Advertisements
Advertisements
प्रश्न
For the demand function x = `25/"p"^4`, 1 ≤ p ≤ 5, determine the elasticity of demand.
उत्तर
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
संबंधित प्रश्न
Find the elasticity of supply for the supply function x = 2p2 + 5 when p = 3.
For the demand function p = 550 – 3x – 6x2 where x is quantity demand and p is unit price. Show that MR =
The total cost function y for x units is given by y = 3x`((x+7)/(x+5)) + 5`. Show that the marginal cost decreases continuously as the output increases.
Find the price elasticity of demand for the demand function x = 10 – p where x is the demand p is the price. Examine whether the demand is elastic, inelastic, or unit elastic at p = 6.
Find the equilibrium price and equilibrium quantity for the following functions.
Demand: x = 100 – 2p and supply: x = 3p – 50.
The total cost function for the production of x units of an item is given by C = 10 - 4x3 + 3x4 find the
- average cost function
- marginal cost function
- marginal average cost function.
Find the elasticity of supply when the supply function is given by x = 2p2 + 5 at p = 1.
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:
A company begins to earn profit at:
