The following table gives the total cost schedule of a firm. It is also given that the average fixed cost at 4 units of output is Rs 5. Find the , , , , and schedules of the firm for the corresponding values of output.
| (Rs) | |
|---|---|
| 1 | 50 |
| 2 | 65 |
| 3 | 75 |
| 4 | 95 |
| 5 | 130 |
| 6 | 185 |
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Start your 14-day free trial to unlock the full solution →Given total cost and one piece of information about average fixed cost, we can recover the entire cost structure: fixed cost remains constant at all output levels, variable cost is the residual, and the per-unit averages and marginal cost follow by division and differencing.
The logic of cost decomposition
Total cost splits into two components: the part that does not change with output (fixed cost, like rent or a manager's salary) and the part that does (variable cost, like raw materials and hourly wages). Mathematically,
Fixed cost is the same whether you produce one unit or six; variable cost starts at zero when output is zero and rises as production expands. Once we know , everything else falls into place: is simply , average fixed cost is , average variable cost is , short-run average cost (also called or ) is , and short-run marginal cost is the increment in total cost when output rises by one unit, .
The question hands us a single anchor: at , average fixed cost is Rs 5. That tells us
Because fixed cost never changes, at every level of output. Now we can fill in the rest.
Step-by-step construction of the schedules
For :
: not defined for the first unit in this table (no prior output to compare), though one could interpret it as the change from zero output; we'll compute it from onward.
For :
For :
For :
(matches the given information)
For :
For :
Notice that falls continuously as output rises—fixed cost is being spread over more units. Meanwhile first falls (from 15 to 10), then rises sharply, a pattern consistent with diminishing marginal returns in the short run.
The complete cost schedules …
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