Marginal Cost

Marginal cost is the change in total cost when additional unit of output is produced.

As said by Ferguson “Marginal cost is the addition to total cost due to the addition of one unit of output.”

Symbolically,

MC_n = TC_n – TC_n-1 OR

MC = Change in total cost / Change in output

MC_n = Marginal cost of ‘n’ units of output

TCn = Total cost of ‘n’ units of output

TC_n-1 = Total cost of ‘n-1’ units of output

Tabular representation of calculating MC

Units of Output	Total Fixed        Cost	Total  Variable         Cost	Total Cost	Marginal Cost
0 1 2 3 4 5 6 7 8	10 10 10 10 10 10 10 10 10	0 10 18 24 28 32 38 46 62	10 20 28 34 38 42 48 56 72	- 10 8 6 4 4 6 8 16

When 4 units of output is produced,

MC = TC₄ – TC₃

      = 38 – 34 = 4          

When 8 units of output is produced,

MC = TC₈ – TC₇

      = 72 – 56 = 16

Diagrammatic representation of MC curve

Diagrammatically, the marginal cost for any level of output can be calculated by taking the slope of the total cost curve corresponding to that level of output.

marginal cost

Following observation can be made with regards to marginal cost

1) Marginal cost is U shaped, due to Law of Variable proportion..

As output increases, MC curve slopes downwards (up to OQ units), reaches the minimum (at point A) and then starts sloping upwards beyond OQ level of output.

MC tends to fall initially and eventually it tends to rise.

Falling MC is in accordance with rising MP (when there are increasing returns to a factor).

Rising MC is in accordance with falling MP (when there are dimnishing returns to a factor).

MP and MC are exactly opposite to each other

2) MC is variable cost only

MC is an additional cost . Additional cost by definition cannot be fixed cost ( there is no addition or change in the fixed cost with an increase in output), it can only be variable cost.MC is independent of fixed cost.

MC can be estimated in either of the following ways:

a) MC_n = TC_n – TC_n-1 OR

b) MC_n = TVC_n – TVC_n-1

proof:

MC_n = TCn – TC_n-1

            = (TFC_{n +} TVC_n ) – (TFC_n-1  + TVC_n-1)

Since, TC = TFC + TVC

            = TFC_n + TVC_n  – TFC_n-1  - TVC_n-1

(TFC_n = TFC_n-1  , because TFC is constant)

            = TVC_n  – TFC_n-1  

 Also Total cost exceeds the total variable cost by the constant amount (the amount of fixed cost), the addition in total cost for the additional unit of output would be the same as addition in the total variable cost.

MC curve Derived from TVC is same as derived from TC curve.

As also shown is the above table:

 When 4 units of output is produced,

MC = TVC₄ – TVC₃

      = 28 – 24 = 4          

When 8 units of output is produced,

MC = TVC₈ – TVC₇

      = 62 – 46 = 16