Advertisements
Advertisements
Question
The marginal cost of production of a firm is given by C'(x) = `20 + x/20` the marginal revenue is given by R’(x) = 30 and the fixed cost is ₹ 100. Find the profit function
Advertisements
Solution
C'(x) = `20 + x/20`
Fixed cost k1 = ₹ 100
C(x) = `int "C"_1 (x) "d"x + "k"_1`
C = `int (20 + x/20) "d"x +"k"_1`
= `20x + x^2/40 + "k"_1`
= `20x + x^2/40 + 100`
R'(x) = 30
R(x) = `int "R'"(x) "d"x + "k"_2`
R = `int 30 "d"x + "k"_2`
R = `30 "d"x+ "k"_2`
When x = 0
R = 0
⇒ k2 = 0
∴ R = 30x
Profit function P = `"R" - "C"`
= `(30x) - (20x + x^2/40 + 100)`
∴ P = `10x - x^2/10 - 100`
APPEARS IN
RELATED QUESTIONS
A firm’s marginal revenue function is MR = `20"e"^((-x)/10) (1 - x/10)`. Find the corresponding demand function
The marginal cost function of a commodity is given by MC = `14000/sqrt(7x + 4)` and the fixed cost is ₹ 18,000. Find the total cost and average cost
If MR = 20 – 5x + 3x2, Find total revenue function
Calculate consumer’s surplus if the demand function p = 50 – 2x and x = 20
Choose the correct alternative:
When x0 = 2 and P0 = 12 the producer’s surplus for the supply function Ps = 2x2 + 4 is
Choose the correct alternative:
The producer’s surplus when the supply function for a commodity is P = 3 + x and x0 = 3 is
Choose the correct alternative:
The demand and supply function of a commodity are D(x) = 25 – 2x and S(x) = `(10 + x)/4` then the equilibrium price p0 is
Choose the correct alternative:
If the marginal revenue of a firm is constant, then the demand function is
A company has determined that marginal cost function for x product of a particular commodity is given by MC = `125 + 10x - x^2/9`. Where C is the cost of producing x units of the commodity. If the fixed cost is ₹ 250 what is the cost of producing 15 units
The price elasticity of demand for a commodity is `"p"/x^3`. Find the demand function if the quantity of demand is 3 when the price is ₹ 2.
