Question

The Law of Diminishing Returns in Economics is related to the idea of concavity. As an example of the law, a farmer who owns a given acreage of land will find that a certain number of laborers will yield the maximum output per worker. If he should hire more workers, the combination of land and labor would be less efficient because the proportional increase in the overall output would be less than the expansion of the labor force. The output per worker would therefore fall. This law holds in any process of production unless the technique of production also changes. 1a. If R(x) is the revenue and x is the amount spent on advertising, find the point of diminishing returns for the input-output function below. R(x) = (600x^2 - x^3)/50,000, for 0 ≤ x ≤ 500 1b. Use a number in the interval to the left of the point of diminishing returns to test for the sign of the second derivative of R(x). 1c. Use a number in the interval to the right of the point of diminishing returns to test for the sign of the second derivative of R(x). 1d. What conclusion can you draw from this?

          The Law of Diminishing Returns in Economics is related to the idea of concavity. As an example of the law, a farmer who owns a given acreage of land will find that a certain number of laborers will yield the maximum output per worker. If he should hire more workers, the combination of land and labor would be less efficient because the proportional increase in the overall output would be less than the expansion of the labor force. The output per worker would therefore fall. This law holds in any process of production unless the technique of production also changes.

1a. If R(x) is the revenue and x is the amount spent on advertising, find the point of diminishing returns for the input-output function below.
R(x) = (600x^2 - x^3)/50,000, for 0 ≤ x ≤ 500

1b. Use a number in the interval to the left of the point of diminishing returns to test for the sign of the second derivative of R(x).

1c. Use a number in the interval to the right of the point of diminishing returns to test for the sign of the second derivative of R(x).

1d. What conclusion can you draw from this?

Added by Ricky A.

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