Question 2.10b: The company that sells chicken snack boxes for £3.50 each ha......
The company that sells chicken snack boxes for £3.50 each has fixed costs of £800 per day and variable costs of £1.50 for each chicken snack box.
(a) Write down the equation for (i) total revenue, (ii) total costs, (iii) profit.
(b) Calculate the number of chicken snack boxes that must be produced and sold if the company is to break even.
(c) Graph the profit function. From the graph estimate the break-even quantity.
(a) (i) TR = 3.5Q, (ii) TC = 800 + 1.5Q, (iii) π = 3.5Q − (800 + 1.5Q) = 2Q − 800.
(b) The firm breaks even when TR = TC:
3.5Q = 800 + 1.5Q
2Q = 800
Q = 400
Alternatively, the firm breaks even when profit is zero: π = 2Q − 800 = 0; Q = 400.
(c) Profit is represented graphically by a straight line, π = 2Q − 800. It may be graphed by calculating values of π for any values of Q, e.g., Q = 0, 200, 400, 800. These points are calculated in Table 2.7 and then plotted in Figure 2.26.
| Table 2.7 | ||
| Q (compare to x) | π = 2Q − 800 (y = mx + c) | Point (Q, π) |
| 0 | π = 2(0) − 800 = −800 | (0,−800) |
| 200 | π = 2(200) − 800 = −400 | (200,−400) |
| 400 | π = 2(400) − 800 = 0 | (400, 0) |
| 800 | π = 2(800) − 800 = 800 | (800, 800) |
