Analyzing Production Data for Concavity
A farm manager is testing a new fertilizer. With a fixed plot of land and other inputs, they record the total bushels of corn produced for different amounts of fertilizer applied:
- 1 gallon of fertilizer yields 50 bushels.
- 2 gallons of fertilizer yield 90 bushels.
- 3 gallons of fertilizer yield 120 bushels.
Based on this data, is it likely that the production function for fertilizer is strictly concave? Justify your answer by calculating and explaining the trend in the average product of fertilizer.
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