8a.Profit Maximization by a competitive firm: a. Cost and Revenue: Total, Average and Marginal
Costs
The cost of producing any level of output is determined by the quantity of inputs used, and the price per unit the firm must pay for them.
We need to distinguish between 3 types of costs: Total, Average and Marginal
The Total Cost (TC) of production is the sum of Total Fixed Costs (TFC) and Total Variable Costs (TVC) of production.
TC = TFC + TVC
Output (Q) / TC / TFC / TVC0 / 3 / 3 / 0
1 / 4 / 3 / 1
2 / 6 / 3 / 3
3 / 9 / 3 / 6
4 / 13 / 3 / 10
5 / 18 / 3 / 15
6 / 24 / 3 / 21
7 / 31 / 3 / 28
Table 8.a.1Total Costs for Firm X
As seen in table 8.a.1, total cost is the sum of total fixed costs and total variable costs.
Total Fixed Costs: We assume the total fixed cost to be $3. Since this does not change with output, it is a horizontal line in figure 8.a.2.
Total Variable Costs: With zero output, there will be no use of variable factors. Hence at output 0, TVC is 0. Thus the TVC curve starts from the origin. (refer to figure 8.a.2)
Total Cost: Since TC = TVC + TFC, the TC curve is the TVC curve shifted upwards by the TFC = $3. (refer to figure 8.a.2
Figure 8.a.2
Average Cost(AC) is defined as the cost per unit of production, or total cost divided by the quantity of output produced. AC = TC / Q
As illustrated in table 8.a.3, the average cost is the total cost divided by the output. Thus, the average cost of producing the 1st unit of output is $4/$1 = $4. The average cost of producing the 2nd unit of output is $6/$2= $3.
Like total cost, average cost can be divided into average variable cost and average fixed cost. Average cost can be defined as the sum of average variable cost (AVC = TVC/Q) and average fixed cost (AFC = TFC / Q):
AC = AFC + AVC
Average Fixed Cost = TFC/ Q. When output increases, AFC falls because TFC is a constant at any output level
Average Variable Cost = TVC/Q. AVC may increase, fall or remain constant as output changes. It depends on whether output increases at a faster or slower rate than TVC.
In the diagram above, we can see that ATC is always above AVC curve at any output level by a vertical distance = AFC since ATC = AVC + AFC. As the level of output increases, AFC falls continuously as TFC is divided by larger output levels. AVC approaches ATC but never equals it because AFC is never zero.
Marginal Cost (MC) is defined as the extra cost of producing one more extra unit of output. It is the change in total cost for a one unit increase in output.
MC= ∆TC/∆Q
For example, as illustrated in table 8.a.3, we can see that the MC for producing the 1st unit of output is 1 (Cost of producing the second unit of output, $4 – Cost of producing the first unit of output, $3). The MC for producing the 2nd unit of output is 2 (Cost of producing the third unit of output, $6 – cost of producing the second unit of output, $4)
Output (Q) / TC / AC / TFC / AFC / TVC / AVC / MC0 / 3 / undefined / 3 / undefined / 0 / Undefined / -
1 / 4 / 4 / 3 / 3 / 1 / 1 / 1
2 / 6 / 3 / 3 / 1 / 3 / 0.50 / 2
3 / 9 / 3 / 3 / 1 / 6 / 2 / 3
4 / 13 / 3.25 / 3 / 0.75 / 10 / 2.50 / 4
5 / 18 / 3.60 / 3 / 0.60 / 15 / 3 / 5
6 / 24 / 4 / 3 / 0.50 / 21 / 3.50 / 6
7 / 31 / 4 / 3 / 0.43 / 29 / 4.14 / 7
Table 8.a.3 Fixed, Average and Marginal Costs for Firm X
Figure 8.a.4 Average and Marginal cost curves
In Figure 8.a.4, the marginal cost curve cuts the AC curve along its minimum point. As the marginal cost is below the average cost, the average cost must fall, and when the marginal cost is above the average cost, the average cost must rise. When the marginal cost is equal to the average cost (intersection point of MC and AC curve), the average cost is constant.
The average variable cost curve approaches average cost curve because the average fixed cost decreases as output increases.
Revenue
The revenue derived from any level of output is the amount of price the company can get multiplied by the quantity sold. It is the earnings the firm gets per period of time from the sale of a given quantity of output (Q).
