Question 2.9: A pumpkin grower has fixed production costs of £10 for the r......
A pumpkin grower has fixed production costs of £10 for the rent of a stall at a farmers’ market and variable production costs of £2 per pumpkin
(a) Write down the equation for the total cost function.
(b) Graph the total cost function
(a) FC = £10; while VC = £2 × Q, since to produce
1 unit VC = 2(1)
2 units VC = 2(2)
3 units VC = 2(3)
Q units VC = 2Q
That is, the total variable cost incurred in producing Q pumpkins is £2Q. With TC = FC + VC, the total cost incurred in producing Q pumpkins is
TC = 10 + 2Q
Note: This is the same as the line y = 10 + 2x, where y ≡ TC and x ≡ Q.
(b) Graphically, the TC function is a straight line, with costs measured on the vertical axis and units of the good produced on the horizontal axis. Since the vertical intercept = 10 (level of FC) and the slope = 2 are known, the total cost function may be plotted. Alternatively, total costs may be plotted by calculating at least two points on the line and joining these points. A number of points are calculated in Table 2.5 and then graphed in Figure 2.24
| Table 2.5 Fixed, variable and total costs | |||
| Q | Variable costs (at £2 per unit) | TC = FC + VC (TC = 10 + 2Q) | Point(Q, TC) (x, y) |
| 0 | 0 | TC = 10 + 0 = 10 | (0, 10) |
| 1 | 1(2) = 2 | TC = 10 + 2 = 12 | (1, 12) |
| 2 | 2(2) = 4 | TC = 10 + 4 = 14 | (2, 14) |
| 3 | 3(2) = 6 | TC = 10 + 6 = 16 | (3, 16) |
| 4 | 4(2) = 8 | TC = 10 + 8 = 18 | (4, 18) |
| 5 | 5(2) = 10 | TC = 10 + 10 = 20 | (5, 20) |
| 6 | 6(2) = 12 | TC = 10 + 12 = 22 | (6, 22) |
