Advertisements
Advertisements
Question
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
Solution
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
RELATED QUESTIONS
The elasticity of demand with respect to price for a commodity is given by `((4 - x))/x`, where p is the price when demand is x. Find the demand function when the price is 4 and the demand is 2. Also, find the revenue function
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 cost function of x units of output is `"a"/sqrt("a"x + "b")` and if the cost of output is zero. Find the total cost as a function of x
The demand function for a commodity is p = e–x .Find the consumer’s surplus when p = 0.5
Choose the correct alternative:
The given demand and supply function are given by D(x) = 20 – 5x and S(x) = 4x + 8 if they are under perfect competition then the equilibrium demand 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
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 marginal revenue function for a firm given by MR = `2/(x + 3) - (2x)/(x + 3)^2 + 5`. Show that the demand function is P = `(2x)/(x + 3)^2 + 5`
A company requires f(x) number of hours to produce 500 units. It is represented by f(x) = 1800x–0.4. Find out the number of hours required to produce additional 400 units. [(900)0.6 = 59.22, (500)0.6 = 41.63]
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.
