The table below represents the output level of a particular firm producing soft drinks. Use...
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