This question attracted many candidates and few of them scored above average marks. The question required candidates to calculate total cost, average cost, marginal cost and profit at different levels of output of a firm. Most candidates were able to calculate the total cost and average cost in the (a) and (b) parts of the question but were unable to calculate marginal cost and profit in the (c) and (d) parts respectively. This made most of them to score average marks.
The candidates were expected to provide the following answers to obtain the maximum marks.
Given the cost equation of a firm as C = 24 + 3q
Where C = Total cost; q = quantity produced.
The total cost of producing
(a) (i) 12 units
C = 24 + (3 x 12)
= 24 + 36
= $60
(ii) 36 units
C = 24 + (3 x 36)
= 24 + 108
= $132
(b) (i) Average cost at 48 units
AC = TC
Q
TC = 24 + 3 (48)
= 24 + 144
= 168
48
= $3.50
(ii) Average cost at 58 units
AC = TC
Q
TC = 24 + 3 (58)
= 24 + 174
= 198
58
= $3.41
(c) (i) Marginal cost when 23 units are produced
MC = TC2 - TC1
Q2 – Q1
TC2 = 24+ 3(23) = $ 93.00
TC1 = 24+ 3(12) = $ 60.00
Q2 = 23 units
Q1 = 12 units
MC 23 = 93 - 60 = 33
23 - 12 11
= $3.00
(ii) Marginal cost at 36 units
MC 36 = TC36 – TC23
Q36 – Q23
TC36 = 24+ 3(36) = $ 132.00
TC23 = 24+ 3(23) = $ 93.00
Q36 = 36 units
Q23 = 23 units
MC 36 = 132 - 93 = 39
36 - 23 13
= $3.00
(d) (i) Profit = TR - TC
TR = $5 x 23 units = $115
TC = 24 + 3q = 24 + (3)(23)
= 24 + 69
= $ 93
Profit = $115 - $93 = $22
(ii) Profit = TR - TC
TR = $5 x 48 units = $240
TC = 24 +3(48)
= 24 + 144
= $168
Profit = $$240 - 168
= $72
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