5 QUESTIONS ON MARGINAL, AVERAGE, FIXED, VARIABLE AND TOTAL COST

Being the diligent student that you are, your mind would have already been ingrained with the components of economic costs. 

These are fixed cost, the variable cost, marginal cost, the total cost, average variable cost, average fixed cost, average total cost. 

In this blog post, I am going to be teaching you how to solve each one of them by going through these examples


Question 1
Given that accompanying cost schedule of a firm producing oranges
Cost schedule

Find the total cost, average total cost, average fixed cost of producing 4, 9, 13, 16 oranges

Answer
Before I continue, note that all figure in this first question is in dollars.
 
Ok, let's solve for the total cost(TC) of producing each 4,9,13,16
 
Recalled that
 
$$TC=TVC+TFC$$
 
When producing:
 
4 oranges
$TC=20+25$
     $=45$
 
9 oranges
$TC=20+50$
    $=70$
 
13 oranges
$TC=20+ $75
     $=95$
At 
 
16 oranges 
$TC=20+100$
     $=120$

Now, let's solve for the average total cost(ATC)

Recall that

ATC=$\frac{TC}{OUTPUT}$

When producing:

4 oranges

ATC=$\frac{45}{4}=1.25$

9 oranges

ATC=$\frac{70}{9}=7.8$

13 oranges

ATC=$\frac{95}{13}=7.3$

16 oranges

ATC=$\frac{120}{16}=7.5$

Let's solve for the average fixed cost(AFC)
Recalled that:

$$AFC=\frac{\text{fixed cost}}{\text{output}}$$
When producing:
4 oranges
AFC=$\frac{20}{4}$
       =$5$
9 oranges
AFC=$\frac{20}{9}$
       =$2.2$
13 oranges
AFC=$\frac{20}{13}$
       =$1.5$
16 oranges
AFC=$\frac{20}{16}$
       =$1.25$

Question 2
A firm's average variable cost(AVC) is €360, its average total cost(ATC) is $\$400$ and its total fixed cost(TFC) is $\$4000$, find its output?
 
Answer
Recalled that, 
ATC=AVC+AFC
$\$400=\$360+AFC$

collect like term
$\$400-\$360=AFC$
$\$40=AFC$
$AFC=\$40$

Now, let's solve for the output
Recalled:
$$AFC=\frac{\text{fixed costs}}{\text{output}}$$
€40= $\frac{\$4000}{\text{output}}$

Cross multiply
$\$40\times \text{output}=\$4000$

Divide both side by €40
$\frac{\$40\times \text{output}}{40}=\frac{\$4000}{\$40}$
$\text{output}=\$100$

Question 3
A firm marginal cost is \(\$60\), its average total cost is \(\$100\), and its output is 1600 units. find the total cost of producing the 1601 units.
 
Answer
Recalled that
$$ATC=\frac{TC}{output}$$
$\$100=\frac{TC}{1600}$

Cross multiply
$TC=\$100\times 1600$
$TC=\$160000$
 
To find the total cost of the 1601 unit
We add MC(cost of producing one more unit) to the total cost
So 
TC of 1601 units=$\$160000+\$60$
                             $=\$160060$
Related post
Question 4
A firm's average variable cost and the average total cost are $\$225$ and $\$240$ respectively, and its output is 150 units. Find its total fixed cost.
 
Answer
First of all, Let's solve for the average fixed cost(AFC)
Recalled:
$ATC=AFC+AVC$

Ok, let make AFC the subject of the formula
Collect like term
$AFC=ATC-AVC$
$AFC=\$240-\$225$
       $=\$15$
Also, remember that
AFC=$\frac{TFC}{output}$
€15=$\frac{TFC}{150}$

cross multiply
TFC=$\$15\times 150=\$750$

Question 5
A firm's average total cost is $\$160$, its fixed cost is $\$2000$, and its output is 200 units, find its average variable cost.
 
Answer
Recalled that
ATC=AVC+AFC

But we need to find the value of AFC, 
$AFC=\frac{\text{fixed cost}}{\text{output}}$
$AFC=\frac{\$2000}{200}$
       $=\$10$

Now, let's solve for AVC
$\$160=AVC+\$10$

collect like terms
$\$160-\$10=AVC$
$\$150=AVC$
$AVC=\$150$

I hope with this, you can now calculate any question on the components of economic costs. Please, if you have any questions, suggestions, feel free to tell me in the comment box.
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