Advertisements
Advertisements
Question
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
Advertisements
Solution
`"dc"/("d"x)` = 100 – 10x + 0.1x2 and k = ₹ 500
dc = (100 – 10x + 0.1 x2) dx
Integrating on both sides,
`int "dc" = int(100 - 10x + 0.1x^2) "d"x`
C = `100x - 10(x^2/2) + 0.1(x^3/3) + "k"`
Total cost C = `100x - 5x^2 + 0.1(x^3/3) + 500`
Average cost A.C = `"C"/x = (100x - 5x^2 + 0.1(x^3/3) + 500)/x`
A.C = `100 - 5x + 0.1(x^2/3) + 500/x`
A.C = `100 - 5x + x^2/30 + 500/x`
APPEARS IN
RELATED QUESTIONS
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 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
If MR = 20 – 5x + 3x2, Find total revenue 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
The demand and supply functions under perfect competition are pd = 1600 – x2 and ps = 2x2 + 400 respectively. Find the producer’s surplus
The demand equation for a products is x = `sqrt(100 - "p")` and the supply equation is x = `"P"/2 - 10`. Determine the consumer’s surplus and producer’s surplus, under market equilibrium
Choose the correct alternative:
The marginal cost function is MC = `100sqrt(x)`. find AC given that TC = 0 when the output is zero is
A manufacture’s marginal revenue function is given by MR = 275 – x – 0.3x2. Find the increase in the manufactures total revenue if the production is increased from 10 to 20 units
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
