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Sum

A manufacturing company produces x items at a total cost of ₹ 40 + 2x. Their price is given as p = 120 – x. Find the value of x for which also find an elasticity of demand for price 80.

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#### Solution

Given, the price is p = 120 - x

∴ x = 120 - p

where, x = demand

∴ `"dx"/"dp" = 0 - 1 = - 1`

`eta = (-"p")/"x" * "dx"/"dp"`

∴ `eta = (-"p")/(120 - "p") * (- 1)`

∴ `eta = "p"/(120 - "p")`

p = 80 ....(Given)

∴ `eta = 80/(120 - 80) = 80/40 = 2`

∴ The elasticity of demand for p = 80 is η = 2.

Concept: Application of Derivatives to Economics

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