Advertisements
Advertisements
Question
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?
Advertisements
Solution
Given that p = `(50 - x)/5`
Revenue, R = px
`= ((50 - x)/5)`x
`= (50x - x^2)/5`
`= 1/5` (50x – x2)
Marginal Revenue (MR) = `"d"/"dx"`(R)
= `"d"/"dx" 1/5 (50x - x^2)`
= `1/5 "d"/"dx" (50x - x^2)`
= `1/5 (50 - 2x)`
Marginal revenue when x = 0 is, MR = `1/5` (50 – 2 × 0)
`= 1/5 xx 50`
= 10
When x = 25, marginal revenue is MR = `1/5` (50 – 2 × 25)
`= 1/5 (50 - 50)`
= 0
APPEARS IN
RELATED QUESTIONS
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.
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.
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 equilibrium price and equilibrium quantity for the following functions.
Demand: x = 100 – 2p and supply: x = 3p – 50.
The demand and cost functions of a firm are x = 6000 – 30p and C = 72000 + 60x respectively. Find the level of output and price at which the profit is maximum.
If the demand function is said to be inelastic, then:
For the cost function C = `1/25 e^(5x)`, the marginal cost is:
Instantaneous rate of change of y = 2x2 + 5x with respect to x at x = 2 is:
