Question 3.21: A firm receives £2.5 per unit for a particular good. The fix......
A firm receives £2.5 per unit for a particular good. The fixed costs incurred are £44 while each unit produced costs £1.4.
(a) Write down the equations for (i) total revenue, and (ii) total cost.
(b) Calculate the break-even point algebraically.
(c) If the government imposes a tax of £0.70 per unit, recalculate the break-even point. Show the graphical solutions to parts (b) and (c) on the same diagram (using Excel).
(a) (i) TR = P × Q = 2.5Q
(ii) TC = FC + VC = 44 + 1.4Q
(b) Break-even occurs when TR = TC:
- Algebraically:
2.5Q = 44 + 1.4Q
1.1Q = 44
Q = 40
When Q = 40, then TR = TC = 100.
(c) If a tax per unit is imposed, either the total revenue function or the total cost function may be adjusted for the tax as follows:
- Algebraically:
The net revenue per unit is (price – tax): TR = (2.5 – 0.7)Q = 1.8Q
Break-even is at TR = TC→1.8Q = 44 + 1.4Q→Q = 110
- Graphically:
To show the break-even points on a graph, choose values of Q such as Q = 0 to Q = 160. Set up the table of points in Excel and plot the graph as shown in Figure 3.18. (Since the graph is a straight line, a minimum of two points is required.)
| A | B | C | D | E | F | |
| 1 | Q | 0 | 40 | 80 | 120 | 160 |
| 2 | TR (no tax) | 0 | 100 | 200 | 300 | 400 |
| 3 | TR (taxed) | 0 | 72 | 144 | 216 | 288 |
| 4 | TC | 44 | 100 | 156 | 212 | 268 |
