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