The Law of Diminishing Returns (A2 Microeconomics)

This refers to the cost of production to firms in the short run, where short run is considered to be the period of time when at least one factor of production is fixed. 

The law of diminishing returns relies on the assumption that capital is a fixed factor. It states that as a firm increases the amount of inputs of a variable factor (such as labour), it will gradually derive less additional output per unit of labour for each further increase. This is a result of the fixed factor of production, which limits the capacity of cost efficient production. For example if a manufacturing firms owns 100 sewing machines, as the number of machine operators employed by the firm passes 100 and employees are required to share machines the output per worker will begin to fall.

As it becomes more expensive to produce each additional unit of output, marginal cost (MC) and average variable cost (AVC) will start to rise. 

Eventually, the rise in AVC will exceed the fall in average fixed cost (AFC) which generally occurs as fixed costs can be spread to a larger amount of units of output. When this happens, average total cost (AC) will also start to rise.

Source http://www.bized.co.uk/

Here, where MC is below AC, AC must be falling. This is because an additional unit of output that is cheaper than the average unit cost will pull down the average cost of production. Once the MC curve meets the AC curve, average costs begin to rise as they are exceeded by the marginal cost of output. If an additional unit of output is more expensive to produce that the average cost, the new average cost including this additional unit will be greater. 

This relationship results in the MC curve cutting the AC curve at its lowest point. This is where costs of production are at a minimum. Profit maximising firms will aim to produce at this point.