Elasticity for optimal price

We assume that the purpose of business is the greatest current income (we consider other options separately).

Fixed costs - is the cost of production, the value of which does not depend on the volume of production. These include, for example, rent, salaries of management personnel.

Variable costs - it costs, the magnitude of which depends on the volume of production. These include, for example, raw materials, components, workers' wages.

The current profit can be written as follows:

P = (P-Cv) * Q (P)-Cc




P - sale price

Q (P) - number of sales as the value function,

CV-variable costs per unit of production;

SS-fixed costs;

We find the price at which the maximum of this function. For this we take the derivative of price and equate it to zero.

As a result, we obtain the relation

Q (P) + (P-Cv) * Q '(P) = 0,


P * Q '(P) / Q (P) = Cv * Q' (P) / Q (P) -1


Q '(P)-derivative of the function of demand.

Expression of P * Q '(P) / Q (P), taken modulo, as is well known, determines the elasticity of demand. Thus the expression for the elasticity can be written as

E = | Q '* Cv/Q-1 |

In this expression, Cv and Q is greater than zero by definition. In the classical dependence of demand on prices Q 'is always less than zero. Consequently, the elasticity modulus greater than unity, if the aim of sales is the highest profit. All the goods are elastic under this assumption,




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