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
The marginal cost function of a product is given by `"dc"/("d"x)` = 100 – 10x + 0.1x2 where x is the output. Obtain the total and the average cost function of the firm under the assumption, that its fixed cost is ₹ 500
Find the revenue function and the demand function if the marginal revenue for x units is MR = 10 + 3x – x2
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
The demand function p = 85 – 5x and supply function p = 3x – 35. Calculate the equilibrium price and quantity demanded. Also, calculate consumer’s surplus
If the supply function for a product is p = 3x + 5x2. Find the producer’s surplus when x = 4
Choose the correct alternative:
If the marginal revenue function of a firm is MR = `"e"^((-x)/10)`, then revenue is
Choose the correct alternative:
When x0 = 5 and p0 = 3 the consumer’s surplus for the demand function pd = 28 – x2 is
Choose the correct alternative:
For a demand function p, if `int "dp"/"p" = "k" int ("d"x)/x` then k is equal to
For the marginal revenue function MR = 6 – 3x2 – x3, Find the revenue function and demand function
The demand equation for a product is Pd = 20 – 5x and the supply equation is Ps = 4x + 8. Determine the consumers surplus and producer’s surplus under market equilibrium
