Thermal Power Plant Simulator, Cold, warm and Hot rolling of Steam TurbineManohar Tatwawadi
The presentation describes the cold rolling, warm rolling and hot rolling and synchronising of steam turbine. The Temperature Matching Chart for Turbine metal and Steam is also discussed in the presentation
This document provides information about gas turbine and steam power plant cycles. It describes the Brayton cycle used in gas turbines and the Rankine cycle used in steam power plants. It discusses components, processes, thermal efficiencies and improvements to the cycles such as regeneration, intercooling and reheating. Examples are provided to calculate efficiency, work and heat inputs/outputs for simple and improved cycles.
This document is a 14-day internship report submitted by Meer Muhammad to Sir Rizwan Arain about their time at the JPCL Jamshoro Thermal Power Station in Sindh, Pakistan. It provides an overview of the major mechanical components of the power station, including the boilers, steam turbines, condenser, feedwater pumps, cooling towers, fans, and flue gas stack. It concludes that the internship was a valuable learning experience that provided insight into the interesting procedures and equipment used at a thermal power plant.
The vapor compression refrigeration cycle is commonly used to transfer heat from a low temperature medium to a high temperature medium. It involves four main processes: (1) compression of a refrigerant vapor, (2) heat rejection in a condenser, (3) expansion of the refrigerant through a throttle valve, and (4) heat absorption in an evaporator. The coefficient of performance (COP) is used to measure the efficiency of refrigerators and heat pumps. Actual vapor compression cycles are less efficient than the ideal Carnot cycle due to irreversibilities.
1) A firm aims to minimize costs by producing a given output level using the smallest amount of inputs.
2) For a Cobb-Douglas production function, the firm's conditional input demand functions are derived by setting the slope of the isoquant equal to the slope of the isocost line.
3) The firm's total cost function is the sum of expenditures on each input using the conditional input demand functions.
This document provides an overview of the key components and processes in a thermal power plant. It describes how coal is pulverized and burned to generate high-temperature steam in a boiler. The steam then drives turbines which power electrical generators, after which the steam is condensed back into water and recycled through the system in a closed-loop Rankine cycle. The document outlines the basic working principle and lists the main parts of a thermal power plant, including coal conveyors, pulverizers, boilers, turbines and condensers.
Industrial training at NTPC ShaktinagarRishikesh .
This document provides an overview of industrial training at a thermal power station in Singrauli, Madhya Pradesh, India. It describes the basic process of how coal is converted into electricity through various components of the power plant. Key components discussed include the coal handling plant, pulverizer, boiler, turbine, condenser, cooling towers, and burner management system. The document also includes diagrams illustrating the general layout and coal to electricity process of a typical coal-fired thermal power station.
Using Multiple Sensors to Determine Posture (midterm)odcsss
Using multiple sensors, including a SenseCam camera, BodyMedia device, and heart rate monitor, the project aims to classify user activities and determine posture over time based on sensor data. The goals are to correctly identify posture, plot sensor graphs, and find differences in the graphs between activities using a classifier. Challenges include inputting sensor data and outputting the differences corresponding to various activities.
Thermal Power Plant Simulator, Cold, warm and Hot rolling of Steam TurbineManohar Tatwawadi
The presentation describes the cold rolling, warm rolling and hot rolling and synchronising of steam turbine. The Temperature Matching Chart for Turbine metal and Steam is also discussed in the presentation
This document provides information about gas turbine and steam power plant cycles. It describes the Brayton cycle used in gas turbines and the Rankine cycle used in steam power plants. It discusses components, processes, thermal efficiencies and improvements to the cycles such as regeneration, intercooling and reheating. Examples are provided to calculate efficiency, work and heat inputs/outputs for simple and improved cycles.
This document is a 14-day internship report submitted by Meer Muhammad to Sir Rizwan Arain about their time at the JPCL Jamshoro Thermal Power Station in Sindh, Pakistan. It provides an overview of the major mechanical components of the power station, including the boilers, steam turbines, condenser, feedwater pumps, cooling towers, fans, and flue gas stack. It concludes that the internship was a valuable learning experience that provided insight into the interesting procedures and equipment used at a thermal power plant.
