Question

Illustrate the relation between Marginal Cost (MC), Average Total Cost (ATC),
Average Variable Cost (AVC) and Average Fixed Cost (AFC) curves. Given a total
cost function,
TC(Q) = 7Q2 + 5Q + 75
where Q represents quantity of output produced. Find the expression for Variable cost
(VC), Fixed cost (FC), AVC, AFC and ATC.

Answer 1

Answer:

While the total cost of production helps firms understand the overall expenses incurred, the average costs help identify the expenditures involved in manufacturing a single unit. In this article, we will look at the short run average costs and marginal costs of production.

Short Run Average Costs

1. Average Fixed Cost (AFC)

The average fixed cost is the total fixed cost divided by the number of units produced. Hence, if TFC is the total fixed cost and Q is the number of units produced, then

AFC = \frac {TFC}{Q}

Therefore, AFC is the fixed cost per unit of output.

Example: The TFC of a firm is Rs. 2,000. If the output is 100 units, the average fixed cost is,

AFC = \frac {TFC}{Q} = \frac {2000}{100} = Rs. 20

If the output is increased to 200 units, then

AFC =\frac {TFC}{Q} = \frac {2000}{200}= Rs. 10

Since TFC is constant, any increase in output decreases the AFC. Note that, while the AFC can become really small, it is never zero.

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2. Average Variable Cost (AVC)

The second aspect of short-run average costs is an average variable cost. Average variable cost is the total variable cost divided by the number of units produced. Hence, if TVC is the total fixed cost and Q is the number of units produced, then

$$AVC =\frac {TVC}{Q}$$

Therefore, AVC is the variable cost per unit of output.

Usually, the AVC falls as the output increases from zero to normal capacity output. Beyond the normal capacity, the AVC rises steeply due to the operation of diminishing returns.

3. Average Total Cost (ATC)

The average total cost is the sum of the average variable cost and the average fixed costs. That is,

ATC = AFC + AVC

In other words, it is the total cost divided by the number of units produced.

The diagram below shows the AFC, AVC, ATC, and Marginal Costs (MC) curves:

Answer 2

Cost refers to the obligation incurred by the firm for producing any given level of output.

Explanation:

Now we will discuss various types of costs and their relationships .

• AVERAGE FIXED COST: The average fixed cost is the per unit cost of the fixed factors. It is obtained by dividing the total fixed cost with the total unit of output produced.

Symbolically $AFC= TFC\div Q$

The average fixed cost falls as the output increases because the numerator remains the same while the denominator increases. For the very small output average fixed cost is high and for large output it is low.

The slope of the AFC curve is downward from left to right showing continuous falls in average fixed cost as the output increases. The AFC curve never touches the x-axis average fixed cost cannot be zero.

• AVERAGE VARIABLE COST : Average variable cost is the per unit cost of the variable factors of production.

Symbolically $AVC= TVC\div Q$

The average variable cost curve is the U-shaped. It means that the AVC curve first falls, reaches its minimum and then start rises. The u shape of AVC follows directly from law of variable proportion.

• AVERAGE TOTAL COST : Average total cost or simply the average cost is the per unit cost of both the fixed and variable factors of production . It is obtained by dividing the total cost with the total unit of output.

Symbolically $ATC= TC\div Q$

Average total cost curve is the vertical summation of average fixed cost curve and average variable cost cost curves. It is U shaped which indicates the the if falls initially, reaches its minimum and then starts increasing.

• MARGINAL COST : Marginal cost is the addition to total cost as one more unit of output is produced.

Symbolically $MC= \Delta TC\div \Delta Q$

Marginal cost curve is the U shaped. As the output increases the marginal cost curve slopes downward, reaches its minimum and then start sloping upward.

From the cost function in the question

Variable cost = $7Q^{2}+5Q$

Fixed cost = $75$

Average variable cost = $7Q+5$

Average fixed cost = $75\div Q$

Average total cost =$7Q+5+75\div Q$