Sure! Let's solve this step-by-step.
1. Calculate Total Variable Cost (TVC):
The Total Variable Cost (TVC) is determined by multiplying the Average Variable Cost (AVC) by the total number of units produced.
[tex]\[
TVC = AVC \times \text{units produced}
\][/tex]
Given:
[tex]\[\text{AVC} = 10\][/tex]
[tex]\[\text{Units Produced} = 537\][/tex]
[tex]\[
TVC = 10 \times 537 = 5370
\][/tex]
2. Calculate Total Fixed Cost (TFC):
The Total Fixed Cost (TFC) is found by multiplying the Average Fixed Cost (AFC) by the total number of units produced.
[tex]\[
TFC = AFC \times \text{units produced}
\][/tex]
Given:
[tex]\[\text{AFC} = 8\][/tex]
[tex]\[\text{Units Produced} = 537\][/tex]
[tex]\[
TFC = 8 \times 537 = 4296
\][/tex]
3. Calculate Total Cost (TC):
The Total Cost (TC) is the sum of the total variable cost and total fixed cost.
[tex]\[
TC = TVC + TFC
\][/tex]
Using the values obtained:
[tex]\[
TC = 5370 + 4296 = 9666
\][/tex]
4. Calculate Total Revenue (TR):
In a perfectly competitive market, the price (P) is equal to the marginal cost (MC). The Total Revenue (TR) is found by multiplying the market price by the total number of units produced.
[tex]\[
TR = P \times \text{units produced}
\][/tex]
Given:
[tex]\(\text{MC} = 21\)[/tex], implying [tex]\(\text{P} = 21\)[/tex]
[tex]\(\text{Units Produced} = 537\)[/tex]
[tex]\[
TR = 21 \times 537 = 11277
\][/tex]
5. Calculate Profit:
Profit is the difference between the total revenue and the total cost.
[tex]\[
\text{Profit} = TR - TC
\][/tex]
Using the values obtained:
[tex]\[
\text{Profit} = 11277 - 9666 = 1611
\][/tex]
Thus, the profit for the firm is [tex]\( \text{1611} \)[/tex].