The vapor compression refrigeration cycle is commonly used to transfer heat from a low temperature medium to a high temperature medium. It involves four main processes: (1) compression of a refrigerant vapor, (2) heat rejection in a condenser, (3) expansion of the refrigerant through a throttle valve, and (4) heat absorption in an evaporator. The coefficient of performance (COP) is used to measure the efficiency of refrigerators and heat pumps. Actual vapor compression cycles are less efficient than the ideal Carnot cycle due to irreversibilities.
1) A firm aims to minimize costs by producing a given output level using the smallest amount of inputs.
2) For a Cobb-Douglas production function, the firm's conditional input demand functions are derived by setting the slope of the isoquant equal to the slope of the isocost line.
3) The firm's total cost function is the sum of expenditures on each input using the conditional input demand functions.
This document provides an overview of the key components and processes in a thermal power plant. It describes how coal is pulverized and burned to generate high-temperature steam in a boiler. The steam then drives turbines which power electrical generators, after which the steam is condensed back into water and recycled through the system in a closed-loop Rankine cycle. The document outlines the basic working principle and lists the main parts of a thermal power plant, including coal conveyors, pulverizers, boilers, turbines and condensers.
Industrial training at NTPC ShaktinagarRishikesh .
This document provides an overview of industrial training at a thermal power station in Singrauli, Madhya Pradesh, India. It describes the basic process of how coal is converted into electricity through various components of the power plant. Key components discussed include the coal handling plant, pulverizer, boiler, turbine, condenser, cooling towers, and burner management system. The document also includes diagrams illustrating the general layout and coal to electricity process of a typical coal-fired thermal power station.
Using Multiple Sensors to Determine Posture (midterm)odcsss
Using multiple sensors, including a SenseCam camera, BodyMedia device, and heart rate monitor, the project aims to classify user activities and determine posture over time based on sensor data. The goals are to correctly identify posture, plot sensor graphs, and find differences in the graphs between activities using a classifier. Challenges include inputting sensor data and outputting the differences corresponding to various activities.
Experiencia web 2.0 corporativa- caso Telefónicasebasparigi
El documento discute el surgimiento de las redes sociales y la web 2.0, y cómo esto está cambiando la comunicación corporativa y de marketing. Propone que las empresas adopten un modelo 2.0 aprovechando las redes sociales y la comunicación viral para llegar a nuevas audiencias a bajo costo. También analiza cómo mundos virtuales como Second Life están creando oportunidades para las marcas.
The document discusses cultural exchanges and human rights issues in China and the United States. It argues that China must develop in a way suited to its own conditions, neither copying Western models nor mechanically following other socialist models. It also emphasizes upholding national unity and a peaceful environment as fundamental to China's development. Regarding the US, it describes American society as multicultural rather than a melting pot, defined more by integration than assimilation of cultures.
Uma mulher no aeroporto ficou irritada ao ver um homem pegando seus biscoitos, mas descobriu que seus biscoitos ainda estavam intactos em sua bolsa e na verdade ela havia se confundido. O homem dividiu gentilmente os biscoitos dele.
The document discusses Chinese culinary culture and dining traditions. It describes the key characteristics of China's four major cuisines, how Chinese cooking is judged, what a standard Chinese banquet includes, the types of alcohol typically served, and the tradition of sharing dishes communally at the table. It also briefly discusses American and Western dining cultures.
The document discusses the concept of virtue. It provides several definitions and descriptions of virtue, including goodness, fine quality, love for truth, noble behavior, beauty of mind, sharing others' pain, conferring happiness, and thinking and doing what is right. It also discusses virtue as the basis of dignity, esteem, honesty, diligence, modesty, temperance, and charity. The conclusion states that virtue embodies kindness, honesty, courage, modesty, perseverance and temperance, and means conferring benefits and never inflicting pains.
