a.
i. Table 1 below represents the output levels of a firm producing hand sanitizer. Use the information to answer the questions that follow.
Table 1
| Output (units) | 0 | 10 | 18 | 28 | 36 | 45 |
If the cost function of the firm is given as C = 30 + 4q, where C is the total cost and q is the units produced, calculate the:
total cost in dollars of producing:
18 units
ii. Table 1 below represents the output levels of a firm producing hand sanitizer. Use the information to answer the questions that follow.
Table 1
| Output (units) | 0 | 10 | 18 | 28 | 36 | 45 |
If the cost function of the firm is given as C = 30 + 4q, where C is the total cost and q is the units produced, calculate the:
total cost in dollars of producing:
36 units
b.
i. Average costs in dollars of producing:
28 units
ii. Average costs in dollars of producing:
45 units
c. What is the marginal cost in dollars of producing 28 units?
d. Determine the profit made from producing 45 units when the market price is fixed at $5.00 per unit.
e. Determine the fixed cost of the firm. Explain your answer.
Explanation
ai.
C = 30 + 4q
when q = 18units
C = 30 + 4(18)
= 30 + 72
= 102 dollars
aii.
C = 30 + 4q
when q = 36 units
C = 30 + 4(36)
= 30 + 144
= 174 dollars
bi.
At 28 units
Average cost = \(\frac{Total Cost}{Quantity}\)
NOTE: TC = C = 30 + 4q
Therefore, AC =\(\frac{30+4q}{q}\)
= \(\frac{30+4(28)}{q}\)
=\(\frac{142}{28}\)
= 5.07 dollars
bii.
At 45 units
Average cost = \(\frac{Total Cost}{Quantity}\)
NOTE: TC = C = 30 + 4q
Therefore, AC =\(\frac{30+4q}{q}\)
= \(\frac{30+4(45)}{45}\)
=\(\frac{210}{45}\)
= 4.66 dollars
c.
Marginal cost at 28 units produced = Total cost at 28 units - Total cost at 18 units
=\(\frac{30+4(28)-30+4(18)}{28-18}\)
= \(\frac{142-102}{10}\)
= $4.00
d.
Profit (π) = Total sales at 45 units - Total cost at 45 units
= ($5 x 45) - ( 30 + 4(45))
= 225 - 210
= $15.00
e.
Fixed cost is zero. Fixed cost is a cost that does not change, i.e when q = 0 then C = 30 +4(0)
= C = 30 + 4(0)
= 30 + 0
= $30