Key Points

A production function describes the technological relationship between inputs used and the maximum output that can be produced by a firm.

In the short run, at least one factor of production is fixed, while others are variable. In the long run, all factors of production can be varied.

Total Product is the total quantity of output produced by a firm with a given quantity of a variable input, keeping all other inputs fixed.

Average Product is the output per unit of variable input ($\frac{TP}{L}$). Marginal Product is the additional output from one more unit of variable input ($\frac{\Delta TP}{\Delta L}$).

This law states that as we increase one input while keeping other inputs fixed, the marginal product of the variable input will initially rise, but eventually fall.

Both AP and MP curves are inverse U-shaped. The MP curve cuts the AP curve from above at the AP curve's maximum point.

Returns to scale show how output responds to a proportional change in all inputs. It can be Increasing (IRS), Constant (CRS), or Decreasing (DRS).

Total Fixed Cost (TFC) is the cost of fixed inputs and does not change with output. Total Variable Cost (TVC) is the cost of variable inputs and changes with output.

Total Cost is the sum of Total Fixed Cost and Total Variable Cost. $TC = TFC + TVC$.

Average Fixed Cost (AFC) is $\frac{TFC}{q}$. Average Variable Cost (AVC) is $\frac{TVC}{q}$. Short-run Average Cost (SAC) is $\frac{TC}{q}$, and it is also the sum of AFC and AVC.

Short-run Marginal Cost is the change in total cost from producing one additional unit of output. It is calculated as $\frac{\Delta TC}{\Delta q}$.

The AFC curve is a downward-sloping rectangular hyperbola. The AVC, SAC, and SMC curves are typically U-shaped due to the law of variable proportions.

The SMC curve intersects both the AVC and SAC curves from below at their respective minimum points.

In the long run, there are no fixed costs, so Total Cost equals Total Variable Cost. The Long Run Average Cost (LRAC) and Long Run Marginal Cost (LRMC) curves are also U-shaped.

The downward sloping part of the LRAC curve corresponds to Increasing Returns to Scale (IRS), while the upward sloping part corresponds to Decreasing Returns to Scale (DRS).