The document discusses the concept of time through various proverbs and quotations from different cultures and celebrities. It explores different perspectives on time including that it is life, money, victory, speed and strength. It also provides translations of Chinese proverbs and quotes about time from figures such as Benjamin Franklin, Thomas Fuller, and Aristotle. The document then presents some modern Chinese expressions and concludes with examples for interpreting between English and Chinese.
The document provides information about Shanghai, describing it as China's major eastern gateway to the world and largest seaport. It notes that Shanghai used to be divided by foreign concessions but is now an important center for economy, finance, trade, shipping, science, technology, information and culture. The summary concludes that Shanghai is a historic cultural city, the birthplace of the Communist Party of China, with a variety of architectural styles that have earned it a reputation as an exhibition of world architecture.
The document discusses success and provides quotes from famous figures about success. It defines success as the completion of tasks and achievement of goals and desires. It then shares quotes from celebrities such as Harding, Napoleon, and Pasteur about success requiring effort, willpower, and patience. Additional quotes discuss formulas for success involving work, play, and silence from Einstein and keeping one aim without hesitation from Pavlova.
The document discusses the concept of time through various proverbs and quotations from different cultures and celebrities. It explores different perspectives on time including that it is life, money, victory, speed and strength. It also provides translations of Chinese proverbs and quotes about time from figures such as Benjamin Franklin, Thomas Fuller, and Aristotle. The document then presents some modern Chinese expressions and concludes with examples for interpreting between English and Chinese.
Experiencia web 2.0 corporativa- caso Telefónicasebasparigi
El documento discute el surgimiento de las redes sociales y la web 2.0, y cómo esto está cambiando la comunicación corporativa y de marketing. Propone que las empresas adopten un modelo 2.0 aprovechando las redes sociales y la comunicación viral para llegar a nuevas audiencias a bajo costo. También analiza cómo mundos virtuales como Second Life están creando oportunidades para las marcas.
The document discusses cultural exchanges and human rights issues in China and the United States. It argues that China must develop in a way suited to its own conditions, neither copying Western models nor mechanically following other socialist models. It also emphasizes upholding national unity and a peaceful environment as fundamental to China's development. Regarding the US, it describes American society as multicultural rather than a melting pot, defined more by integration than assimilation of cultures.
Uma mulher no aeroporto ficou irritada ao ver um homem pegando seus biscoitos, mas descobriu que seus biscoitos ainda estavam intactos em sua bolsa e na verdade ela havia se confundido. O homem dividiu gentilmente os biscoitos dele.
The document discusses Chinese culinary culture and dining traditions. It describes the key characteristics of China's four major cuisines, how Chinese cooking is judged, what a standard Chinese banquet includes, the types of alcohol typically served, and the tradition of sharing dishes communally at the table. It also briefly discusses American and Western dining cultures.
The document discusses the concept of virtue. It provides several definitions and descriptions of virtue, including goodness, fine quality, love for truth, noble behavior, beauty of mind, sharing others' pain, conferring happiness, and thinking and doing what is right. It also discusses virtue as the basis of dignity, esteem, honesty, diligence, modesty, temperance, and charity. The conclusion states that virtue embodies kindness, honesty, courage, modesty, perseverance and temperance, and means conferring benefits and never inflicting pains.
The document discusses the concept of time through various proverbs and quotations from different cultures and celebrities. It explores different perspectives on time including that it is life, money, victory, speed and strength. It also provides translations of Chinese proverbs and quotes about time from figures such as Benjamin Franklin, Thomas Fuller, and Aristotle. The document then presents some modern Chinese expressions and concludes with examples for interpreting between English and Chinese.
The document provides information about Shanghai, describing it as China's major eastern gateway to the world and largest seaport. It notes that Shanghai used to be divided by foreign concessions but is now an important center for economy, finance, trade, shipping, science, technology, information and culture. The summary concludes that Shanghai is a historic cultural city, the birthplace of the Communist Party of China, with a variety of architectural styles that have earned it a reputation as an exhibition of world architecture.
The document discusses success and provides quotes from famous figures about success. It defines success as the completion of tasks and achievement of goals and desires. It then shares quotes from celebrities such as Harding, Napoleon, and Pasteur about success requiring effort, willpower, and patience. Additional quotes discuss formulas for success involving work, play, and silence from Einstein and keeping one aim without hesitation from Pavlova.
The document discusses the concept of time through various proverbs and quotations from different cultures and celebrities. It explores different perspectives on time including that it is life, money, victory, speed and strength. It also provides translations of Chinese proverbs and quotes about time from figures such as Benjamin Franklin, Thomas Fuller, and Aristotle. The document then presents some modern Chinese expressions and concludes with examples for interpreting between English and Chinese.
The document discusses several famous tourist attractions and historical sites in China. It mentions the Great Wall, Forbidden City, Palace Museum, Peking Man fossils found at Zhoukoudian, Terracotta Army near Xi'an, Mogao Grottoes in Dunhuang, Huangshan Mountain known for its strangely shaped pines and rock formations, and the Potala Palace in Lhasa built during the Songtsan Gambo period. It provides brief descriptions highlighting the significance and features of these important cultural and historical locations.
The speaker welcomes guests to the opening ceremony of the Shanghai International Containerized Transport Conference. He expresses gratitude to the organizing committee for their hard work in making the conference possible. He hopes delegates will take the opportunity to learn about Shanghai's development and wishes the conference success.
The document discusses different definitions and perspectives on love. It provides over 20 quotes and sayings about love from various celebrities and authors. Some key points made include that love is the salt of life, a mixture of happiness and sadness, loyalty and understanding, and the pursuit of delight through agony.
The document discusses the concept of life through various quotes and passages. It explores life as a journey with ups and downs, and emphasizes making the most of life through love, living fully and enjoying each moment. It encourages taking on life's duties, struggles and mysteries with perseverance. In the end, it concludes that life is what you make of it, so one should love life and live it joyfully.
8. 同样一元钱购买商品 1 所得到的边际效用少于商品 2 ,理性消费者会减少商品 1 的购买,增加商品 2 的购买。 同样一元钱购买商品 1 所得到的边际效用多于商品 2 ,理性消费者会增加商品 1 的购买,减少商品 2 的购买。 同样一元钱购买商品 1 所得到的边际效用等于商品 2 ,此时消费者获得效用最大。 在购买两种商品的情况下的消费者效用的最大化的均衡条件为: P 1 X 1 + P 2 X 2 = I MU 1 MU 2 P 1 P 2 = = λ 分析: MU 1 MU 2 P 1 P 2 〈 ① MU 1 MU 2 P 1 P 2 〉 ② ③ MU 1 MU 2 P 1 P 2 =
9. 4. 需求曲线的推导 单个消费者的均衡条件 MU P = λ 它表示:消费者对任何一种商品的最优购买量应该是使最后一元钱购买该商品所带来的边际效用相等。由于对于任何一种商品来说,随着需求量的不断增加,边际效用 MU 是递减的,在货币的边际效用 λ 不变的前提下,商品的需求价格 P 必然同比例于 MU 的递减而递减。 5. 消费者剩余( CS ) 概念:消费者在购买一定数量的某种商品时愿意支付的最高价格和实际支付的总价格之间的差额。可用消费者需求曲线以下、市场价格线之上的面积来表示,如右图中阴影部分面积。 P=f ( Q )
10. 第 二 节 消费者偏好 序数效用论提出了关于消费者偏好的三个基本假定: 第一个假定是偏好的完全性。 偏好的完全性指消费者总是可以比较和排列所给出的不同商品组合。对于两个不同的偏好 A 和 B ,只能作出三种判断中的一种: A > B , A 优于 B ; B > A , B 优于 A ; A = B , A 、 B 无差异。 第二个假定是偏好的可传递性。 如果 A > B , B > C 那么一定 A > C 第三个偏好的非饱和性。 如果两个商品组合的区别仅在于其中一种商品数量的不同,那么,消费者总是偏好于含有这种商品数量较多的那个商品组合。(注意:消费者认为值得拥有的商品都是“好的东西”,而不是诸如空气污染、噪音等“坏的东西”。 一、关于偏好的假定
11. 二、无差异曲线 1. 概念 无差异曲线是用来表示消费者偏好相同的两种商品的所有组合的。或者说,它是表示能给消费者带来相同的效用水平或满足程度的两种商品的所有组合的。如下图,横轴代表食品消费量,纵轴代表衣物消费量: 0 衣物 食品 A B C U
12. 0 2. 特征 ① 在同一坐标平面图上可以有无数条无差异曲线通过,离原点越远的无差异曲线代表的效用水平越高。如下图: U 1 U 2 U 3 衣物 食物 ② 在同一坐标平面上的任何两条无差异曲线不会相交。下图中的无差异曲线违反偏好假定:
13. 若相交, A 与 B 效用相同, B 与 C 效用相同,根据效用的传递性, B 与 C 效用相同,而组合 B 上每一种商品的数量都多于 C ,即根据偏好的非饱和性, B 要优于 C ,与 B 与 C 效用相同矛盾。 1. 概念 在维持效用水平不变的前提下,消费者增加一单位某种商品的消费数量时所需要放弃的另一种商品的消费数量。 2. 公式 Y X 0 U X 1 X 2 Y 1 Y 2 △ X △ Y ● ● ● 衣物 食物 0 A B C U 1 U 2 ③ 无差异曲线是凸向原点的,向下方倾斜,斜率为负。 三、边际替代率 MRS XY = – △ Y △ X
16. 一、预算线(又名消费可能线、价格线) 1. 含义: 表示在消费者的收入和商品的价格给定的条件下,消费者的全部收入所能购买到的两种商品的各种组合。 2. 表达式: OA = 预算线 AB 的方程式: 或 : Y = ·X 预算线斜率 : – OA OB = – I/P Y I/P X = 第 三 节 预算约束 X 和 Y 为两种商品的消费量, I 为既定收入, P X 、 P Y 为 X 、 Y 商品的价格。图中,预算线 AB 内如 b 点表示消费者的全部收入在购买该点的商品组合以后还有剩余,预算线外如 a 点表明消费者用全部收入都不可能实现的组合。 ·b · a 0 Y X B A I P Y OB = I P X P X ·X + P Y ·Y = I I P Y – P X P Y – P X P Y
