1/7/2024 0 Comments Production function![]() Mathematics for economists: An introductory textbook, 4th ed. Read more: Section 7.3 (especially page 127) and Section 8.2 of Malcolm Pemberton and Nicholas Rau. That is to say, its slope decreases as increases, which means that its second derivative is negative: Another property of the production function in the figure is that it gets gradually less steep as increases. These two properties are typical of most production functions. So its slope, which is given by the derivative of the function, is positive. Secondly, the function is increasing: that is, as increases, so does. ![]() First we can see that if the input is zero, no grain is produced, and if the input is greater than zero the amount of grain is strictly positive: ![]() If we let be the labour input (number of farmers) and be the amount of grain produced (in kilograms), we can write the production function as:Ĭould be any function, but if it is to represent a production function like the one in the figure, it must have certain properties. The farmer’s production function: Diminishing average product of labour.
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