The table below represents the output level of a particular firm producing soft drinks. Use the information in the table to answer the questions that follow.
output (units)
0
12
23
36
48
58
Give the cost equation of the firm in Naira as C = 20 + 2q where C is total cost and q is quantity produced, calculate: (a) The total cost of producing: (i) 12 units of output (ii) 36 units of output. (b) The average cost when: (i) 48 units were produced (ii) 58 units were produced. (c) The marginal cost when: (i) 23 units were produced (ii) 36 units were produced. (d) If the firm is operating in a perfectly competitive market and the market price is N5 per unit, determine the profit when: (i) 23-units are produced (ii) 48 units are produced.
Explanation
Given the cost equation of a firm as C = 20 + 2q, Where C = Total cost; q = quantity produced. The total cost of producing (a)(i) 12 units C = 20 + 2 (12) = 20 + (2 x 12) = 20 + 24 = #44 (ii) 36 units C = 20 + 2 (36), = 20 + (2 x (36) . = 20 + 72 =#92 ) (b)(i) Average cost at 48 units AC= \(\frac{T} {Q}\) TC = 20 + 2 (48) TC = 20 + 2 (2 x 48) = 20 + 96 = \(\frac{116} {48}\) = N2.42 48 (iii) Average cost at 58 units TC = 20 + 2(58), TC = 20 + ( 2 x 58) TC = 20 + 116 = N136 AC = \(\frac{136} {58}\) = 2.34 (c)(i) Marginal cost when 23 units are produced MC= \(\frac{TC_2 - TC_1}{q_2 - q_1}\) at 23 units, TC\(_2\) = N66 TC = N44 q\(_2\) = 23 units q\(_1\) - 12 units MC = \(\frac{66-44}{23-12}\) = \(\frac{22}{11}\) = 23 (d)(i) Profit = TR - TC TR = N5 x 23 units = N115, TC=20 +2q=20 +2 (23)=20 + 46 = N66 P = N115 - N66 = N49 (ii) TR = N 5 x 48 units = N240, TC = 20 + 2 (48) 20 + 96 = N116 P = N240 - N116 = N124
