コストの恒等式、平均曲線および限界曲線
導入済み| English | 意味 |
|---|---|
| marginal cost/ˈmɑːdʒɪnl kɒst/ | 限界コスト |
| average fixed cost/ˈævrɪdʒ fɪkst kɒst/ | 固定費平均額 |
A decision you can investigate
- A higher total bill need not mean a higher cost per unit. An additional unit below the existing average pulls the average down.
- Define the denominator and compare the right cost measures.
Build the explanation
- TC=TFC+TVC. At positive Q, ATC=TC/Q, AFC=TFC/Q and AVC=TVC/Q, so ATC=AFC+AVC. MC=ΔTC/ΔQ; with unchanged fixed cost it also equalsΔTVC/ΔQ. Fixed costs stay unchanged over the relevant short-run range, so AFC declines as positive output rises. Variable costs depend on activity; they need not be proportional to output.
- An MC below an average cost pulls that average down; MC above it pushes the average up. In a smooth interior model MC crosses AVC and ATC at their respective minima. Do not interchange total and average curves. Short-run curves hold some capacity fixed, whereas LRAC describes the lowest achievable average cost when the firm can choose its input scale. A short-run operating point need not be the cheapest long-run scale.
Work through the evidence
- A fictional firm has TFC60. At Q10, TVC140 gives TC200, AVC14, AFC6 and ATC20. At Q12, TVC168 gives TC228, AVC14, AFC5 and ATC19. The two-unit interval MC=(228−200)/(12−10)=14. ATC falls because this interval cost14 is below the starting average20; AVC stays14 because variable cost here is locally proportional.
- A separate smooth illustration uses TC=60+20Q−3Q²+0.2Q³. Then MC=20−6Q+0.6Q², AVC=20−3Q+0.2Q², AFC=60/Q and ATC=AVC+60/Q for Q>0. At Q10, MC20, AVC10, AFC6 and ATC16. AVC reaches8.75 at Q7.5 where MC also8.75. These smooth values are a different model from the earlier finite table, not data to splice together.
有限の例において、Q12でのATCはいくらですか？
難易度 1/5 · 100 コイン + 今日初回完了時に小ボーナス付与
TC228 を12 で割ると19 となる。
2単位の区間におけるMCは何か？
難易度 1/5 · 100 コイン + 今日初回完了時に小ボーナス付与
コストは2単位あたり28上昇し、単位あたりのコストは14となる。
平均総コストは、固定費をゼロで割ることで、生産量ゼロにおいて定義される。
難易度 1/5 · 100 コイン + 今日初回完了時に小ボーナス付与
平均コストには正の生産量が必要であり、ゼロにおける商は未定義である。
Test the limits
- At Q0, average costs are undefined because division by zero is not allowed; total fixed cost may still exist. Fixed means fixed over a specified period/output range, not unavoidable forever. A rent can become avoidable when a contract ends.
- Step-fixed capacity costs can jump; marginal costs then require the actual interval rather than a smooth derivative. MC intersects an average at a minimum only under appropriate smooth conditions; discontinuous data may straddle it. LRAC is not the same as a single SRATC curve. Compare feasible scales, input prices, technology and demand before interpreting low average cost as high profit.
滑らかな図におけるQ7.5 でのAVCは何か？
難易度 1/5 · 100 コイン + 今日初回完了時に小ボーナス付与
20−3×7.5+0.2×7.5²=8.75.
Apply and explain your answer
- Why does ATC fall while AVC remains14 in the finite example?
- Fixed cost60 is spread over more output: AFC falls6→5, while variable cost per unit remains14.
用語とそれぞれの意味を結びつけよ。
難易度 2/5 · 140 コイン + 今日初回完了時に小ボーナス付与
各用語を、その明示された経済的関係に用いること。
Use the terms precisely
- average fixed cost 平均固定成本: Fixed cost divided by positive output.
- marginal cost 边际成本: Change in total cost per additional output unit over a stated interval, or its derivative in a smooth model.
A fictional firm has TFC60. At Q10, TVC140 gives TC200, AVC14, AFC6 and ATC20. At Q12, TVC168 gives TC228, AVC14, AFC5 and ATC19. The two-unit interval MC=(228−200)/(12−10)=14. ATC falls because this interval cost14 is below the starting average20; AVC stays14 because variable cost here is locally proportional. A separate smooth illustration uses TC=60+20Q−3Q²+0.2Q³. Then MC=20−6Q+0.6Q², AVC=20−3Q+0.2Q², AFC=60/Q and ATC=AVC+60/Q for Q>0. At Q10, MC20, AVC10, AFC6 and ATC16. AVC reaches8.75 at Q7.5 where MC also8.75. These smooth values are a different model from the earlier finite table, not data to splice together.
At Q0, average costs are undefined because division by zero is not allowed; total fixed cost may still exist. Fixed means fixed over a specified period/output range, not unavoidable forever. A rent can become avoidable when a contract ends. Step-fixed capacity costs can jump; marginal costs then require the actual interval rather than a smooth derivative. MC intersects an average at a minimum only under appropriate smooth conditions; discontinuous data may straddle it. LRAC is not the same as a single SRATC curve. Compare feasible scales, input prices, technology and demand before interpreting low average cost as high profit.
TC=TFC+TVC. At positive Q, ATC=TC/Q, AFC=TFC/Q and AVC=TVC/Q, so ATC=AFC+AVC. MC=ΔTC/ΔQ; with unchanged fixed cost it also equalsΔTVC/ΔQ. Fixed costs stay unchanged over the relevant short-run range, so AFC declines as positive output rises. Variable costs depend on activity; they need not be proportional to output.