17. 二、收入和价格变化对预算的影响 1. 两商品的价格不变,消费者的收入 I 发生变化,这时,相应的预算线的位置会发生平移。收入增加则预算线右移,收入减少则预算线左移。如下图: 2. 消费者的收入 I 不变,两商品的价格同比例同方向发生变化,这时,相应的预算线的位置也会发生平移。两商品价格同比例上升,则预算线左移;两商品价格同比例下降,则预算线右移。如上图。 A´´ A A´ B´ B B´´ Y X 0
18. 3. 当消费者的收入 I 不变,商品 X 的价格 P X 发生变化而商品 Y 的价格 P Y 保持不变,这时,预算线的斜率 – P X / P Y 会发生变化,预算线的横截距 I/ P X 也会发生变化,但是,预算线的纵截距 I/ P Y 保持不变。如 P X 下降,则预算线 AB 以 A 为轴心,外移至 A B´ ;若 P X 上升,则预算线内移至 A B´´ 。如下图: 0 B´´ B A B´ X Y
19. 同理,当消费者收入 I 不变,商品 Y 的价格 P Y 下降或上升,商品 X 价格 P X 保持不变,则预算线以横轴为轴心,向上或向下旋转。如下图: 4. 消费者的收入 I 与两商品的价格 P X 和 P Y 都同比例同方向发生变化,这时预算线不发生变化。 0 X Y B A´´ A A´
23. 在图中, X 1 、 X 2 表示两种商品的消费量, P 1 表示商品 1 的价格,商品 2 的价格保持不变。当商品 1 的初始价格为 P 1 1 时相应的预算线为 AB ,与对应的无差异曲线 U 1 相切于 E 1 点。 一、价格变化 : 价格 - 消费曲线 含义: 价格 - 消费曲线是在消费者的偏好、收入以及其他商品价格不变的条件下,与某一种商品的不同价格水平相联系的消费者效用最大化的均衡点的轨迹。 B" U 1 U 3 U 2 若商品 1 的价格下降为 P 1 2 ,相应的预算线由 AB 移至 A B' ,与较高的无差异曲线 U 2 相切于均衡点 E 2 。若价格继续降至 P 1 3 ,则相应的预算线移至 A B" ,与更高的无差异曲线相切于均衡点 E 3 ······· ,随着商品 1 的价格的不断变化 , 可以找到无数个诸如 E 1 、 E 2 和 E 3 那样的均衡点 , 它们的轨迹就是价格—消费曲线 . 第五节 价格和收入变化对消费者均衡的影响 价格 - 消费曲线 E 1 E 3 E 2 B B' A 0 0 X 1 X 1 = f ( P 1 ) X 1 X 2 P 1 a c b X 1 3 X 1 1 X 1 2 X 1 3 X 1 1 X 1 2 P 1 ¹ P 1 3 P 1 2 消费者需求曲线
24. 二、消费者需求曲线 把上图中每一个 P 1 数值与相应的均衡点上的 X 1 数值绘制在商品的价格—数量坐标图上,便可以得到单个消费者的需求曲线, 注意曲线上每一价格对应的消费量都是给消费者带来最大效用的均衡数量。 三、收入变化:收入 - 消费曲线 含义:收入 - 消费曲线 是在消费者的偏好和商品的价格不变的条件下,与消费者的不同收入水平相联系的消费者效用最大化的均衡量的轨迹。 X 1 X 1 X 2 X 2 O O A B A ' B ' A " B " E 1 E 2 E 3 U 1 U 2 U 3 A B A ' B ' A " B " E 1 E 2 E 3 U 1 U 2 U 3 X 1 1 X 1 1 X 1 2 X 1 3 X 1 2 X 1 3 向右上方倾斜的收入 - 消费曲线 向后弯曲的收入 - 消费曲线 左图中,随着收入水平的不断增加,预算线由 AB 移至 A ‘ B’ 、 A”B” ,形成了不同收入水平下的消费者效用最大化的均衡点,连接便得到收入——消费曲线,随着收入水平的增加,消费者对商品 1 和 2 的需求量都是上升的,表明两种商品都是正常品。右图中,收入水平增加,消费者对商品 1 的需求量先增加后减少,表明在一定的收入水平上,商品 1 由正常品变成了劣等品。
26. 如图,替代效应和收入效应都为正,与价格呈反方向变动,因此,正常品的需求曲线是向右下方倾斜的。 第 六节 替代效用和收入效应 一、替代效应和收入效应的含义 一种商品价格变动所引起的该商品需求量变动的总效应可以被分解为替代效应和收入效应两个部分,即总效应 = 替代效应 + 收入效应。其中,由商品的价格变动所引起的实际收入水平变动,进而由实际收入水平变动所引起的商品需求量的变动,为收入效应。由商品的价格变动所引起的商品相对价格的变动,进而由商品的相对价格变动所引起的商品需求量的变动为替代效应。 二、正常物品的替代效应和收入效应 0 A B F G U 1 U 2 a c b B ' X 1 X 2 X 1 ' '" X 1 X 1 " 总效应 收入效应 替代效应
