Maximisation By Marginal Examination

Illustration 13

Presume a firm has the following total revenue and total cost functions:

TR       =          640Q – 4Q^2
TC       =          3600 + 100Q + 6Q^2

You are required to ascertain (1) the level of productivity at which the firm optimises profit and (2) the level of productivity which optimises total revenue.

Solution

The profit optimising productivity can be ascertained by procuring MR and MC from the given Total Revenue and Total Cost functions correspondingly. The MR and MC are evaluated by the inclines at a point on these curves. Incline at a point of a function is weighed by the first derivative of the function. Considering the first derivative of total revenue function:

MR      =          ΔTR     =          640 – 8Q
ΔQ

Considering the first derivative of the total cost function,

MC      =         ΔTC     =          100 + 12Q
ΔQ

Setting MR = MC, we procure,

640 – 8Q         =          100 + 12Q

20Q                 =          540

Q                     =          540 / 20           =          27

Therefore, profit optimising level of productivity is 27.

It must be renowned that if we use total revenue total cost approach to procure maximum level of productivity, we will procure the same outcome.

Therefore,

Profits π          =          TR – TC

π          =          (640Q – 4Q^2) – (3600 + 100Q + 6Q^2)

π          =          640Q – 4Q^2 – 3600 - 100Q - 6Q^2

π          =          540Q – 10Q^2 – 3600

Derivative of 540Q – 10Q^2 – 3600 is equal to

=          540 – 20Q
dQ

Now, profits will be optimised when the first derivative of total profit function is null or zero. Therefore, constructing

=          0, we procure,
dQ

540 – 20Q       =          0

20Q                 =          540

Q                     =          540 / 20           =          27.

Incremental Analysis

Incremental Cost

Incremental costs consists of current period explicit cost which incorporates costs incurred on direct labour on buying of inputs etc, opportunity costs which is forgoing alternative for accomplishing best use and Future costs that is any type consequents from a given decision. It may be noted that anticipated present value is evaluated and incorporated in the incremental cost of the decision.

Incremental Revenue

Incremental revenue is diverse from revenue of consequents from implementing a decision. Enhancement in total revenue taken place by pronouncing about a connectively huge variation in productivity and innovation of fresh commodity line or a new skill or instigating an advertisement campaign outlay is termed as incremental revenue.

Nevertheless, clangers are usually taken place by ailing informed supervisors about all incremental costs and incremental revenues. As described above, for optimal decision making only all relevant costs and revenues should be regarded while estimating the outcome of diverse decisions.

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