Question 2
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:
(a) total cost in dollars of producing:
(i) 18 units;
(ii) 36 units.
(b) average cost in dollars of producing:
- 28 units;
- 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.
This is the alternative data response question, majority of the candidates who attempted this question scored above average marks. Few of the candidates did not show the full workings required in arriving at the answers to the (a), (b), (c) and (d) parts of the question; some omitted formulae while others missed important steps in the calculations. Few candidates were unable to calculate marginal cost in the (c) part. Some other candidates could not also explain why fixed cost is $30 in the (e) part of the question thereby losing valuable marks.
The candidates were expected to provide the following answers to obtain the maximum mark.
(a) (i) TC18 = 30 + 4 (18) = 30 + 72 = $ 102
(ii) TC36 = 30 + 4 (36) = 30 + 144 = $ 174
(b) (i) AC28 = TC28 = 30 + 4 (28) = 142 = $ 5.07 or $ 5.1
28 28 28
(ii) AC45 = TC45 = 30 + 4 (45) = 210 = $ 4.67 or $ 4.7
45 45 45
(c) MC28 = TC28 – TC18 = (30 + 4 (28)) – (30 + 4 (18)) = 142 – 102 = $ 4.00
28 – 18 28 – 18 10
(d) Profit = TR – TC = ($ 5 × 45) – $ 210
= $ (225 – 210)
= $ 15
(e) Fixed cost of the firm is $ 30 when q = 0, C = 30 + 4 (0) = $ 30
or At output 0, Total Fixed Cost incurred is $ 30.