Fixed inputs, product and marginal cost
| English | 中文 | Pinyin · 拼音 |
|---|---|---|
| diminishing marginal returns/dɪˈmɪnɪʃɪŋ ˈmɑːdʒɪnl rɪˈtɜːnz/ | 边际报酬递减 | biān jì bào chóu dì jiǎn |
| marginal product/ˈmɑːdʒɪnl ˈprɒdʌkt/ | 边际产量 | biān jì chǎn liàng |
A decision you can investigate
- Adding a worker to a fixed workshop may initially improve teamwork. Later workers share crowded equipment. Total production can still rise even when each extra worker adds less.
- Diminishing marginal returns 边际报酬递减 are not falling total output or long-run diseconomies of scale.
Build the explanation
- The short run has at least one fixed input. Holding that input and technology constant, diminishing marginal returns occur when additional variable input eventually adds less extra output. Total product TP is total output; marginal product 边际产量 MP=ΔTP/Δinput; average product AP=TP/input. Falling positive MP means TP still rises, but more slowly. Negative MP would make TP fall; the two statements differ.
- With labour the only variable input and constant wage w, TVC=wL. Over a one-worker interval, MC=ΔTVC/ΔQ=w/MP; low marginal productivity means high marginal cost under these assumptions. AVC=w/AP for the stated labour-only variable costs. The total-product relation can be inverted to show the variable labour/cost required for an output. In the long run all inputs can vary; changing scale is different from adding labour to fixed capital.
Work through the evidence
- A fictional fixed workshop employs L0,1,2,3,4,5 with total output0,10,25,35,42,47. The successive marginal products are10,15,10,7,5: diminishing returns start after the second worker in this schedule. At L2, AP25/2=12.5; at L5, AP47/5=9.4. Output still rises35→42→47 while marginal product falls.
- With wage30 per worker, TVC at L2 is60 and at L5 is150. Successive interval marginal costs are30/10=3,30/15=2,30/10=3,30/7≈4.286 and30/5=6 per extra output unit. At L5, AVC150/47≈3.191, also30/9.4. Fixed costs do not enter these variable-cost calculations, but they do enter total/average total cost.
What is the fifth worker’s marginal product?
Total output increases47−42=5.
What is interval MC for the fifth worker at wage30?
Additional cost30 divided by additional output5 gives6.
Diminishing marginal returns require total product to decline.
Total product still increases while marginal product is positive.
Test the limits
- The inverse cost relationships require constant wage, comparable workers, labour as the only variable input and no output-measure changes. Material costs, overtime premiums or changing quality alter the calculation. Average product is not marginal product, and AP/AVC does not determine ATC without fixed costs.
- Diminishing returns describe a short-run input experiment. Long-run economies can coexist with short-run diminishing returns because capital can expand too. A lower wage changes costs without necessarily changing physical productivity; a technical improvement changes the product schedule. When using data, check the input interval and distinguish workers, hours and full-time equivalents before comparing MP.
What is AP at two workers?
Total output25 divided by labour2 equals12.5.
Apply and explain your answer
- Why does a fall in marginal product from7 to5 not imply total output falls?
- Both increments remain positive: total output rises42→47, but the fifth worker adds less than the fourth.
Match the terms to their meanings.
Use each term for its stated economic relationship.
Use the terms precisely
- marginal product: Extra output per additional unit of a specified input, other conditions stated.
- diminishing marginal returns: Eventually smaller output increments from additional variable input when another input and technology are fixed.
A fictional fixed workshop employs L0,1,2,3,4,5 with total output0,10,25,35,42,47. The successive marginal products are10,15,10,7,5: diminishing returns start after the second worker in this schedule. At L2, AP25/2=12.5; at L5, AP47/5=9.4. Output still rises35→42→47 while marginal product falls. With wage30 per worker, TVC at L2 is60 and at L5 is150. Successive interval marginal costs are30/10=3,30/15=2,30/10=3,30/7≈4.286 and30/5=6 per extra output unit. At L5, AVC150/47≈3.191, also30/9.4. Fixed costs do not enter these variable-cost calculations, but they do enter total/average total cost.
The inverse cost relationships require constant wage, comparable workers, labour as the only variable input and no output-measure changes. Material costs, overtime premiums or changing quality alter the calculation. Average product is not marginal product, and AP/AVC does not determine ATC without fixed costs. Diminishing returns describe a short-run input experiment. Long-run economies can coexist with short-run diminishing returns because capital can expand too. A lower wage changes costs without necessarily changing physical productivity; a technical improvement changes the product schedule. When using data, check the input interval and distinguish workers, hours and full-time equivalents before comparing MP.
The short run has at least one fixed input. Holding that input and technology constant, diminishing marginal returns occur when additional variable input eventually adds less extra output. Total product TP is total output; marginal product MP=ΔTP/Δinput; average product AP=TP/input. Falling positive MP means TP still rises, but more slowly. Negative MP would make TP fall; the two statements differ.