北大微观经济学课件英文版Ch29Exchange
微观经济学Microeconomics-精品课件
• 参考教材 ：黄亚钧 郁义鸿主编 《微观经 济学》，高等教育出版社，2003年。
• 参考书目： • [美]H.范里安著 《微观经济学：现代观
点》，上海三联书店 上海人民出版社， 1994年； • [美]平狄克 鲁宾费尔德 著 《微观经济 学》，中国人民大学出版社，1997年。 • 黎诣远 《微观经济分析》，清华大学出 版社
13、He who seize the right moment, is the right man.谁把握机遇，谁就心想事成。21.7.1421.7.1 401:18:2501:18 :25July 14, 2021
•
14、谁要是自己还没有发展培养和教 育好， 他就不 能发展 培养和 教育别 人。202 1年7月 14日星 期三上 午1时1 8分25 秒01:18:2521.nomic Man 经济人
• 如果说，稀缺是社会存在的经济概括， 那么，经济人这个概念就是对社会意 识的经济学概括。
• 经济学并不研究稀缺本身，而是研究 在稀缺条件下人的行为，也就是研究 经济人的行为。
© copyrights by Changde Zheng 2004. Economic college，Southwest University For Nationalities.
ii) Scarcity means that to have more of some things there must be less of others (Opportunity Cost): Production Possibilities Frontier
iii) Scarcity implies choice
•
15、一年之计，莫如树谷；十年之计 ，莫如 树木； 终身之 计，莫 如树人 。2021 年7月上 午1时1 8分21. 7.1401:18July 14, 2021
《微观经济学》课件(全)
实证表述还是规范表述？
➢（1）股市繁荣，裙子变短（股市是经济的晴雨表）； ➢（ 2 ） 在 美 国 ， 收 入 最 高 的 1 0 % 家 庭 占 据 了 总 收 入 的 2 5 % ， 而 最 低 的
一、生产可能性边界
➢1.资源与稀缺 ➢（ 1 ） 劳 动 是 人 们 用 于 生 产 物 品 和 劳 务 付 出 的 时 间 和 努 力 。 ➢（ 2 ） 土 地 是 人 们 日 常 所 说 的 自 然 禀 赋 。 ➢（ 3 ） 资 本 是 用 于 生 产 其 它 物 品 的 物 品 。 ➢（4）企业家才能是把土地、劳动和资本组织起来的人力资源。
一、绝对优势与比较优势
➢1.绝对优势 ➢与另一个经济体相比 ，某一经济体用较少的资源生产相同的物品 ，该经
济体在生产该物品上就具有绝对优势。 ➢比 如 ， 假 定 中 国 生 产 一 件 衬 衫 需 要 2 小 时 劳 动 ， 美 国 生 产 一 件 衬 衫 需 要 3
一、生产可能性边界
➢2.什么是生产可能性边界 ➢生产可能性边界是指在既定的资源和技术条件下 ，充分利用现有资源，一
个经济体所能得到的两种产品的最大产出组合。
一、生产可能性边界
➢2.什么是生产可能性边界 ➢很显然，生产可能性边界模型隐含了一些假设： ➢（ 1 ） 假 定 一 个 经 济 体 资 源 的 数 量 与 技 术 是 不 变 的 。 ➢（ 2 ） 假 定 一 个 经 济 体 仅 仅 生 产 两 种 产 品 ， 比 如 黄 油 与 大 炮 ， 黄 油 满 足 吃 的
北大微观经济学课件(英文版)ch3 Preferences
中级微观经济学
Assumptions about Preference Relations
Transitivity
(传递性): If x is at least as preferred as y, and y is at least as preferred as z, then x is at least as preferred as z; i.e.
x1
2012-10-9 中级微观经济学
Indifference Curves Exhibiting Satiation
x2
Satiation (bliss) point Better
2012-10-9
中级微观经济学
Extreme Cases of Indifference Curves; Perfect Substitutes
x2
15 I2 8 Slopes are constant at - 1.
I1
Bundles in I2 all have a total of 15 units and are strictly preferred to all bundles in I1, which have a total of only 8 units in them. x1 8 15
x
f y and y f z ~ ~
x f z.
~
2012-10-9
中级微观经济学
Indifference Curves
Take
a reference bundle x’. The set of all bundles equally preferred to x’ is the indifference curve containing x’; the set of all bundles y ~ x’. Since an indifference “curve” is not always a curve a better name might be an indifference “set”.
微观经济学英文课件Ch
• Patent laws are a form of technology policy that give the individual (or firm) with patent protection a property right over its invention.
Examples of Negative Externalities 负的外部性的例子
• Automobile exhaust • Cigarette smoking • Barking dogs (loud pets) • Loud stereos in an apartment building • Stinky Toufu
Pollution and the Social Optimum...
Price of Aluminum
Cost of pollution
Social cost
Supply
(private cost)
Optimum
Equilibrium
Demand
(private value)
0
Qoptimum QMARKE
0
QMARKET QOPTIMUM
Quantity of Robots
Positive Externalities in Production
• The intersection of the demand curve and the social-cost curve determines the optimal output level.
T
Quantity of Aluminum
Negative Externalities in Production 生产中的负的外部性
微观经济学英文课件
Edited by Yong, E.L.
Continuously,
Microeconomics is also used for evaluating broad question in regards to government policy (although this is more to macroeconomics).
Edited by Yong, E.L.
Continuously,
If the firm produces 6 units of apple and 12 units of apple pie wants to increase the production of apple pie by one unit to the 13th unit. It has to forgo 2 units of apple so that resources can be shifted to produce the additional apple pie; Opportunity Cost is thus 2.
Edited by Yong, E.L.
Continuously,
If the firm produces 10 units of apple and 6 units of apple pie wants to increase the production of apple pie by one unit to the 7th unit. It has to forgo 1 unit of apple so that resources can be shifted to produce the additional apple pie; Opportunity Cost is thus 1.
北大微观经济学课件(英文版)ch1 Intrduction
2012-10-9
中级微观经济学
Market Demand Curve for Apartments
p
QD
2012-10-9 中级微观经济学
Modeling Apartment Supply
Supply:
It takes time to build more close apartments so in this short-run the quantity available is fixed (at say 100).
Economics Graduates
Type of Employer Traditional Business % Graduates 23.3
Government
Financial Business Graduate School Consulting Services Private/public School Law Firm Other
“low”
2012-10-9
中级微观经济学
Competitive Market Equilibrium
Quantity
demanded = quantity available price will neither rise nor fall so the market is at a competitive equilibrium.
2012-10-9
中级微观经济学
助教
廖志鹏,
zpliao@ 张沈伟，jeswest@ 赵洪春 ，zhaohongchun@ Office Hours: Tuesdays 4:00-5:00pm
2012-10-9
中级微观经济学
微观经济学原理英文--Thinking Like an Economist ppt课件
Some Familiar Models
A model of human anatomy from high school biology class
© 2015 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use.
© Accord/
5
Some Familiar Models
© Olga Rosi/
A model airplane
6
© 2015 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use.
© ittipon/
7
Our First Model:
The Circular-Flow Diagram
The Circular-Flow Diagram: a visual model of the economy, shows how dollars flow through markets among households and firms
微观经济学英文版PPT课件
10
2.2 the definition of microeconomics
The starting point of economics searching The definition of Microeconomics People how to make decision Why need to bargain Why need to build market economics
Economics is a study, learning selection of scarce resources with different uses; The goal is effective allocation of scarce resources to produce goods and services, and in the present or future, let them reasonable allocated to social members or group for consumption.
8
Production possibilities curve
PPC is a graph that shows the combinations of output that the economy can possibly produce given the available factors of production and the available production technology.
微观经济学英文版精品PPT课件
Chapter 1: The Fundamentals of Economics（A. Introduction）
1.2 Microeconomics and Macroeconomics
What is Microeconomics ?
It is concerned with the behavior of individual entities such as markets, firms and households.
You want to buy a computer which is $2510. while it is $2500 in the supermarket in downtown. Wherever you buy the computer, it would return to the producer if there is any problem. Where would you buy it？
There are three types of economies:
Market economy Command economy Mixed economy
Chapter 1: The Fundamentals of Economics (C. Society’s technological possibilities)
Chapter 1: The Fundamentals of Economics（A. Introduction）
1.1 Scarcity and Efficiency
What is economics ?
