Posts

Could there have been any sort of collusion between either of the two boys with one or more of the witnesses?

/in /by

Serial Episode Six

https://serialpodcast.org/season-one/6/the-case-against-adnan-syed

Part I – Listen to the Serial Episode and post a thoughtful question in our class forum as described in the Syllabus.  Some of the subjects in this episode related to the legal aspects of evidence and procedure include the following:

  • Credibility of witnesses
  • Corroboration
  • Police Interrogation of suspects
    • What would a sociopath’s response sound like?
  • “Admit nothing, deny everything, demand proof” defense

Part II – Respond thoughtfully to at least one other student’s question as described in the Syllabus.

Something that this episode made clear is how much the prosecution’s case relies on witness testimony. While there are a few pieces of physical evidence, such as the partial handprint, there is nothing that comes even close to proving that Adnan and Hae were together that day, let alone that he killed her. Therefore, Adnan’s guilt comes down to circumstantial evidence and other people’s memories. The problem with that is how different people’s recollections of events contradict each other. Laura sounded truthful when recounting what she heard from the neighbor boy, but he vehemently denied ever saying anything. If she’s telling the truth, there has to be a reason for him to have recanted his story. Of course, we have to take into consideration that he reportedly told her the story after Adnan had already been in custody for a few months. People who knew him said that he was a gossip, and because he was friends with Jay, he might have heard inside details about the case and felt that making up a story for Laura was the only way to share them. The contrasting stories of Laura and the neighbor boy seem to further the divide between the two possible versions of events: what Jay says happened and what Adnan says happened. The question that raises for me is this: could there have been any sort of collusion between either of the two boys with one or more of the witnesses?

Fill out Top 5 law schools under each country with information of the size of the law school, e.g. student numbers, tuition, degrees offered, contact.

/in /by

Law schools in the U.S.

Fill out Top 5 law schools under each country with information of the size of the law school, e.g. student numbers, tuition, degrees offered, contact. It would be also helpful to see whether the school has any partnership with law schools in the U.S.

Write an essay based on marketing tactics on 5 to 6 pages. Write common ways of selling anything to anyone.

/in /by

How to sell Anything

Write an essay based on marketing tactics on 5 to 6 pages. Write common ways of selling anything to anyone.

Write a literature review or meta analysis using case studies , cohort studies to highlight implicit bias . Focus on how implicit bias affects medicine and medical treatment as it relates to culturally diverse and those of transgender subsets. T

/in /by

Effect of gender and cultural biases in medicine

Write a literature review or meta analysis using case studies , cohort studies to highlight implicit bias . Focus on how implicit bias affects medicine and medical treatment as it relates to culturally diverse and those of transgender subsets. Tests that address and possibly quantify implicit bias. How to address implicit bias in clinicians beginning in medical training.

What is this section about? What is the author saying in this section? What is the author doing in this paragraph or section? Does the author make a claim? What does he or she argue? What evidence is provided to advance the argument?

/in /by

Argument Analysis Assignment

Follow the instructions outlined here to complete the article analysis and discussion board posts.
*Introductory note about debate articles. Please be aware that journal articles come in two forms. There are primary source articles and secondary source articles. Primary source articles are original, empirical articles written by researchers for the purpose of describing specific research that they conducted. These articles include methods and results sections (e.g., actual data). Secondary source articles or chapters come in two general forms²the meta- analysis or the literature review article. Here, a researcher will describe a specific area of research conducted by him or herself in the past and/or by other researchers. Literature review articles do not contain data. Instead they contain descriptions of data. A meta-analysis may also be described as a secondary source article because a meta-analysis is a mathematical and descriptive summary of a broad range of findings.
The important point is that debate articles take both forms. Sometimes an author will make claims in a primary source article (by discussing his or her own data collection and results), and sometimes an author will make a claim and support it via the use of previous research conducted on the topic. One source type is not inherently better or worse than the other. An author who describes his or her own data collection may be just a flawed in his or her reasoning (or as brilliant) as an author who describe progress through the semester.

Step 1: Summarize both articles
Before you are able to analyze an argument you must be able to summarize it. Good summaries include a description of the authors ideas including any claims made by the author. Good summaries also review evidence used to advance the argument.
To prepare to summarize the text, read it to get a general idea about the points. Then, reread the text and mark it up by circling key terms and underlining claims. Finally, chart individual paragraphs or sections and examine the overall structure of the text. As you read, take note of:
x What is this section about? What is the author saying in this section?
x What is the author doing in this paragraph or section (use verbs like introducing, reviewing, interpreting, challenging, asserting, illustrating)?
x Does the author make a claim? What does he or she argue? Make note of central claims.
x What evidence is provided to advance the argument?
Be aware of your own biases and avoid inaccurate interpretations. Keep this portion for yourself. Do not turn it in.

Step 2: Analyze both articles
Choose one or two central claims made by the author(s) and describe and analyze the evidence that is used to support it (i.e., for the assignment discuss at three pieces of evidence). Finally, evaluate the evidence used by the authors. The questions below should serve as a guide to help you evaluate evidence. Some questions will not be relevant to the article that you are reading.
A. Use the questions below to evaluate the evidence. First decide what type of evidence the author using. Then, describe the evidence and then analyze it. The questions below will help you analyze and evaluate the argument.
x Is the evidence based on generalization?
x Is the evidence based on analogy, specific cases, personal experience or anecdote?
x Is the evidence based on authority?
o The author uses an authority figure (another author, a doctor, an academic) or an institutional authority to support claims
x Does the author provide empirical evidence? Is the evidence based on experimental data?
Observational data? Survey data? To evaluate empirical evidence consider the questions below.

o Is a causal claims made (recall that only true experiments allow for causal inferences)? If yes, is a causal claim possible? Was random assignment used? Was an experiment used?
o Is a correlational claim made (recall these are claims about the strength and/or direction of a relationship between two or more variables)? ƒ If yes, are there other potential explanations for the data (e.g., potential third variables)?
o Decide if the evidence/data is generalizable (e.g., is the data externally valid) ƒ Is the data robust? Can it replicate in a number of settings with different samples (e.g., is there overreliance a specific sample)? ƒ Is it ecologically valid? Would it happen in real life, outside of the lab?
ƒ Is it relevant? Does it matter? Are the findings useful for solving problems or improving the quality of life?
B. Why is the author using this evidence? Is it convincing?
C. To write an argument analysis, describe the main claims and explain how the author supports each claim.
x What are the main claims? Æ(describe the main claims)
x How does the author support and/or advance the argument? Æ (describe the evidence)
x What kind of evidence is used to support the claim? Æ (evaluate the evidence)
x Based on your evaluation of the evidence, how convincing is the evidence used to support the (what are your conclusions)

Explain the significance of the quote. Why does it matter? What effect or impact does it have on the audience? What is the poet teaching his/her reader?

/in /by

Dylan thomas

1. Intro Paragraph
Thesis Statement: Think about multiple similar poems that address a universal theme.

a. Biographical information on poet (who, what, when, where, why?)

b. Walt Whitman was born on Long Island, New York in 1819. He worked as a teacher and journalist in addition to writing poetry. Much of his poetry was influenced by nature and the American frontier. At first, readers didn’t care for his poetry because it didn’t follow the traditional structure and his subject matter was considered risque/vulgar. He didn’t gain popularity and influence until after his death in 1892.

c. Walt Whitman uses elaborate lists, rich imagery, and his unique style of free verse poetry to convey the theme of the freedom of the human body.

2. First, the elaborate lists that Walt Whitman uses in his poetry have a repetitive effect on the reader. It broadens the scope of his poetry.

Throughout the poem, the audience may get lost and wonder whether it qualifies as “true poetry.” This effect, I submit, is intentional.

a. For example, in section nine of “I Sing the Body Electric”, Whitman lists human body parts like an anatomy book’s glossary. It never rhymes or uses a fixed meter. But the effect it creates is a structure much like a poem (beginning, middle, end, head, body, legs, arms, feet). In fact, the final lines of the poem insist “O I say these are not the parts and poems of the body only, but of the soul, O I say now these are the soul.” Whitman uses this extended metaphor of body imagery to compare our selves to how poetry is shaped and structured purposefully to have a
beginning, middle, and end just as one would describe a person: starting with the
head, face, eyes, and then move downward in order. That’s what Whitman is
convincing his audience of: beauty, order, human dignity.

b. Citation/Text evidence from a poem. Introduce the poem’s subject with a paraphrase or summary. Then quote directly (unless very long lines).

c. Explain the significance of this example and why it is important.

3. Next, Whitman’s rich imagery provides the senses with intense visuals throughout his poetry.

a. For example, in section three of “I Sing the Body Electric”, he describes a farmer in a short narrative or characterization sketch. This section contrasts with the rest of the poem as it is the only section that focuses on a specific person and isn’t dominated by lists of the human body. The man he describes is “of wonderful vigor, calmness, beauty of person…” The effect this section has on the reader is to teach the audience what humans are capable of. Later in that section, he continues to describe the man as “six feet tall” and “over eighty years old” as well as “the most beautiful and vigorous of the gang.” This anecdote provides a more personal, specific image that might change the audience’s mind about the endurance of the human body.

b. Citation/textual evidence from another poem (same poem?)

c. Explain the significance of the quote. Why does it matter? What effect or impact does it have on the audience? What is the poet teaching his/her reader?

d. Compare and contrast? Why is this important?

4. In addition, his style of free verse poetry does not rely on a fixed meter or rhyme scheme. Therefore, the audience isn’t restrained by a specific word choice or syllables in each line. For example, in every section of the poem, the lines vary anywhere from a few words to as many as 15 words. This may seem disorganized and chaotic to some readers who are used to a sonnet or limerick’s phrasing. However, the free verse style sets one
free from those strict rules and allows a better focus on imagery and the overall message. Whereas in the traditional poems, one might have to cut back on word choice or find synonyms to accommodate meter or rhyme, Whitman’s free verse liberates us to say what is most meaningful. And liberation is exactly what Whitman fought for in his era: abolition, freedom, humanity, the love humans have for one another.

5. In conclusion, Walt Whitman’s poetry is most certainly a diversion from tradition. Thus, my thesis exists to show how poetry, as an art form, can influence public opinion about social matters. When the majority of Americans clung to traditions or refused to accept a progressive philosophy about emancipation, his poetry affected attitudes enough to contribute to major changes. In short, words have power.

Explore current methods of feedback, challenge the academic evidence and reflect on your own experiences of providing feedback. What are the views from a learner and educator viewpoint? How may these views affect the wider organisation?

/in /by

Teaching and learning

Assignment briefing and mapping to Learning Outcomes (LO) and taught sessions

The student will demonstrate, critical analysis and reflective skills by producing a 6000–word report. The completed document will provide evidence that the student has met ALL of the learning outcomes.
The following guidance is designed to aid with your assignment planning but is not exhaustive, you are able to include any information that will enhance the overall document and improve your learning.The portfolio will comprise of 5 sections.

Section 1 You as a teacher and facilitator of learning – reflective account

LO1 Evaluation and application of contemporary issues and models of teaching and learning in the healthcare setting using a critical reflective approach of their own practice.

Session 1 Learning & teaching 1: How adults learn – key theory, perspectives, relevance to your role as a teacher. Scope and range of roles in
learning and teaching – what knowledge and skills required

Session 2 Learning & teaching 2: Educational theory and links to practice

Session 3 Development and learning 1: Teaching and learning styles

Overview This section is a reflection of you as a teacher in your working environment. By using a critical reflective approach, you will be able to
demonstrate how you apply and evaluate teaching and learning theory to improve the student’s educational experience.

Section 4 Patient education, patient and carer participation and involvement in teaching, learning and assessment.

LO2 Evaluation of the impact of patient/carer education, involvement and engagement models on professional practice and education of healthcare staff.

Session 7 Contemporary issues in education 2: Patient education, Patient
involvement and engagement

Overview This section explores in depth the impact of including the patient and carers in healthcare education using current literature to argue the
advantages and disadvantages. Reflection of your own experiences may also be used.

Section 3 Innovation and contemporary practice & development in teaching and learning (technology, simulation, games, experiential learning, distance, communities of practice, problem–based learning etc.)

LO3 Selection and appropriate use of technology and innovation within education and learning, whilst critically evaluating their effectiveness.

Session 6 Contemporary issues in education 1: Technology, innovation, interactive approaches (games, simulation, experiential learning)

Session 8 Contemporary issues in education 3: Inter professional education and learning, Communities of Practice

Overview You are to explore ways of enhancing the student experience using innovative methods. Challenge the historical trends in education by
critically evaluating if approaches discussed in sessions 6 and 8 are effective. What is the evidence?

Section 4 Learner development – role of feedback approaches and adjustments for learning needs/support.

LO 4 Critical analysis and application of current theoretical and methodological approaches in learner assessment, feedback and support.

