The cost function for a certain commodity is $C(x)=3+2x-\frac{1}{4} x^2$. Write the various cost components (TC, TFC, TVC, AC, AFC, AVC) when 4 items are produced. Verify your result.
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → $TC=₹7, TFC=₹3, TVC=₹4, AC=₹1.75, AFC=₹0.75, AVC=₹1$
Total cost TC or $C(x) = 3 + 2x-\frac{1}{4}x^2$
Total fixed cost, $TFC = \left.C(x)\right|_{x = 0} = 3$
Total variable cost, $TVC=2x-\frac{1}{4}x^2$
Average cost, $AC=\frac{C(x)}{x}=\frac{3}{x}+2-\frac{1}{4}x$
Average fixed cost, $AFC=\frac{TFC}{x}=\frac{3}{x}$
Average variable cost, $AVC=\frac{TVC}{x}=2-\frac{1}{4}x$
When $x = 4$, we get
Total cost = $C(4) = 3 + 2 × 4-\frac{1}{4}×4^2=7$
Total fixed cost $TFC = 3$
Total variable cost $TVC = 2 × 4-\frac{1}{4}×4^2=7$
We see that $TC = 7=3+4= TFC + TVC$
Average cost $AC =\frac{3}{4} +2-\frac{1}{4}×4=1\frac{3}{4}$
Average fixed cost $AFC =\frac{3}{4}$
Average variable cost $AVC = 2-\frac{1}{4}×4=1$
We see that $AC=1\frac{3}{4}=\frac{3}{4}+1=AFC+AVC$