Advertisements
Advertisements
Question
For the demand function p = 550 – 3x – 6x2 where x is quantity demand and p is unit price. Show that MR =
Advertisements
Solution
Given p = 550 – 3x – 6x2
Revenue, R = px = (550 – 3x – 6x2)x = 550x – 3x2 – 6x3
Marginal Revenue (MR) = `"d"/"dx"`(R)
`= "d"/"dx"` (550x – 3x2 – 6x3)
= 550 – 6x- 18x2
Now ηd = `- "p"/x * "dx"/"dp"`
p = 550 – 3x – 6x2
`"dp"/"dx"` = 0 - 3 - 12x
∴ ηd = `- "p"/x * 1/("dp"/"dx")`
`= - [(550 - 3x - 6x^2)/x] xx 1/((- 3 - 12x))`
`= (550 - 3x - 6x^2)/(-x) xx 1/((- 3 - 12x))`
`= (550 - 3x - 6x^2)/(3x + 12x^2)`
`therefore 1 - 1/eta_"d" = 1 - 1/(((550 - 3x - 6x^2)/(3x + 12x^2)))`
`= 1 - (3x + 12x^2)/(550 - 3x - 6x^2)`
`= (550 - 3x - 6x^2 - 3x - 12x^2)/(550 - 3x - 6x^2)`
`= (550 - 6x - 18x^2)/(550 - 3x - 6x^2)`
`therefore "p"[1 - 1/eta_"d"] = (((550 - 3x - 6x^2)(550 - 6x - 18x^2))/(550 - 3x - 6x^2))`
`= 550 - 6x - 18x^2` = MR
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
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 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.
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.
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 out the indicated elasticity for the following function:
p = xex, x > 0; ηs
Average fixed cost of the cost function C(x) = 2x3 + 5x2 – 14x + 21 is:
Instantaneous rate of change of y = 2x2 + 5x with respect to x at x = 2 is:
The demand function is always
