Read a cost table in a fixed order
Read a cost table in a fixed order: this Effortless Math guide explains the topic in plain language, shows how it works through solved examples, and gives you free practice to try immediately, so the idea sticks instead of staying abstract.
Complete totals before averages and averages before decisions.
When a table omits several cells, begin with identities. Recover variable cost from VC=TC-FC, then divide by output to obtain AVC and ATC. Calculate MC last from the change in total cost between adjacent rows. This order keeps fixed cost from leaking into a marginal calculation. If output rises by two units rather than one, divide the total-cost change by two.
A blank zero-output row often reveals fixed cost. If TC at Q=0 is $120, then FC is $120. Use that value down the table. At Q=10 with TC of $300, VC is $180, AFC is $12, AVC is $18, and ATC is $30. Fill each identity before interpreting profit or shutdown.
| Step | Calculation | Built-in check |
|---|---|---|
| 1. Fixed cost | Read TC at zero output | Same FC at every row |
| 2. Variable cost | TC-FC | Usually zero at zero output |
| 3. Averages | Divide each total by Q | ATC=AFC+AVC |
| 4. Marginal cost | Δ TC/Δ Q | Equals Δ VC/Δ Q |
| 5. Decision | Compare with price or MR | Use AVC for shutdown, ATC for profit |
Next ask what changed. A higher lease payment raises fixed cost at every positive output, so TC, AFC, and ATC rise. VC, AVC, and MC do not. A higher per-unit material cost raises variable and marginal costs. Both events raise total cost, but they do not alter the next unit in the same way. That is why an option saying only “cost rises” can be true yet too incomplete to answer a curve-specific question.
Watch the quantity interval. If TC rises from $400 at 30 units to $460 at 33 units, the average marginal cost across those units is (460-400)/(33-30)=$20. Reporting $60 ignores that three units were added. Without intermediate rows, the separate MC of each unit cannot be recovered.
Reconstruct a row and decide
At 40 units, TC is $920 and fixed cost is $200. Then VC is $720, AFC is $5, AVC is $18, and ATC is $23. If price is $21, the firm covers AVC but not ATC: it operates in the short run and earns a $2-per-unit loss. The cost table supports both the operation and profit conclusions.
Do not round too early when values are close. Keep enough decimals to compare price with AVC or MR with MC, then round the final reported number. A premature rounded equality can change a discrete output decision.
After completing the table, scan for impossible relationships. ATC cannot be below AVC when fixed cost is positive. AFC cannot rise as quantity grows with constant fixed cost. MC from TC and VC changes must match. These audits catch transcription errors before they become economic conclusions.
Finally, separate average and marginal rows. An MC value comes from the gap leading into a quantity, while AVC and ATC are calculated at that quantity. The table may visually align them, but their formulas use different information.
Use the cost identity as an error check
At every positive output, ATC=AVC+AFC, so ATC must lie above AVC. If a table or calculated option violates that identity, it cannot be correct.
As output rises, average fixed cost will
- rise and then fall
- remain constant
- equal marginal cost
- become negative
- continually fall
continually fall The same fixed cost is divided across more units, causing average fixed cost to decline continuously.
Marginal cost is below average total cost. As output increases by one unit, average total cost must
- rise
- remain unchanged
- equal average fixed cost
- become negative
- fall
fall A marginal value below the current average pulls the average downward.
If marginal product is below average product but remains positive, adding a worker will
- reduce total product and average product
- raise total product but reduce average product
- raise both total product and average product
- leave total product unchanged
- make marginal product negative
raise total product but reduce average product A positive marginal product raises total product, but a marginal value below the current average pulls average product down.
When marginal product is greater than average product, average product must
- rise
- fall
- equal marginal product
- be negative
- remain fixed
rise A marginal value above the current average pulls the average upward.
Watch the idea in action
A focused video lesson from Matt Birch.
Reza is an experienced Math instructor and a test-prep expert who has been tutoring students since 2008. He has helped many students raise their standardized test scores--and attend the colleges of their dreams. He works with students individually and in group settings, he tutors both live and online Math courses and the Math portion of standardized tests. He provides an individualized custom learning plan and the personalized attention that makes a difference in how students view math.
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