Production Functions Ap Econ 10/4

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Production Function Production function is the relationship between a firm’s quantity of output which depends on the quantity of inputs Fixed input: quantity fixed for period of time – cannot be varied Variable input: quantity can be varied at any time – depends on the level of output Example – wheat farm Fixed inputs: Land Variable inputs: Workers

Short Run Vs. Long Run ***Whether an input is fixed or not depends on time “Long run vs. Short run” Short Run (fixed plant): the period of time too brief for a firm to alter its plant capacity, yet long enough to permit a change in the degree to which the fixed plant is used (output can vary) Long run (variable plant): the period of time long enough for a firm to adjust the quantities of all the resources it employs including plant capacity Also includes enough time for firms to enter or leave the industry

Production Function Land: fixed input Labor: variable input Marginal Product of Labor (MP) shows the change in quantity of output generated by adding one more worker MP= ∆𝑄 ∆𝐿 Average Product (AP), also called labor productivity, is the output per unit of labor input AP = 𝑇𝑃 𝑄𝐿 Quantity of Labor Quantity of Wheat (total product) Marginal Product (MP) of Labor Average Product (AP) -- 1 19 2 36 17 18 3 51 15 4 64 13 16 5 75 11 6 84 9 14 7 91 8 96 12

Total Product Curve Quantity of wheat (bushels) Quantity of labor L Quantity of wheat Q MP of labor MPL =  Q /  L (worker) (bushels) (bushels per worker) Adding a 7th worker leads to an increase in output of only 7 bushels 19 1 19 17 2 36 15 Total product, TP 3 51 100 Adding a 2nd worker leads to an increase in output of 17 bushels 13 4 64 11 80 5 75 9 6 84 7 60 7 91 5 8 96 40 20 1 2 3 4 5 6 7 8 Quantity of labor (workers) Although the total product curve in the figure slopes upward along its entire length, the slope isn’t constant: as you move up the curve to the right, it flattens out due to changing marginal product of labor.

Marginal Product of Labor Curve Marginal product of labor falls as the number of workers increases Diminishing returns to an input (labor): Adding more workers adds to TP, but TP increases at a decreasing rate – decreasing returns to labor Negative returns: MP of labor is negative – bad! Marginal product of labor (bushels per worker) There are diminishing returns to labor. 19 17 15 13 11 9 7 5 Marginal product of labor, MPL 1 2 3 4 5 6 7 8 Quantity of labor (workers)

MP and AP

Diminishing Returns to Inputs Why? If they continue to add more and more workers without being able to increase their land, they get to a point where more workers are not efficiently being used

Land Increases from 10 Acres to 20 Quantity of wheat (bushels) Marginal product of labor (bushels per worker) 160 30 TP 140 20 25 120 100 20 TP 10 80 15 60 10 40 MPL 5 20 20 MPL 10 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8 Quantity of labor (workers) Quantity of labor (workers) (a) Total Product Curves (b) Marginal Product Curves With more land, each worker can produce more wheat. So an increase in the fixed input shifts the total product curve up from TP10 to TP20. This shift also implies that the marginal product of each worker is higher when the farm is larger. As a result, an increase in acreage also shifts the marginal product of labor curve up from MPL10 to MPL20.