles and Extensions, Hinsdale, IL: Dryden Press, 1972.

N. G. Mankiw, Principles of Microeconomics, Ft. Worth, TX: Dryden Press, 1997.

A. Griffiths and S. Wall., Intermediate Microeconomics: Theory and Applications, New York: Pearson Education, 2000.

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Contributed by: Javier Puértolas

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