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...
Question 1 Report
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.
Answer Details
Given the cost equation \(C = 20 + 2q\) (in Naira), where \(C\) is total cost and \(q\) is output.
(a) Total cost
- (i) 12 units: \(C = 20 + 2(12) = 20 + 24 = \text{N}44\)
- (ii) 36 units: \(C = 20 + 2(36) = 20 + 72 = \text{N}92\)
(b) Average cost \(\left(AC = \dfrac{C}{q}\right)\)
- (i) 48 units: \(C = 20 + 2(48) = 116\); \(AC = \dfrac{116}{48} = \text{N}2.42\)
- (ii) 58 units: \(C = 20 + 2(58) = 136\); \(AC = \dfrac{136}{58} = \text{N}2.34\)
(c) Marginal cost
Marginal cost is the rate of change of total cost, \(MC = \dfrac{dC}{dq} = 2\). Because the coefficient of \(q\) is constant, \(MC = \text{N}2\) at every output.
- (i) 23 units: \(MC = \text{N}2\)
- (ii) 36 units: \(MC = \text{N}2\)
(d) Profit in perfect competition, price = N5
\(\text{Profit} = TR - TC = 5q - (20 + 2q) = 3q - 20\).
- (i) 23 units: \(TR = 5\times 23 = 115\), \(TC = 20 + 46 = 66\), Profit \(= 115 - 66 = \text{N}49\)
- (ii) 48 units: \(TR = 5\times 48 = 240\), \(TC = 20 + 96 = 116\), Profit \(= 240 - 116 = \text{N}124\)
Download The App On Google Playstore
Everything you need to excel in your exams