Economics is the study f how societies use scarce resources to produce valuable commodities and distribute them among different people.
北大微观经济学课件英文版Ch29Exchang参考PPT
Exchange
2020/10/11
1
Exchange
Two consumers, A and B.
Their endowments of goods 1 and 2
are A(1 A ,2 A) and B(1 B ,2 B ).
E.g. A(6,4) and B(2,2).
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3
Starting an Edgeworth Box
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4
Starting an Edgeworth Box
Width = 1 A 1 B 628
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5
Starting an Edgeworth Box
Height =
A 2
B 2
42
6
Width = 1 A 1 B 628
B 2
A 2
The endowment
allocation
OA
A 1
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1A1B
17
Other Feasible Allocations
(x1A,xA 2)denotes an allocation to
consumer A. (xB 1,xB 2) denotes an allocation to consumer B.
One feasible allocation is the beforetrade allocation; i.e. the endowment allocation.
2020/10/11
9
The Endowment Allocation
Height =
《微观经济学microeconomics》英文版全套课件(101页)
The economic constraint:
px p1x1 ... pL xL w
The Walrasian budget set (Definition 2.D.1)
Bp,w {x RL : px w}
or
u(x* ) xl
pl
px w
Solution: Walrasian demand function x*( p, w)
Utility Maximization -- Example
Example 3.D.1: the transformed Cobb-Douglas Utility Function
Expenditure Function
Expenditure function e( p,u) Min px s.t. u(x) u {x}
Properties: 1. Homogeneous of degree of one in p 2. Strictly increasing in u and nondecreasing in p 3. Concave in p 4. Continuous in p and u
Comparative Statics – Wealth Effects
The consumer’s Engel function x( p, w)
The wealth effect xl ( p, w) / w or Dwx( p, w) Normal goods and inferior goods
A choice rule C(B) B
The weak axiom of revealed preference (WARP): if x is revealed at least as good as y, then y cannot be revealed preferred to x
北大微观经济学课件(英文版)Ch31 Welfare
z(2) x(3)
x(2) y(3)
2013-8-8
中级微观经济学
Aggregating Preferences
Bill x(1) y(2) z(3)
Rank-order vote results Bertha Bob (low score wins). x-score = 6 No y-score = 6 state is y(1) z(1) z-score = 6 selected!
Manipulating Preferences
Bill x(1) y(2) z(3) (4)
2013-8-8
Bertha Bob y(1) z(2) (3) x(4) z(1) (2) x(3) y(4)
中级微观经济学
These are truthful preferences. Bob introduces a new alternative and then lies. Rank-order vote results. x-score = 8 y-score = 7 z-score = 6
2013-8-8
中级微观经济学
Aggregating Preferences
Bill x(1) y(2) z(3) Bertha Bob y(1) z(2) x(3) z(1) x(2) y(3)
2013-8-8
中级微观经济学
Aggregating Preferences
Bill x(1) y(2) z(3)
Majority Vote Results x beats y
2013-8-8
中级微观经济学
Aggregating Preferences
Bill x y z Bertha Bob y z x z x y
微观经济学双语完全垄断市场CHMonopolyPPT课件
Monopoly
Content
Monopoly and How It Arises Single-Price Monopoly Price Discrimination Government Intervention
8.1 Monopoly and How It Arises
A monopoly that is able to sell different units of a good or service for different prices
8.2 Single-Price Monopoly
8.2.1 Price and Marginal Revenue
Because in a monopoly there is only one firm, the
8.2.3 Output and Price Decision
Short-Run Equilibrium
Condition: MR = MC Price Decision: Using the demand curve and finding the highest price at which it can sell the profit-maximizing output
Comparison of industrial water prices in some cities of China
firm’s demand curve is the market demand curve P
A single-price monopoly’s marginal revenue curve is not its demand curve
As long as the output is positive, the marginal revenue is less than the price
北大微观经济学课件英文版Ch29Exchange
A 2
OA
2/16/2020
中级微观经济学
1A
B 2
x1A
xB2
Pareto-Improvement
An allocation of the endowment that improves the welfare of a consumer without reducing the welfare of another is a Pareto-improving allocation. Where are the Pareto-improving allocations?
Chapter Twenty-Nine
Exchange
2/16/2020
中级微观经济学
Exchange
Two consumers, A and B.
Their endowments of goods 1 and 2
are
A
(1A
,
A 2
)
and
B
(1B,
B 2
).
E.g. A (6,4) and B (2,2).
2/16/2020
中级微观经济学
Feasible Allocations
What allocations of the 8 units of good 1 and the 6 units of good 2 are feasible?
How can all of the feasible allocations be depicted by the Edgeworth box diagram?
xB2
Pareto-Improvements
Since each consumer can refuse to trade, the only possible outcomes from exchange are Pareto-improving allocations. But which particular Paretoimproving allocation will be the outcome of trade?
微观经济学高级版英文原版课件
Chapter1:Key conceptsFebruary19,20131IntroductionEconomics is the study of choice under scarcity.Typically,consumers want more goods and services than they can afford to buy.Similarly,businesses face constraints in terms what funds and resources that they can ernments and countries also face the same type of problem:a government might want to address a large number of social problems,but they have limited resources with which to do so.Economics is about understanding how a party deals with the fact that when they use their resources to pursue one option,they cannot use those resources to do something else.And so,a consumer may have to choose between a new pair of shoes or a textbook,afirm may have to choose between developing a new product or launching a marketing campaign, and the government may have to choose between improving education or targeting crime.To understand these issues,economics has developed a set of tools that can be used to analyze these problems.This book provides an introduction to those tools.They can be used to help understand economic problems wherever they arise,be it businesses understanding the markets they compete in,or governments trying to develop social policy,or families trying to manage their households.These tools are not meant to capture everything that is occurring in any given situation.Rather,they are designed to simplify(or to model)a complicated and potentially messy real-world issue into a tractable form that can provide valuable insights.Given that resources are limited,the key questions that an economy needs to‘decide’are:(a)what to produce;(b)how to produce it;and(c)who should get what is made.In modern economies,the answers to these questions are largely determined by the market –that is,by the interaction of sellers and buyers in the market.1Sometimes,however, the government also helps determine the answer to these questions,by regulating or intervening in the market.Consequently,our focus in this microeconomics text will be on the study of individuals(consumers,firms,and governments)and their interaction in markets.This chapter provides a few key concepts that underpin the analysis in the rest of the book,as well as economics analysis in general.1By‘market’,we simply mean a place where buyers and sellers of a particular good or service meet, such as a traditional bazaar or an online trading site.12Scarcity and opportunity costAs noted above,it is usually the case that resources are limited,so that not all wants can be met.We call this situation scarcity.Scarcity also means that individuals,businesses and societies face tradeoffs;by choos-ing one thing,a person must give up or miss out on another thing.For example,if a consumer uses their money to buy product X,they cannot then use that same money to buy something else.2We use the concept of opportunity cost to measure that tradeoff. Thus,the opportunity cost of any choice is the value of the best forgone alternative. In the example above,if the consumer buys product X,and the next best thing they could have done is buy product Y,the opportunity cost of buying X is forgoing Y.Individuals also face opportunity costs in terms of their time–that is,if a person spends his time doing one thing,he cannot also spend that time doing another.Example.Suppose Andrew prefers to spend his Saturday afternoon walk-ing.The next best thing that he could have done is to sleep,and his thirdbest choice is to go swimming.Therefore,if Andrew goes for a walk,the op-portunity cost of going for a walk is not sleeping,as this is his best foregoneopportunity.The option of swimming is not relevant here because it is notthe next best opportunity.Opportunity costs include both explicit costs and implicit costs.Explicit costs are costs that involve direct payment(or,in other words,would be considered as costs by an accountant).Implicit costs are opportunities that are forgone,but do not involve an explicit cost.3Example.Suppose Stephen decides to go to university,and his next bestoption is to work at a construction site and earn$80K over the year.Theexplicit costs are those that Stephen must directly pay to go to university,such as student fees,the cost of textbooks,and so on.The implicit costsare the opportunities that Stephen must forgo–that is,working at theconstruction site and earning$80K.It is important to note that opportunity cost only includes costs that could change if a different decision were made.Opportunity cost does not include sunk(or unrecoverable) costs.Sunk costs are costs that have been incurred and cannot be recovered no matter what.For example,if Katrien spends the weekend reading an accounting textbook, no matter what she does(such as whether or not she decides to continue studying accounting),she cannot get that time back.Similarly,if a business spent$100K on an advertising campaign last year,regardless of what they decide to do this year,that money(and effort)cannot be