Profit Maximization · 利润最大化
| English | 中文 | Pinyin · 拼音 |
|---|---|---|
| total revenue/ˈtəʊtl ˈrevənjuː/ | 总收入 | zǒng shōu rù |
| average revenue/ˈævrɪdʒ ˈrevənjuː/ | 平均收入 | píng jūn shōu rù |
| marginal revenue/ˈmɑːdʒɪnl ˈrevənjuː/ | 边际收入 | biān jì shōu rù |
| profit-maximizing rule/ˈprɒfɪt ˈmæksɪmaɪzɪŋ ruːl/ | 利润最大化法则 | lì rùn zuì dà huà fǎ zé |
The one rule every firm follows
- Make too little and you leave easy money on the table.
- Make too much and the last units cost more than they earn.
- Somewhere in between sits the quantity with the biggest profit.
- One simple rule finds it every time.
每家企业都遵守的一条规则
- 生产太少,等于把到手的钱留在桌上。
- 生产太多,最后几个单位的成本超过收益。
- 在两者之间,藏着利润最大的那个数量。
- 一条简单的规则,每次都能找到它。
Three revenue ideas
- Total revenue 总收入 (TR) is all the money from sales: $TR = P \times Q$.
- Average revenue 平均收入 (AR) is revenue per unit: $AR = \tfrac{TR}{Q}$ — this always equals the price.
- Marginal revenue 边际收入 (MR) is the extra revenue from one more unit: $MR = \tfrac{\Delta TR}{\Delta Q}$.
三个收入概念
- 总收入(total revenue,TR)是销售的全部收入:$TR = P \times Q$。
- 平均收入(average revenue,AR)是每单位收入:$AR = \tfrac{TR}{Q}$ —— 它总是等于价格。
- 边际收入(marginal revenue,MR)是多一个单位的额外收入:$MR = \tfrac{\Delta TR}{\Delta Q}$。
Marginal revenue is: · 边际收入是:
MR = ΔTR/ΔQ — the change in total revenue from one more unit sold. · MR = ΔTR/ΔQ——多卖一个单位引起的总收入变化。
Average revenue always equals the price of the good. · 平均收入总是等于商品的价格。
AR = TR/Q = (P × Q)/Q = P. · AR = TR/Q = (P × Q)/Q = P。
Produce where MR = MC
- The profit-maximizing rule 利润最大化法则: make the quantity where marginal revenue equals marginal cost.
- If $MR > MC$, the next unit earns more than it costs — keep going.
- If $MR < MC$, the next unit costs more than it earns — make less.
- Only at $MR = MC$ can profit no longer improve.
在 MR = MC 处生产
- 利润最大化法则(profit-maximizing rule):在边际收入等于边际成本的数量生产。
- 若 $MR > MC$,下一个单位赚的多于花的——继续。
- 若 $MR < MC$,下一个单位花的多于赚的——少做一些。
- 只有在 $MR = MC$ 处,利润才无法再提高。
Cost curves and the best quantity · 成本曲线与最佳数量
A firm maximises profit where marginal revenue meets marginal cost. Explore how the marginal-cost curve sets that best quantity. · 企业在边际收入与边际成本相遇处利润最大化。探索边际成本曲线如何决定这个最佳数量。
A firm maximises profit by producing the quantity where: · 企业通过在这样的数量生产来实现利润最大化:
At MR = MC profit can no longer improve — the profit-maximizing rule. · 在 MR = MC 处利润无法再提高——利润最大化法则。
At the current output, MR is greater than MC. The firm should: · 在当前产量下,MR 大于 MC。企业应该:
MR > MC means the next unit adds to profit, so keep producing until MR = MC. · MR > MC 表示下一个单位增加利润,所以继续生产直到 MR = MC。
Measure the profit
- Once you know the best quantity, measure profit with price and average total cost:
- Economic profit $= (P - ATC) \times Q$.
- If $P > ATC$ there is a profit; if $P = ATC$ the firm breaks even; if $P < ATC$ it makes a loss.
- $MR = MC$ finds the best quantity whether the firm is making a profit or the smallest possible loss.
衡量利润
- 一旦知道最佳数量,就用价格和平均总成本来衡量利润:
- 经济利润 $= (P - ATC) \times Q$。
- 若 $P > ATC$ 有利润;若 $P = ATC$ 盈亏平衡;若 $P < ATC$ 亏损。
- 无论企业是在盈利还是在把亏损降到最小,$MR = MC$ 都能找到最佳数量。
At its best quantity a firm makes Q = 50 units, with price P = 12 and average total cost ATC = 9. What is its economic profit? · 在最佳数量下企业生产 Q = 50 单位,价格 P = 12,平均总成本 ATC = 9。它的经济利润是多少?
Economic profit = (P − ATC) × Q = (12 − 9) × 50 = 150. · 经济利润 = (P − ATC) × Q = (12 − 9) × 50 = 150。
Economic profit at the best quantity equals (P − ______) × Q. · 最佳数量下的经济利润等于 (P − ______) × Q。
Per-unit profit is P − ATC; multiply by Q for total economic profit. · 单位利润是 P − ATC;乘以 Q 得到总经济利润。
Revenue: TR = P × Q, AR = P, and MR is the extra from one more unit. The profit-maximizing rule is MR = MC. Then measure profit as (P − ATC) × Q — positive if P > ATC, break-even if equal, a loss if below.
收入:TR = P × Q、AR = P,MR 是多一个单位的额外收入。利润最大化法则是 MR = MC。然后用 (P − ATC) × Q 衡量利润——P > ATC 为正,相等则盈亏平衡,低于则亏损。