Marginal Cost Curve

The marginal cost of production is equal to the change in total cost due to production of one more one less unit of output. Thus, if n units of output are being produced then the marginal cost or cost of producing n unit is given by the formula

MC_n = TC_n – TC _{(n – 1)}

Where TC_n is the total cost of producing n units and TC_{n – 1} is the cost of producing one unit less than n. thus, mc is the addition made to TC by producing one more unit of output.

Since, in the short – run total fixed cost remains constant, i.e. there is no change in the total cost by producing one more unit of output, this means that whatever change takes place in total cost is due to change in total variable cost. Therefore, marginal cost is equal to change in total variable cost due to a change of one unit in output produced. This can be shown as:

MC_n = TC_{n= - =}TC_{(n – 1)}                 …. (1)
Now,TC = TF_C + TVC                …. (2)

Putting this value of TC in (1),
MC_n = (TFC_n + TVC_n) – (TFC_{n -1} + TVC_{n -1})        …. (3)
= TFC_n + TVC_n – TFC_{n – 1} – TVC_{n – 1}        …. (4)

Since, TFC remains fixed and does not change with output
:. TFC_n = TFC_{n – 1}                    …. (5)

Therefore in Eqn. TFC_n and TFC_{n – 1} cancel out.
Thus,MC_n = TVC_n – TVC_{n – 1}
  ∆ TVC
The marginal cost of the nth unit produced is thus equal to change in the average variable cost due to change of one unit in output. When change in quantity (D Q) is more than one unit, then
MC = ∆TVC / ∆Q
This can also be shown as:
MC = ∆ TC / ∆Q = ∆TFC /∆Q + ∆TVC / ∆Q
Since, there is no change in TFC with any change in Q and so ∆ TFC = 0
:. ∆ TFC /∆Q = 0
Hence,  MC = ∆TFC /∆Q