Production function with one variable input
In the short run a manager has to decide about how much to produce by employing additional variable inputs, due to capacity constraint, since fixed inputs cannot be increased readily at a short notice.
Total Product, Average Product and Marginal Product
The production function shows the maximum output or total product (TP) that can be produced by employing a combination of factors of production at a given time period. The average product (AP) depicts the TP per unit of input used. The marginal product (MP) is the change in the total product resulting from a unit change in a variable input. If we assume labour (L) as a variable input, then
TP=f(Q)
APL=TP/L
MPL=ΔTP/ΔL
To see what happens to the total product in the short run as labour increases, we can derive a short run production function from Table 5.1. We assume capital fixed at 2 units and labour increases by one unit. The TP increases to a maximum of 56 units when 7 units of labour is used and then decreases to 52 units with additional unit of labour. It means that in a year employing 7 full time labourers can produce a maximum of 56 speciality parts.
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