Advertisements
Advertisements
Question
The supply function of certain goods is given by x = a`sqrt("p" - "b")` where p is unit price, a and b are constants with p > b. Find elasticity of supply at p = 2b.
Advertisements
Solution
Given that x = a`sqrt("p" - "b")`
Elasticity of supply: ηs = `"p"/x * "dx"/"dp"`
x = a`sqrt("p" - "b")`
`"dx"/"dp" = "a"(1/(2sqrt "p - b"))`
ηs = `"p"/x * "dx"/"dp"`
`= "p"/("a"sqrt("p" - "b")) xx "a" xx 1/(2sqrt("p" - "b"))`
`= "p"/(2("p - b"))`
Hint for differentiation
Use y = `sqrtx`
`"dy"/"dx" = 1/(2sqrtx)`
(or) x = `"a"sqrt("p - b")`
x = `"a"("p - b")^(1/2)`
`"dx"/"dp" = "a" * 1/2 ("p - b")^(1/2 - 1)`
`= "a"/2 ("p - b")^(- 1/2)`
`= "a"/2 1/(sqrt ("p - b"))`
When p = 2b, Elasticity of supply: ηs = `"2b"/(2("2b" - "b")) = "2b"/"2b" = 1`
APPEARS IN
RELATED QUESTIONS
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
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 – bx)2
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
Find the elasticity of supply for the supply function x = 2p2 + 5 when p = 3.
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.
For the demand function p x = 100 - 6x2, find the marginal revenue and also show that MR = p`[1 - 1/eta_"d"]`
Average fixed cost of the cost function C(x) = 2x3 + 5x2 – 14x + 21 is:
If the average revenue of a certain firm is ₹ 50 and its elasticity of demand is 2, then their marginal revenue is:
Profit P(x) is maximum when