Session 4 Development and learning 2: Role of feedback (assessment, mentoring, coaching)
Session 10 Contemporary issues in education 4: Quality monitoring & evaluation

Overview Explore current methods of feedback, challenge the academic evidence and reflect on your own experiences of providing feedback.
What are the views from a learner and educator viewpoint? How may these views affect the wider organisation?
Section 5 Identification of learning and development to meet business needs, programme design, quality management and evaluation and evidencing impact

LO 5 Analysis of methodologies used for identification of education and learning interventions to meet business needs and evaluation of impact frameworks/methodologies.

Session 9 Identifying learning and development needs/training needs analysis, evaluation and impact/outcome measurement

Session 10 Contemporary issues in education 4: Quality monitoring & evaluation

Overview How do businesses identify education and learning needs? Explore evaluation strategies and how they may impact learning and teaching. What effect may this have on the learner and educator?

What is the author’s thesis? What evidence does the author use to support their argument? Is the argument persuasive? How does the argument shape your view of your military profession and its history?

/in /by

The First World War and the birth of modern warfare: by Jonathan B.A.Bailey –

(The Dynamics of Military Revolution)

The thesis for this essay is “on page 132 – “That development was the birth of modern style of warfare, the advent of three-dimensional conflict through artillery indirect fire as the foundation of planning at the tactical, operational, and strategic levels of war.

Essay Format Structure:

Using the components of the critical review (introduction, main body, conclusion), the student will answer the following four questions:

1. What is the author’s thesis?

2. What evidence does the author use to support their argument?

3. Is the argument persuasive?

4. How does the argument shape your view of your military profession and its history?

 

Compare and contrast how likely the regeneration methods will be in providing habitat for your species at 20 and 100 years post-harvest. Be specific in your description of how these different regeneration methods are expected to influence stand-scale structure over time.

/in /by

Step 1. Select two focal species and research their natural history and habitat requirements from the Oregon coastal region.

The scenario for this assignment is that you have are a forest ecologist working with a private timber company and you have been tasked with evaluating how planned timber harvests may influence populations of terrestrial vertebrates. To do this, first select two focal species – 1 bird and 1 mammal – that are found in conifer forests of the Pacific Northwest; birds and mammals are required for this assignment because most other groups have inadequate information available for completing this assignment. If you are not sure about which species to choose, one good resource is the book Wildlife-habitat relationships in Oregon and Washington by Johnson and O’Neil; it can be downloaded free as PDF here (Links to an external site.).

After you have selected your two focal species, record their common name, scientific name, and a select a photo for inclusion with your assignment (with credit given to the photographer). Next, choose a location in Oregon that is within the geographic range for each species and determine the forest type that would be your selected location based on this map (Links to an external site.). Then collate the following information for both species:

Description of the annual cycle
Summary of life history traits
Key habitat elements needed for population persistence
Description of spatial scale of habitat use
The seral stage(s) of forests required
This information should be obtained from scientific literature (i.e., peer-refereed journal articles) and/or peer-reviewed databases (e.g., Birds of the World) and summarized as a well-crafted summary of approximately 400 words (~200 words per species).

Step 2. Consider how different silvicultural systems may influence your focal species

Once you have obtained background information on your species, the next step is to consider how undertaking two common regeneration methods may influence populations of your focal species. For both species, you will want to research how the species are impacted by both even-aged management (i.e., clearcut harvest) and uneven-aged management practices (i.e., group selection harvest). Your goal is to find scientific literature on your focal species, or on similar species that could be expected to have a similar response. For example, there may not be information about how herbicide spraying influences Song Sparrow (Melospiza melodia) reproduction, but you could use information obtained on how the White-crowned Sparrow (Zonotrichia leucophrys) responds to herbicide application as a proxy.

To structure your review regarding how each species interacts with silvicultural treatments, make sure to address the following questions. In total, your responses to these questions should total approximately 800 words. Please number your responses.