27. 上图中,横纵轴分别表示两种商品的消费量。假定商品 2 价格不变,商品 1 是正常品。当商品 1 的价格下降时,预算线由 AB 外移至 AB ‘ ,并切对应的无差异曲线于 b ,消费变化量为 X 1 ' X 1 ''' ,这便是商品 1 的价格下降引起的总效应。其中,剔除由于商品相对价格变化引起的实际收入水平变化的影响并保持原效用水平 U 1 不变得到的 X 1 ' X 1 " 的变化量为替代效应,商品的价格变化所引起的实际收入水平的变化并改变消费者的效用水平得到的 X 1 " X 1 ''' 的变化量为收入效应。 涉及概念 : 补偿预算线 —— 用来表示以假设的货币收入的增减来维持消费者的实际收入水平不变的一种分析工具。如当商品价格下降引起消费者的实际收入 水平提高时,假设可以取走消费者的一部分货币收入,以使消费者的实际收入维持原有的水平,则补偿预算线在此就可以用来表示使消费者的货币收入下降到只能维持原有的无差异曲线的效用水平(即原有的实际收入水平)这一情况。相反,在商品价格上升引起消费者的实际收入水平下降时,假设可以对消费者的损失给予一定的货币收入补偿,以使消费者的实际收入维持原有的水平,则补偿预算线在此就可以用来表示使消费者的货币收入提高到得以维持原有的无差异曲线的效用水平(即原有的实际收入水平)这一情况。具体做法是作与移动后的预算线(价格变动后)平行且与原无差异曲线(价格变动前)相切的预算线,如图中的 FG 。
31. 一、市场需求函数 一种商品的市场需求—— 是指在一定时期内在各种不同的价格下市场中所有消费者对某种商品的需求数量。 一种商品的市场需求量是每一个价格水平上的该商品的所有个人需求量的加总。 第 七节 从单个消费者的需求曲线到市场需求曲线 假定在某一商品市场上有 n 个消费者,他们都具有不同的个人需求函数 = f i ( P ) , i = 1 , 2 ··· , n , 则该商品市场的需求函数为: i d Q Q d = F ( p ) i=1 n ∑ f i ( P ) =
32. 二、市场需求曲线 单个消费者的需求函数和市场需求函数之间的关系表示为: 水平加总 0 30 10 20 1 6 2 3 4 5 P Q f A ( P ) Q A d = (a) 消费者 A 的需求曲线 0 30 10 20 1 6 2 3 4 5 P Q f B ( P ) Q B d = (b) 消费者 B 的需求曲线 0 30 10 20 1 6 2 3 4 5 P Q (c) 市场需求曲线 40 50 F( P ) Q d = = Q A d + Q B d = i=1 n ∑ D i ( P ) D ( P ) i = 1 , 2 , ··· , n
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34. 三、期望效用和期望值的效用 1. 期望效用 对于一张彩票 L=[p ; W 1 , W 2 ] ,彩票的期望效用函数为: E{U[p ; W 1 , W 2 ] }=pU ( W 1 ) + ( 1-p ) U ( W 2 ) 或 E[U ( W 1 , W 2 ) ] =pU ( W 1 ) + ( 1-p ) U ( W 2 ) 式中, p 和 1-p 分别为 W 1 和 W 2 发生的概率。 2. 期望值的效用 对于一张彩票 L=[p ; W 1 , W 2 ] ,彩票的期望值为: p W 1 + ( 1-p ) W 2 彩票期望值的效用为: U[ p W 1 + ( 1-p ) W 2 ]
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36. 2. 效用曲线 W W W U ( W ) U ( W ) U ( W ) U ( W ) U ( W ) U ( W ) W 1 W 1 W 1 W 2 W 2 W 2 p W 1 + ( 1-p ) W 2 p W 1 + ( 1-p ) W 2 p W 1 + ( 1-p ) W 2 U ( W 1 ) pU ( W 1 ) + ( 1-p ) U ( W 2 ) pU ( W 1 ) + ( 1-p ) U ( W 2 ) U[ p W 1 + ( 1-p ) W 2 ] U[ p W 1 + ( 1-p ) W 2 ] U ( W 2 ) U ( W 2 ) U ( W 2 ) U ( W 1 ) U[ p W 1 + ( 1-p ) W 2 ] pU ( W 1 ) + ( 1-p ) U ( W 2 ) O O O U ( W )表示消费者的效用函数,为增函数; W 表示货币财富量。 风险回避者的效用函数: 严格向上突出 风险爱好者的效用函数 严格向下突出 风险中立者的效用函数:线性 A B A B A
