Advertisements
Advertisements
प्रश्न
The demand function p = 85 – 5x and supply function p = 3x – 35. Calculate the equilibrium price and quantity demanded. Also, calculate consumer’s surplus
Advertisements
उत्तर
Demand function p = 85 – 5x
Supply function p = 3x – 35
W.K.T. at equilibrium prices pd = ps
85 – 5x = 3x – 35
85 + 35 = 3x + 5x
120 = 8x
⇒ x = `120/8`
∴ x = 15
When x = 15
p0 = 85 – 5(15)
= 85 – 75
= 10
C.S = `int_0^x` f(x) dx – x0p0
= `int_0^x` (85 – 5x) dx – (15)(10)
= `[5x - 5(x^2/2)]_0^15 - 150`
= `{85(15) - 5((15)^2/2) - [0]} - 150`
= `[1275 - (5(225))/2] - 150`
= `1275 - 1125/2 - 150`
= 1275 – 562.50 – 150
= 1275 – 712.50
∴ C.S = 562.50 units
APPEARS IN
संबंधित प्रश्न
The marginal cost function is MC = `300 x^(2/5)` and fixed cost is zero. Find out the total cost and average cost functions
If the marginal revenue function for a commodity is MR = 9 – 4x2. Find the demand function.
A firm’s marginal revenue function is MR = `20"e"^((-x)/10) (1 - x/10)`. Find the corresponding demand function
If the marginal cost (MC) of production of the company is directly proportional to the number of units (x) produced, then find the total cost function, when the fixed cost is ₹ 5,000 and the cost of producing 50 units is ₹ 5,625
Calculate the producer’s surplus at x = 5 for the supply function p = 7 + x
Under perfect competition for a commodity the demand and supply laws are Pd = `8/(x + 1) - 2` and Ps = `(x + 3)/2` respectively. Find the consumer’s and producer’s surplus
Choose the correct alternative:
The demand and supply functions are given by D(x) = 16 – x2 and S(x) = 2x2 + 4 are under perfect competition, then the equilibrium price x is
Choose the correct alternative:
The demand and supply function of a commodity are P(x) = (x – 5)2 and S(x) = x2 + x + 3 then the equilibrium quantity x0 is
For the marginal revenue function MR = 6 – 3x2 – x3, Find the revenue function and demand function
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