Compare and contrast how likely the regeneration methods will be in providing habitat for your species at 20 and 100 years post-harvest. Be specific in your description of how these different regeneration methods are expected to influence stand-scale structure over time. For example, what does the forest look like 20/100 years after each silvicultural method? Are critical habitat elements present or absent for each focal species?
Describe the extent to which management actions that often accompany harvest (e.g., herbicide spraying, snag creation) will impact your focal species either positively, negatively, or with a neutral effect.
Provide an overview of the historical disturbance regime for the location you selected, and describe the extent to which the two regeneration methods emulate that natural disturbance for each focal species. Be sure to include at least two components of the historical disturbance regime.
Describe how populations of your focal species are expected to respond over time if the landscape moves from having both of the two regeneration methods in equal abundance to one dominated by even-aged management with short harvest rotations.
Given the projections of future climate change in Oregon (download the Oregon Climate Report here (Links to an external site.)), speculate about how your focal species may be impacted by an interaction between changing climate and the regeneration methods being considered. For example, would you expect climate change to amplify the effects of clearcut harvest on your species? Why or why not?

Step 3. Carefully edit and review your work before turning it in

Be sure that your submission is well-written and demonstrates your ability to succinctly summarize your literature search (~400 words of well-crafted text) and consider questions about how your focal species may be influenced by silvicultural treatments relative to their ecology, life history, and habitat requirements (~800 words). This includes using a minimum of 5 sources located in the scientific literature (i.e., peer-refereed journal articles), in addition to editing your work to make sure it is grammatically correct and lacks spelling errors.

What happens if conditions change, so that the supply and demand sets are altered slightly?  If the equilibrium is disturbed for some reason, what is the result?  How do the suppliers and consumers arrive at the equilibrium?

/in /by

1. Mathematical models in economics

1.1 Introduction
In this book we use the language of mathematics to describe situations which occur in economics. The motivation for doing this is that mathematical arguments are logical and exact, and they enable us to work out in precise detail the consequences of economic hypotheses. For this reason, mathematical modelling has become an indispensable tool in economics, finance, business and management. It is not always simple to use mathematics, but its language and its techniques enable us to frame and solve problems that cannot be attacked effectively in other ways. Furthermore, mathematics leads not only to numerical (or quantitative) results but, as we shall see, to qualitative results as well.

1.2 A model of the market
One of the simplest and most useful models is the description of supply and demand in the market for a single good. This model is concerned with the relationships between two things: the price per unit of the good (usually denoted by p), and the quantity of it on the market (usually denoted by
q). The ‘mathematical model’ of the situation is based on the simple idea of representing a pair of numbers as a point in a diagram, by means of coordinates with respect to a pair of axes. In economics it is customary to take the horizontal axis as the q-axis, and the vertical axis as the p-axis. Thus, for example, the point with coordinates (2000, 7) represents the situation when 2000 units are available at a price of $7 per unit.
How do we describe demand in such a diagram? The idea is to look at those pairs (q, p) which are related in the following way: if p were the selling price, q would be the demand, that is the quantity which would be sold to consumers at that price. If we fill in on a diagram all the pairs (q, p) related in this way, we get something like Figure 1.1.

2 Mathematical models in economics
pDq

Figure 1.1: The demand set
We shall refer to this as the demand set D for the particular good. In economics you will learn reasons why it ought to look rather like it does in our diagram, a smooth, downward sloping curve.
Suppose the demand set D contains the point (30,5). This means that when the price p = 5 is given, then the corresponding demand will be for q = 30 units. In general, provided D has the ‘right’ shape, as in Figure 1.1, then for each value of p there will be a uniquely determined value of q. In this situation we say that D determines a demand function, qD. The value written qD(p) is the quantity which would be sold if the price were p, so that qD(5) = 30, for example.
Example Suppose the demand set D consists of the points (q,p) on the straight line 6q + 8p = 125. Then for a given value of p we can determine the corresponding q; we simply rearrange the equation of the line in the form q = (125 – 8p)/6. So here the demand function is D( ) _ 125 – 8p
q p – 6 .
For any given value of p we find the corresponding q by substituting in this formula. For example, if p = 4 we get
q = qD(4) = (125 – 8 x 4)/6 = 93/6.
o

A model of the market 3
There is another way of looking at the relationship between q and p. If we suppose that the quantity q is given, then the value of p for which (q, p) is
in the demand set D is the price that consumers would be prepared to pay if q is the quantity available. From this viewpoint we are expressing p in
terms of q, instead of the other way round. We write pD(q) for the value of p corresponding to a given q, and we call pD the inverse demand function. Example (continued) Taking the same set D as before, we can now rearrange the equation of the line in the form p = (125 – 6q)/8. So the inverse demand function is
D( ) _ 125 – 6q
p q – 8 .

