Summary

For any combination of inputs, the production function gives the maximum quantity of output the firm can produce with them.

In the short run at least one input is fixed and cannot be varied; in the long run every input is variable.

Total product is the relationship between a variable input and output when all other inputs are held constant.

For any level of employment of an input, the sum of the marginal products of every unit of that input up to that level equals the total product at that level ($TP = \sum MP$).

Both the marginal product and the average product curves are inverse-'U'-shaped, and the marginal product curve cuts the average product curve from above at the maximum point of the average product curve.

To produce any level of output, the firm picks the least-cost combination of inputs.

Total cost is the sum of total variable cost and total fixed cost: $TC = TVC + TFC$.

Average cost is the sum of average variable cost and average fixed cost: $SAC = AVC + AFC$.

The average fixed cost curve is downward sloping (a rectangular hyperbola).

The short run marginal cost ($SMC$), average variable cost ($AVC$) and short run average cost ($SAC$) curves are all 'U'-shaped.

The $SMC$ curve cuts the $AVC$ curve from below at the minimum point of $AVC$.

The $SMC$ curve cuts the $SAC$ curve from below at the minimum point of $SAC$. …