As with costs, we need to distinguish between the 3 types of revenue: Total revenue (TR), Average Revenue (AR) and Marginal Revenue (MR).
Total Revenue: is the firm’s total earnings in a given period of time from the sale of a given quantity of output (Q). If the firm can sell 7units (Q) per month at price $4 each (P), its monthly total revenue will be 7x$4 = $28 (refer to table 8.a.4)
TR= P x Q
Average Revenue is the amount that the firm will get for each unit sold:
AR= TR/Q
For a competitive market where all producers are price takers, the AR will be equals to the price of the good at equilibrium in the market. This is also equals to the demand curve of the market. Looking at table 8.a.5, the average revenue at output 2 is the total revenue at output 2 divided by the output of 2 ($8/2 = $4).
Marginal Revenue is the additional revenue that the firm earns from the sale of one more unit of the good. If the firm gains $4 from the sale of one more unit of its good, its MR = $4.
MR= ∆TR/∆Q
Output / Price / TR / AR / MR0 / 4 / 0 / - / -
1 / 4 / 4 / 4 / 4
2 / 4 / 8 / 4 / 4
3 / 4 / 12 / 4 / 4
4 / 4 / 16 / 4 / 4
5 / 4 / 20 / 4 / 4
6 / 4 / 24 / 4 / 4
7 / 4 / 28 / 4 / 4
Table 8.a.5 Total, Average and Marginal Revenue for Firm X
Combining both concepts, we can come up with a table like 8.a.6.
Output / Price / TC / TR / Profit / AC / TFC / AFC / TVC / AVC / MC / MR0 / 4 / 3 / 0 / -3 / - / 3 / - / 0 / - / - / -
1 / 4 / 4 / 16 / 12 / 4 / 3 / 3 / 1 / 1 / 1 / 4
2 / 4 / 6 / 24 / 18 / 3 / 3 / 1 / 3 / 1.50 / 2 / 4
3 / 4 / 9 / 36 / 27 / 3 / 3 / 1 / 6 / 2 / 3 / 4
4 / 4 / 13 / 52 / 39 / 3.25 / 3 / 0.75 / 10 / 2.50 / 4 / 4
5 / 4 / 18 / 72 / 54 / 3.60 / 3 / 0.60 / 15 / 3 / 5 / 4
6 / 4 / 24 / 96 / 72 / 4 / 3 / 0.50 / 21 / 3.50 / 6 / 4
7 / 4 / 31 / 124 / 93 / 4.43 / 3 / 0.43 / 29 / 4.14 / 7 / 4
Table 8.a.6 Cost and Revenues for Firm X
Profit is defined as the amount earned after subtracting the cost needed. Thus profit at output 3 is $36-$9 = $27
∏ = TR – TC
We can put the AC, AVC, MC and MR curves together to illustrate the profit maximization condition.
Figure 8.a.7 Finding the profit maximization level
The profit maximization level is the point where the MC curve cuts the MR curve. Thus, profit maximization level is at the output where MC = MR.
The unit of output where MR>MC should be produced. By producing this additional unit, the firm is gaining more in revenue (MR) from its sale than adding to its costs (MC) of producing it. As long as MR > MC, profit can be increased by increasing production.
However, if MR<MC, the firm should not produce that unit. It adds more costs than revenue. Hence, as long as MC>MR, cutting back on production increases profit.
Practice questions
1a) Complete the following table of costs for a firm
Output / TC ($) / AC ($) / MC ($)0 / 55 / -
1 / 85
2 / 110
3 / 130
4 / 40
5 / 42
6 / 280
b) How much is the total fixed cost at output 0?
c) How much is the average fixed cost at an output of 4?
d) How much is the total variable cost at an output of 3?
e) How much is the average variable cost at an output of 6?
Answer:
a)
Output / TC ($) / AC ($) / MC ($)0 / 55 / - / -
1 / 85 / 85 / 30
2 / 110 / 55 / 25
3 / 130 / 43.333 / 20
4 / 160 / 40 / 30
5 / 210 / 42 / 50
6 / 280 / 46.667 / 70
b) $55
c) $55 / 4 = $13.75
d) $130 - $55 = $25
e) ($280-$55) / 6 = $37.50
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