Next we turn to the supply side. We assume that there is a supply set S consisting of those pairs (q,p) for which q would be the amount supplied to
the market if the price were p. There are good economic reasons for supposing that S has the general form shown in Figure 1.2.
p
q
Figure 1.2: The supply set
If we know the supply set S we can construct the supply function qS and the inverse supply function pS in the same way as we did for the demand function and its inverse. For example, if S is the set of points on the line 2q – 5p = -12, then solving the equation for q and for p we get
S( ) _ 5p – 12 q p – 2 ‘ S( ) _ 2q + 12 p q – 5 .

4 Mathematical models in economics

1.3 Market equilibrium
The usefulness of a mathematical model lies in the fact that we can use mathematical techniques to obtain information about it. In the case of supply and demand, the most important problem is the following. Suppose we know all about the factors affecting supply and demand in the market for a particular good; in other words, the sets Sand D are given. What values of q and p will actually be achieved in the market? The diagram (Figure 1.3) makes it clear that the solution is to find the intersection of D and S, because that is where the quantity supplied is exactly balanced by the quantity required.
p
D s
Figure 1.3: The equilibrium set E = S n D
q
The mathematical symbol for the intersection of the sets Sand D is S n D, and economists refer to E = S n D as the equilibrium set for the given market. Fortunately, there is a simple mathematical technique for finding the equilibrium set; it is the method for solving ‘simultaneous equations’.
Example Suppose the sets D and S are, respectively, the sets of pairs (q, p) such that’
q + 5p = 40 and 2q -15p = -20.
Then a point (q*, p*) which is in the equilibrium set E = S n D must, by definition, be in both Sand D. Thus (q*, p*) satisfies the two equations
q* + 5p* = 40, 2q* – 15p* = -20.
The standard technique for solving these equations is to multiply the first one by 2 and subtract it from the second one. Working through the algebra,

Excise tax 5
we get q* == 20 and p* == 4. In other words the equilibrium set E is the single point (20,4). D It is worth remarking that in this example we get a single point of equilibrium, because we took the sets D and S to be straight lines. It is possible to imagine more complex situations, such as that we shall describe in Example 2.5, where the equilibrium set contains several points, or no points at all.

1.4 Excise tax
Using only the simple techniques developed so far we can obtain some interesting insights into problems in economics. In this section we study the
problem of excise tax. Suppose that a government wishes to discourage its citizens from drinking too much whisky. One way to do this is to impose a fixed tax on each bottle of whisky sold. For example, the government may decide that for each bottle of whisky the suppliers sell, they must pay the government $1. Note that the tax on each unit of the taxed good is a fixed amount, not a percentage of the selling price. Some very simple mathematics tells us how the selling price changes when an excise tax is imposed. Example In the previous example the demand and supply functions are given by
S 15 q (p) == 2 P – 10 ,
and the equilibrium price is p* == 4. Suppose that the government imposes an excise tax of T per unit. How does this affect the equilibrium price?
The answer is found by noting that, if the new selling price is p, then, from the supplier’s viewpoint, it is as if the price were p – T, because the supplier’s revenue per unit is not p, but p – T. In other words the supply function has changed: when the tax is T per unit, the new supply function qST is given by Of course the demand function remains the same. The new equilibrium values qT and pT satisfy the equations

6 Mathematical models in economics Eliminating qT we get
T 15 T
40 – 5p = 2(P – T) – 10.
Rearranging this equation, we obtain and so we have a new equilibrium price of The corresponding new equilibrium quantity is
qT =40-5pT =20-3T.
For example, if T = 1, the equilibrium price rises from 4 to 4.6 and the equilibrium quantity falls from 20 to 17. Unsurprisingly, the selling price has
risen and the quantity sold has fallen. But note that, although the tax is T per unit, the selling price has risen not by the full amount T, but by the fraction 3/5 of T. In other words, not all of the tax is passed on to the consumer. D

1.5 Comments
1. Economics tells us why the supply and demand sets ought to have certain properties. Mathematics tells us what we can deduce from those properties and how to do the calculations.

2. Mathematics also enables us to develop additional features of the model. In the case of supply and demand, we might ask questions such as the following:

  •  What happens if conditions change, so that the supply and demand sets are altered slightly?
  •  If the equilibrium is disturbed for some reason, what is the result?
  •  How do the suppliers and consumers arrive at the equilibrium? A typical instance of the first question is the excise tax discussed above. In this book we shall develop the mathematical techniques needed to deal withmany other instances of these questions.