recovered.2It is common to hear people refer to the‘economics’of a particular thing.This colloquial statement really means that,given the limited resource available,a choice had to be made and something(possibly worthwhile)could not be done.3Sometimes,economists distinguish between‘economic costs’and‘accounting costs’.Economic costs is just another term for opportunity costs,and therefore includes explicit and implicit costs. Accounting costs refers to explicit costs only.23Marginal analysisTypically,we assume that economic agents are rational and act to maximize their benefits from their economic transactions.4For example,consumers seek to maximize their benefits from consumption andfirms seek to maximize their profits from production. One way that economic agents can solve this maximization problem is by considering the additional benefit or additional cost of any action.This sort of analysis is referred to as marginal analysis and it is a recurring theme both in this book and economics generally.For instance,consider a consumer faced with the decision of whether to buy one more unit of a particular good.That consumer might consider the extra benefit he derives from buying that extra unit;this is referred to as the marginal benefit of that extra unit of the good.The consumer might also consider the additional cost of buying one more unit;this is referred to as the marginal cost of purchasing another unit,which is typically the price of the good.In making theirfinal decision,the consumer will weigh the marginal benefit against the marginal cost of buying that extra unit.For example, if a consumer is considering buying another cup of coffee,and the marginal benefit is$5 and the marginal cost is$3,the consumer will be better offby buying the extra coffee.Each of the marginal terms noted above,and many others,will be discussed at length throughout the book.What is crucial to note is that the term‘marginal’simply means means additional or extra.That is,we interested to see what happens if we increase things(such as the number of coffees bought)by a small amount.4Ceteris paribusThe notion of ceteris paribus is also an important foundation of economic analysis.As noted,because the real world is often complicated and messy,it is often necessary to simplify real-world situations into tractable economic models,in order to better analyze them.Thus,in order to determine the effect of a particular thing,economists tend to examine the impact of one change at a time,holding everything else constant.This is often called ceteris paribus,which roughly means‘other things equal’.For instance,suppose we are interested in how a change in price will affect the quantity demanded of a good.However,in reality,demand for a good can be affected by a number of other factors,such as changes in the tastes or income of consumers,or the availability or price of substitute goods.Therefore,in order to isolate the effect of price upon quantity demanded,we need hold everything else constant.This is not to deny that in the real world multiple changes can occur at a time–they often do.Rather, to fully understand the relationship between price and demand,it is essential to isolate that relationship from other events that might also be occurring.For example,afirm 4We are not suggesting that,in the real word,consumers are always fully rational or thatfirms do not sometimes have other objectives.Rather,we adopt this simplifying assumption because it allows us to analyze the behaviour of economic agents in markets.Such analysis will be fairly accurate,provided that on average individual consumers andfirms act more or less in their own interest.3might be interested in the effect of advertising on demand for its product.To understand the impact of advertising,it is crucial to remove other factors that could affect demand, otherwise advertising could be attributed too much(or too little)influence,which could lead to poor decision-making by thefirm regarding its next advertising campaign.5Correlation and causationAnother factor to keep in mind is the difference between correlation and causation. Correlation refers to a situation in which two or more things are observed to move together(or against each other).On the other hand,causation refers to a situation where changes in one thing brings about or causes change in another thing.To make statements about causation requires an economic theory about how the world works, rather than just observing a statistical relationship between several variables.Sometimes,when we observe correlation between two variables,A and B,it is because one causes the other.Sometimes,it is because a third factor causes changes in A and B(like a rising tide causing two boats to rise in their moorings).Sometimes,there is no connection between the two variables and it is just by chance that we observed the change in both variables at the same time.Without a theory about how a change in one variable affects the other,it is not possible to say which is the case.4。
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The Endowment Allocation
2 OB 2
6 4
OA
2020/4/26
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中级微观经济学
B (2,2)
The Endowment Allocation
2 OB 2
6 4
The endowment allocation
OA 6
2020/4/26
8
中级微观经济学
A (6,4) B (2,2)
xB2
B 2
x
A 2
OA x1A
2020/4/26
A B
1 1 中级微观经济学
Feasible Reallocations
All points in the box, including the boundary, represent feasible allocations of the combined endowments.
