Derivation of short-run average &marginal cost curves

The derivation of short-run average and marginal cost curves an be explained by following elements:

1. Average fixed cost:The average fixed cost can be obtained fixed cost curve.It slopes downwards to the right.As the output increase,the ratio of fixed cost to output decreases.Because,the fixed cost is a fixed quantity.The AFC curve is a rectangular hyperbola.The AFC approaches both the axes but does not touch them.
2. Average variable cost:The variable cost per unit of output is called average variable cost.The average variable cost declines up to the normal capacity.The decrease in AVC in the beginning is due to the operations of law of diminishing returns.After normal capacity,the AVC increase rapidly.The AVC curve in figure represents average variable cost.It slopes downward in the beginning,reaches the minimum point and rises upward thereafter.In general,the AVC curve is'U' shapes.
3. Average total cost :The average total cost is,in fact only average cost.It is the cost per unit of output.The average total cost is obtained by dividing total cost by quantity of output.Alternatively,it may be obtained by adding average fixed cost and average variable cost.ATC is the average total cost.In the beginning,both AFC and AVC fall.So ATC falls rapidly.So ATC continue to fall.But if production is further increased.AVC increase rapidly.Hence,ATC rises after a point.In this way,ATC first falls,reaches minimum point and rises thereafter.Thus the ATC is almost 'U' shaped.
4. Marginal cost:The marginal cost is the addition made to total cost when one more unit is produced.The marginal cost of 2 units of output is obtained by subtracting the total cost of one unit of output from two units of output produced.The marginal cost is the change in total cost due to the change in output.Hence,it is also calculated as :

MC=TC/Q
The marginal cost is independent of the fixed cost.Because the fixed cost does not change with output.The total cost changes due to change in the variable cost.Hence,the marginal cost is also calculated as:
MC=VC2-VC1
As shown in the figure,the marginal cost first,reaches the minimum point and increases thereafter.Hence,the MC curve also first slopes downward,reaches the minimum point and rises thereafter.