Applications of Calculus in Commerce and Economics

  • Rate of change of cost of a commodity is expressed in terms of various factors. Cost of a commodity depends upon a number of factors. These factors are: ‘Level of Output’, ‘Technology‘, ‘Price of Raw Materials’, ‘Size of the Plant’ and many others.
  •  Fixed costs are those which are incurred regardless of the level of production - like interest, rent, wages of permanent staff, etc.
  • TFC = TC, when x = 0.
  • Variable costs are those which vary with output. Example: raw materials and wages of casual labour.
  • Cost of a commodity is known as total cost. Therefore, the total cost can be expressed as
  • Total Cost = Total Fixed Cost + Total Variable Cost
  • Average of cost is obtained by dividing the cost by level of output.
  • Therefore, the average cost = [TFC + TVC]/x.

Here,

o    TFC = Total fixed cost

o    TVC = Total variable cost

o    x = number of output

•    If the demand of the item depends upon the price of the item, then the demand function is given by

o    x = f(p).

•    If the price of the item depends upon the demand of the item, then the demand function is given by

o    p = f(x).

  • Revenue means the amount received by a company by selling a certain number of units of a commodity.
  • Profit Function:
  • The profit function P(x) of producing and selling x units of a commodity is P(x) = R(x) – C(x), where, R(x) is revenue function and C(x) is total cost function.
  • The breakeven point is the level of production where the revenue from sales is equal to the total cost of production.

        Keywords: Average Cost Curve, Constant variable cost, Demand Function, Revenue Function, Breakeven Analysis, Marginal Functions

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  • Q1

    Marks:1
    Answer:

    The breakeven point is the level of production where the revenue from sales is equal to the total cost of production.

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  • Q2

    Marks:1
    Answer:

    Revenue means the amount received by a company by selling a certain number of units of a commodity.

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  • Q3

    What is average cost?

    Marks:1
    Answer:

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  • Q4

    What is variable cost?

    Marks:1
    Answer:

    Variable cost is the cost that vary with output, for example, raw materials and wages of casual labour.

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  • Q5

    What are the two components of total cost?

    Marks:1
    Answer:

    The two components of total cost are fixed cost and variable cost.

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