Advertisements
Advertisements
प्रश्न
The demand function for a commodity is p = e–x .Find the consumer’s surplus when p = 0.5
Advertisements
उत्तर
The demand function p = e–x
When p = 0.5
⇒ 0.5 = e–x
`1/2 = 1/"e"^x`
⇒ ex = 2
∴ x = log 2
∴ Consumer’s surplus
C.S = `int_0^x` (demand function) dx – (Price × quantity demanded)
= `int_0^log2 "e"^-x "d"x - (0.5) log 2`
= `(("e"^-x)/(-1))_0^log2 - 1/2 log 2`
= `((-1)/"e"^x)_0^log2 - 1/2 log 2`
= `((-1)/"e"^log2) - ((-1)/"e"^0) - 1/2 log 2`
= `(-1)/2 + ((-1)/"e"^0) - 1/2 log 2`
= `(-1)/2 + 1 - 1/2 log 2`
= `1/2 - 1/2 log 2`
C.S = `1/2 [1 - log 2]` units
APPEARS IN
संबंधित प्रश्न
A company receives a shipment of 500 scooters every 30 days. From experience, it is known that the inventory on hand is related to the number of days x. Since the shipment, I(x) = 500 – 0.03x2, the daily holding cost per scooter is ₹ 0.3. Determine the total cost for maintaining inventory for 30 days
Determine the cost of producing 200 air conditioners if the marginal cost (is per unit) is C'(x) = `x^2/200 + 4`
The marginal revenue (in thousands of Rupees) functions for a particular commodity is `5 + 3"e"^(- 003x)` where x denotes the number of units sold. Determine the total revenue from the sale of 100 units. (Given e–3 = 0.05 approximately)
If the marginal revenue function for a commodity is MR = 9 – 4x2. Find the demand function.
Find the revenue function and the demand function if the marginal revenue for x units is MR = 10 + 3x – x2
If MR = 14 – 6x + 9x2, Find the demand function
The demand function p = 85 – 5x and supply function p = 3x – 35. Calculate the equilibrium price and quantity demanded. Also, calculate consumer’s surplus
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 marginal revenue and marginal cost functions of a company are MR = 30 – 6x and MC = – 24 + 3x where x is the product, then the profit function is
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`
