尼克尔森微观经济学课件中文版ch09

eq,p < -1 （需求有弹性） eq,p = -1（单位弹性） eq,p > -1（需求无弹性） MR > 0 MR = 0 MR < 0
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The Inverse Elasticity Rule 逆弹性规则
• Because MR = MC when the firm maximizes profit, we can see that因为企业最大化其利润时，MR = MC ，我们可 以看到
eq,p
dq / q dq p dp / p dp q
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Marginal Revenue and Elasticity 边际收益和弹性
• This means that这意味着
q dp q dp 1 MR p p 1 p 1 e dq p dq q ,p
• if the demand is infinitely elastic, eq,p = - and marginal revenue will equal price如果需求是无限弹性的， eq,p = -，则 边际收益将等于价格
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Marginal Revenue and Elasticity 边际收益和弹性
d 2 d' (q ) 0 2 dq q q * dq q q *
• “marginal” profit must be decreasing at the optimal level of q“边际”利润在最优水平q一定是递减的
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Profit Maximization利润最大化
revenues & costs Profits are maximized when the slope of the revenue function is equal to the slope of the cost function 在收益函数的斜率等于成本函数斜率的点处，利润得以 最大化 C
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The Inverse Elasticity Rule 逆弹性规则
p MC 1 p eq,p
• If eq,p > -1, MC < 0 如果eq,p > -1, MC < 0 • This means that firms will choose to operate only at points on the demand curve where demand is elastic这意味着，企业会仅选择 在需求曲线上需求有弹性处运行
(q) = R(q) – C(q) = p(q)q –C(q)
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Output Choice产出决策
• The necessary condition for choosing the level of q that maximizes profits can be found by setting the derivative of the function with respect to q equal to zero 选择利润最大化的q水平的必要条件，可以由令函数对 q的导数为零推得
– examine the marginal profit obtainable from producing one more unit or hiring one additional laborer检验通过额外雇佣一单位劳动力或多生 产一单位产品，所能得到的边际利润
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Output Choice产出决策
• Most economists treat the firm as a single decisionmaking unit大多数经济学家把企业看做一个单一的决 策制定单位 – the decisions are made by a single dictatorial manager who rationally pursues some goal 决策是由理性地 追求某些目标的单个独裁管理者做出的 • usually profit-maximization（其目标）一般是利润 最大化
– seeks to maximize the difference between total revenue and total economic costs 寻求总收益和总经济成本之间差别的最大化
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Profit Maximization利润最大化
• If firms are strictly profit maximizers, they will make decisions in a “marginal” way 如果企业是严格的利润最大化者，它们会 以“边际”方式做出决定
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Example：Marginal Revenue and Profit Maximization 例：边际收益及利润最大化
• Suppose that the demand curve for a sub sandwich is假设对潜艇三明治 的需求函数为
q = 100 – 10p
• Solving for pቤተ መጻሕፍቲ ባይዱice, we get求解价格，我们得到
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Marginal Revenue and Elasticity 边际收益和弹性
• The concept of marginal revenue is directly related to the elasticity of the demand curve facing the firm边际收益的 概念与企业所面临的需求曲线的弹性直接相关 • The price elasticity of demand is equal to the percentage change in quantity that results from a one percent change in price需求的价格弹性等于由价格变动百分之一引起 的需求数量的变化百分比
dR d [ p(q ) q ] dp marginal revenue MR(q ) pq dq dq dq
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Marginal Revenue边际收益
• If a firm faces a downward-sloping demand curve, marginal revenue will be a function of output如果企业面临一个向下倾斜的 需求曲线，边际收益将是产出的函数 • If price falls as a firm increases output, marginal revenue will be less than price 如果价格随着企业增加产出而降低，那 么边际收益将小于价格
• To determine the profit-maximizing output, we must know the firm’s costs为了决定利润最大化的产出水平，我们 必须知道企业的成本 • If subs can be produced at a constant average and marginal cost of $4, then如果三明治的平均成本和边际 成本为$4 ，那么 MR = MC -q/5 + 10 = 4 q = 30
d dR dC ' (q ) 0 dq dq dq dR dC dq dq
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Output Choice产出决策
• To maximize economic profits, the firm should choose the output for which marginal revenue is equal to marginal cost 为了最大化经济利 润，企业会选择边际收益等于边际成本的产 出水平
p = -q/10 + 10
• This means that total revenue is这意味着总收益为
R = pq = -q2/10 + 10q
• Marginal revenue will be given by边际收益为
MR = dR/dq = -q/5 + 10
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Example：Marginal Revenue and Profit Maximization 例：边际收益及利润最大化
dR dC MR MC dq dq
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Second-Order Conditions二阶条件
• MR = MC is only a necessary condition for profit maximization MR = MC仅仅是利润最大化的一阶条件 • For sufficiency, it is also required that 充分性还要求
1 MC p1 e q ,p
p MC 1 p eq,p
• The gap between price and marginal cost will fall as the demand curve facing the firm becomes more elastic价格和边际成本之间的差别将随着企业所面临 的需求曲线弹性增加而降低
Chapter 9 第九章
PROFIT MAXIMIZATION 利润最大化
Copyright ©2005 by South-Western, a division of Thomson Learning. All rights reserved.
1
Modeling Firms’ Behavior 企业行为模型
– if the demand curve slopes downward, eq,p < 0 and MR < p 如果需求曲线是向下倾斜的，eq,p < 0 ，则 MR < p – if the demand is elastic, eq,p < -1 and marginal revenue will be positive如果需求是有弹性的，eq,p < -1，则边际收益为正
2
Profit Maximization利润最大化
• A profit-maximizing firm chooses both its inputs and its outputs with the sole goal of achieving maximum economic profits 利润最大化的企业，仅为了达到最大的 经济利润的目的，选择投入和产出
• Total revenue for a firm is given by 企业的总收益为 R(q) = p(q)q • In the production of q, certain economic costs are incurred [C(q)] 生产q，存在某些经济成本[C(q)] • Economic profits () are the difference between total revenue and total costs 经济利润()是总收益和总成本之差
R
The second-order condition prevents us from mistaking q0 as a maximum 二阶条件避免了把q0错作为最 大值
q0
q*
output
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Marginal Revenue边际收益
• If a firm can sell all it wishes without having any effect on market price, marginal revenue will be equal to price 如果企业无论售掉多少商品都不影响市场价格，那么边际 收益将等于价格 • If a firm faces a downward-sloping demand curve, more output can only be sold if the firm reduces the good’s price 如果企业面对向下倾斜的需求曲线，只有在企业降低其商 品价格时才可以卖掉更多的产出