### Cost function

Cost function ( the output-cost relationship is the cost function of the firm.)

Certain quantity of output can be produced by different input combinations. With the input prices given, it will choose that combination of inputs which is least expensive. So, for every level of output, the firm chooses the least cost input combination.. and this output-cost relationship is the cost function of the firm.
or
In order to produce output, the firm chooses least cost input combinations. this process of selecting and producing is called the cost function.

Total Cost

Total cost is the sum of total variable cost and the total fixed cost.

Fixed Cost
- is the cost of fixed factors of production. Fixed Cost remains the same in the short run.

Variable Cost
- is the cost of variable factors of production. Variable Cost increases with the increase in the quantity of production.
TC = TFC + TVC

(
Fixed factors of production refers to the factors of production whose supply cannot be increased in the short run. E.g. – Land is a fixed factor of production in the short run.

Variable factors of production
refer to the factors of production whose supply can be increased in the short run as well as long run.

Duration of short run and long run varies according to industry. For some industries like steel plant 1 year is a short run, but for other industries like plastic factory, 1 year is a long run.)

Average Fixed Cost is the total fixed cost divided by the quantity produced.
AFC = TFC/Q

Average Variable Cost is the total variable cost divided by the quantity produced.
AVC = TVC/Q

Average Total Cost is the sum of average variable cost and average fixed cost. or we can say, average cost is equal to the total cost divided by the number of units produced.
ATC = TC/Q

Marginal Cost is the addition made to the total cost by producing 1 additional unit of output.
Marginal Cost = Total cost of nth unit - Total cost of (n-1)th unit.
MC = TCn – TCn-1 (e.g. – MC of 6 th unit = Total cost of 6th unit – Total cost of 5th unit)

Marginal cost can also be defined as the change in total cost (∆TC) due to change in quantity demanded(∆Q).
MC = ∆TC/∆Q