Advertisements
Advertisements
Question
For the demand function x = `25/"p"^4`, 1 ≤ p ≤ 5, determine the elasticity of demand.
Advertisements
Solution
The demand function, x = `25/"p"^4`, 1 ≤ p ≤ 5
The elasticity demand, ηd = `- "p"/x * "dx"/"dp"`
x = `25/"p"^4`
x = 25 × p-4
`"dx"/"dp" = (25)(-4)"p"^(-4-1)`
`= 25 xx -4 xx "p"^(-5)`
`= 25 xx (-4)xx1/"p"^5`
Hint for differentiation
`"d"/"dx"(1/"x"^"n") = "-n"/("x"^("n + 1"))`
x = `25/"p"^4`
`"dx"/"dp" = 25((-4)/"p"^5)`
∴ ηd = `- "p"/x * "dx"/"dp"`
`= (-"p")/(25/"p"^4) xx 25 xx (-4)xx1/"p"^5`
`= (-"p"^5)/25 xx 25 xx (-4) xx 1/"p"^5` = 4
APPEARS IN
RELATED QUESTIONS
A firm produces x tonnes of output at a total cost of C(x) = `1/10x^3 - 4x^2 - 20x + 7` find the
- average cost
- average variable cost
- average fixed cost
- marginal cost and
- marginal average cost.
The total cost of x units of output of a firm is given by C = `2/3x + 35/2`. Find the
- cost when output is 4 units
- average cost when output is 10 units
- marginal cost when output is 3 units
Revenue function ‘R’ and cost function ‘C’ are R = 14x – x2 and C = x(x2 – 2). Find the
- average cost
- marginal cost
- average revenue and
- marginal revenue.
Find the elasticity of demand in terms of x for the following demand laws and also find the value of x where elasticity is equal to unity.
p = a – bx2
The demand curve of a commodity is given by p = `(50 - x)/5`, find the marginal revenue for any output x and also find marginal revenue at x = 0 and x = 25?
The demand function of a commodity is p = `200 - x/100` and its cost is C = 40x + 120 where p is a unit price in rupees and x is the number of units produced and sold. Determine
- profit function
- average profit at an output of 10 units
- marginal profit at an output of 10 units and
- marginal average profit at an output of 10 units.
If demand and the cost function of a firm are p = 2 – x and C = -2x2 + 2x + 7 then its profit function is:
If the demand function is said to be inelastic, then:
Relationship among MR, AR and ηd is:
Instantaneous rate of change of y = 2x2 + 5x with respect to x at x = 2 is:
