Advertisements
Advertisements
Question
Find out the indicated elasticity for the following function:
p = xex, x > 0; ηs
Solution
Given p = xex
Differentiating with respect to 'x' we get,
`"dp"/"dx" = x*e^x + e^x(1) = e^x (x + 1)`
`"dx"/"dp" = 1/(e^x(x + 1))`
Elasticity of demand
`eta_"d" = "p"/x * "dx"/"dp"`
`therefore eta_"d" = cancel(x e^x)/(cancel x) (1/(cancel(e^x) (x + 1)))`
`= 1/(x + 1)`
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 – bx)2
Show that MR = p`[1 - 1/eta_"d"]` for the demand function p = 400 – 2x – 3x2 where p is unit price and x is quantity demand.
Find the equilibrium price and equilibrium quantity for the following functions.
Demand: x = 100 – 2p and supply: x = 3p – 50.
The cost function of a firm is C = x3 – 12x2 + 48x. Find the level of output (x > 0) at which average cost is minimum.
Find out the indicated elasticity for the following function:
p = `10 e^(- x/3)`, x > 0; ηs
Instantaneous rate of change of y = 2x2 + 5x with respect to x at x = 2 is:
A company begins to earn profit at:
