It is known that cost of producing 100 units of a commodity is ₹250 and cost of producing 200 units is ₹300. Assuming that AVC is constant, find the cost function.
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → $C(x)=200+\frac{1}{2}x$
Let the total fixed cost TFC be a.
Let AVC constant = b
Then $TVC = (AVC) x = bx$
$∴ TC= TFC + TVC = a + bx$
Given that when $x = 100, TC = ₹250$ and when $x = 200, TC = ₹300$
$∴ a + 100b = 250$ ...(i)
$a + 200b = 300$ ...(ii)
Subtracting (i) from (ii),
$100b=50 ⇒ b=\frac{1}{2}$
Putting this value of b in (i),
$a + 100.\frac{1}{2}=250 ⇒a=200$
Hence, the cost function is $C (x) = 200 +\frac{1}{2}x$