37. 五、风险与保险 假定某消费者拥有的一笔财产,其价值为 W 万元,如果风险发生他将损失 L 万元,风险发生的概率为 p ,假设该消费者为回避此项财产风险愿意向保险公司支付的保险费为 S 万元。则 S 满足的原则是:消费者愿意支付的保险金额 S 应该等于他的财产的期望损失( S=p·L+ ( 1-p ) ·0 )或者说消费者支付的保险金额 S 应该使得保险后的稳妥可靠的财产 W-S 等于在风险条件下的财产期望值( W-S=p· ( W-L ) + ( 1-p ) ·W )。 前提假定:需求方为风险回避者,供给方为风险中立者 对于保险公司来说,其目的是追求利润的最大化,期望收益为 p · ( S-L ) + ( 1-p ) ·S= -p·L+S , 只要保险公司的期望收益 -p·L+S ≥ 0 或 S ≥p·L 或 p ≤ S/L 则保险公司就愿意接受这项投保业务。
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39. 3. 无差异曲线 1 )无差异曲线的一般形状 性质:无差异曲线不能交叉,原因在于消费者偏好的传递性公理;消费者更偏好于离原点远的无差异组合(其前提是无差异曲线有无数条),因为我们假设商品越多越好,即消费者偏好具有单调性;无差异曲线凸向原点。 X Y O 2 )无差异曲线可能的形状 O O O O X X X X Y Y Y Y 完全替代品 边际替代率: 常数 完全互补品 边际替代率: 0 Y 是劣质品 边际替代率: 小于 0 Y 是中性商品 边际替代率: 无穷
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44. 2. 如果某商品是吉芬商品,则当其价格上升时,其他条件不变,该商品( ) A. 购买增加,因收入效应绝对值大于替代效应绝对值 B. 购买增加,因收入效应绝对值小于替代效应绝对值 C. 购买减少,因收入效应绝对值大于替代效应绝对值 D. 购买减少,因收入效应绝对值小于替代效应绝对值 ( 答案: A ) 思路:吉芬商品的需求曲线向右上倾斜,其原因是它是低档品且收入效应大于替代效应。 3. 水与钻石的价值之谜(水相对而言更有用,但价格却低得多)可用下列说法解释的是( ) A. 钻石的总效用高 B. 钻石的边际效用高 C. 水的边际效用高 D. 钻石的需求曲线向右上方倾斜 (答案: B ) 思路:按消费者均衡的条件看,有 MU 钻石 /P 钻石 =MU 水 /P 水 ,因此解释 P 钻石 >P 水 的原因为 B 。
45. 4. 假如消费者面临两种商品 X 、 Y , MRSxy 恒等于 1/3 ,价格比 Px/Py=1/2 ,则消费者( ) A. 不买 X B. 不买 Y C. 在预算约束内任意的 X 、 Y 组合都是 合理的 D. 收入增加后 X 、 Y 都会适当增加 (答案: A ) 思路: MRSxy 为常数,意味着无差异曲线是直线,此时的消费者均衡点位于坐标轴上(即有角点解),画出相应的无差异曲线和预算线,可看出均衡点在 X 的购买量为 0 。 正确的预算线 错误的预算线 无差异曲线 X Y O
46. 5. 如果甲消费者想用商品 X 交换乙消费者的商品 Y ,结果得到了乙的同意,可以推断在当时( ) A. 甲的 MRSxy >Px/Py> 乙的 MRSxy B. 乙的 MRSxy >Px/Py> 甲的 MRSxy C. 甲的 MRSxy > 乙的 MRSxy >Px/Py D . Px/Py > 乙的 MRSxy > 甲的 MRSxy (答案: B ) 思路:可以从边际效用递减规律和消费者均衡点的决定来考虑:因为 MRSxy=MUx/MUy ,当甲用 X 换取 Y 后,意味着 MUx 增加, MUy 减少, MRSxy 增加,显然只有当 MRSxy 小于均衡点的值时,上述交换对甲才是有利的,同理可讨论乙的情况。 6. 判断题:总效用决定一种商品的价格,边际效用决定消费数量。 答案:错误。 思路:商品的价格由商品的边际效用 MU 和货币的边际效用 λ (通常假定不变)共同决定。根据公式 MU/P= λ 可得结论。另外 MU=0 ,或者总效用最大时候的消费数量即为商品最终的消费数量。