- Cobb-Douglas Production Function Calculator
- Testing for Returns to Scale in a Cobb-Douglas Production Function
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It is always a good idea to look at some numbers, to get an understanding for the beast at hand. With increasing returns to scale, a proportional increase in all inputs will increase output by more than the proportional constant. Our Cobb-Douglas production function might now have the form:. With the same factor prices as before, we compute the cost of producing the product using the cost minimizing combination of inputs, obtaining the cost function, and the average cost and marginal cost functions.

## Cobb-Douglas Production Function Calculator

Now we see that both average cost and marginal cost are decreasing, with marginal cost below average cost, a consequence of increasing returns to scale. If we splice together the two cases above, we do get something like the U-shaped average and marginal costs that I used in the oligopoly model.

We usually assume that capital is fixed in the short run. Suppose our firm is to operate efficiently using the cost minimizing combination of inputs producing product in the 25 - 35 unit range using the decreasing returns Cobb-Douglas production function.

Because marginal cost is virtually a linear function of q, total cost with capital fixed is virtually a quadratic function of q since its derivative, marginal cost, is linear. By fixing the amount of input for one factor, we obtain a 2-dimensional isoquant curve.

The red rays emanating from the origin in the diagrams intersect each isoquant at the same angle. The mean elasticity conditional on the absence of publication bias, disaggregated data, and inclusion of information from the first-order condition for capital is 0.

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To obtain this result, we collect 3, estimates of the elasticity reported in studies, codify 71 variables that reflect the context in which researchers produce their estimates, and address model uncertainty by Bayesian and frequentist model averaging. We employ nonlinear techniques to correct for publication bias, which is responsible for at least half of the overall reduction in the mean elasticity from 0.

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## Testing for Returns to Scale in a Cobb-Douglas Production Function

Our findings also suggest that a failure to normalize the production function leads to a substantial upward bias in the estimated elasticity. The weight of evidence accumulated in the empirical literature emphatically rejects the Cobb-Douglas specification.

Handle: RePEc:zbw:esprep as. Corrections All material on this site has been provided by the respective publishers and authors.

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Louis Fed. Besides its statistical elegance, it has no theoretical basis and the assumption that the output elasticities of labor and capital and total factor productivity in future will be the same as in past is not very sound. You are welcome to learn a range of topics from accounting, economics, finance and more.

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