The total quantities available
are 1A 1B 6 2 8 units of good 1
and
A 2
B 2
4
2
6
units of good 2.
2020/4/26
中级微观经济学
Exchange
Edgeworth and Bowley devised a diagram, called an Edgeworth box, to show all possible allocations of the available quantities of goods 1 and 2 between the two consumers.
2020/4/26
中级微观经济学
Edgeworth’s Box
x
A 2
xB1
1B OB
A 2
OA
2020/4/26
中级微观经济学
1A
B 2
x1A
xB2
Pareto-Improvements
x
A 2
xB1
1B OB
A 2
B 2
OA The set of Pareto-
1A
x1A
20i2m0/4/2p6 roving alloca中级ti微o观n经济s学
中级微观经济学
Pareto-Improvements
2020/4/26
中级微观经济学
Pareto-Improvements
Trade
improves both
A’s and B’s welfares.
This is a Pareto-improvement
over the endowment allocation.
Which allocations make both consumers better off?
2020/4/26
中级微观经济学
Adding Preferences to the Box
x
A 2
For consumer A.
A 2
OA
2020/4/26
1A
x1A
中级微观经济学
Adding Preferences to the Box
allocation is A (6,4) and B (2,2).
Width = 1A 1B 6 2 8
2020/4/26
中级微观经济学
The Endowment Allocation
Height =
A 2
B 2
4 2
6
Width = 1A 1B 6 2 8
2020/4/26
Other Feasible Allocations
(x1A , xA2 ) denotes an allocation to
consumer A.
(xB1 , xB2 ) denotes an allocation to
consumer B.
An allocation is feasible if and only if
2020/4/26
中级微观经济学
Feasible Allocations
What allocations of the 8 units of good 1 and the 6 units of good 2 are feasible?
How can all of the feasible allocations be depicted by the Edgeworth box diagram?
2020/4/26
中级微观经济学
Pareto-Optimality
A is strictly better off but B is strictly worse off
B is strictly better off but A is strictly worse off
2020/4/26
中级微观经济学
xB2
Pareto-Improvements
Since each consumer can refuse to trade, the only possible outcomes from exchange are Pareto-improving allocations. But which particular Paretoimproving allocation will be the outcome of trade?
For consumer B.
B 2
OB
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1B
中级微观经济学
xB1
Adding Preferences to the Box
xB1
For consumer B.
B 1
OB
B 2
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中级微观经济学
xB2
Adding Preferences to the Box
x
A 2
中级微观经济学
A (6,4) B (2,2)
The Endowment Allocation
OB
6
OA
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8
中级微观经济学
A (6,4) B (2,2)
The Endowment Allocation
OB
6 4 OA
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6 8
中级微观经济学
A (6,4)
中级微观经济学
Pareto-Optimality
Better for consumer A
Better for consumer B
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中级微观经济学
Pareto-Optimality
A is strictly better off but B is strictly worse off
This is a Pareto-improvement
over the endowment allocation.
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Pareto-Improvements
Further trade cannot improve both A and B’s welfares.
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A 2
B 2
4 2
6
Width = 1A 1B 6 2 8
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中级微观经济学
Starting an Edgeworth Box
Height =
A 2
B 2
4 2
6
The dimensions of the box are the quantities available of the goods.
Width = 1A 1B 6 2 8
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中级微观经济学
Feasible Allocations
What allocations of the 8 units of good 1 and the 6 units of good 2 are feasible? How can all of the feasible allocations be depicted by the Edgeworth box diagram?
x1A xB1 1A 1B
and
xA2
xB2
A 2
B 2
.
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Feasible Reallocations
xB1
OB
A 2
xB2
B 2
x
A 2
OA
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x1A
A B
1 1 中级微观经济学
Feasible Reallocations
xB1
OB
A 2
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中级微观经济学
Feasible Reallocations
All points in the box, including the boundary, represent feasible allocations of the combined endowments.
Which allocations will be blocked by one or both consumers?
Pareto-Optimality
Both A and
B are worse
A is strictly better off
off
but B is strictly worse
off
B is strictly better off but A is strictly worse off
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Chapter Twenty-Nine