# 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 costo    TVC = Total variable costo    x = number of output•    If the demand of the item depends upon the price of the item, then the demand function is given byo    x = f(p).•    If the price of the item depends upon the demand of the item, then the demand function is given byo    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

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

• Q2

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

• Q3

What is average cost?

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• Q4

What is variable cost?

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