# 0.1 The use of mathematics in principles of economics

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(This appendix should be consulted after first reading Welcome to Economics! ) Economics is not math. There is no important concept in this course that cannot be explained without mathematics. That said, math is a tool that can be used to illustrate economic concepts. Remember the saying a picture is worth a thousand words? Instead of a picture, think of a graph. It is the same thing. Economists use models as the primary tool to derive insights about economic issues and problems. Math is one way of working with (or manipulating) economic models.

There are other ways of representing models, such as text or narrative. But why would you use your fist to bang a nail, if you had a hammer? Math has certain advantages over text. It disciplines your thinking by making you specify exactly what you mean. You can get away with fuzzy thinking in your head, but you cannot when you reduce a model to algebraic equations. At the same time, math also has disadvantages. Mathematical models are necessarily based on simplifying assumptions, so they are not likely to be perfectly realistic. Mathematical models also lack the nuances which can be found in narrative models. The point is that math is one tool, but it is not the only tool or even always the best tool economists can use. So what math will you need for this book? The answer is: little more than high school algebra and graphs. You will need to know:

• What a function is
• How to interpret the equation of a line (i.e., slope and intercept)
• How to manipulate a line (i.e., changing the slope or the intercept)
• How to compute and interpret a growth rate (i.e., percentage change)
• How to read and manipulate a graph

In this text, we will use the easiest math possible, and we will introduce it in this appendix. So if you find some math in the book that you cannot follow, come back to this appendix to review. Like most things, math has diminishing returns. A little math ability goes a long way; the more advanced math you bring in, the less additional knowledge that will get you. That said, if you are going to major in economics, you should consider learning a little calculus. It will be worth your while in terms of helping you learn advanced economics more quickly.

## Algebraic models

Often economic models (or parts of models) are expressed in terms of mathematical functions. What is a function? A function describes a relationship. Sometimes the relationship is a definition. For example (using words), your professor is Adam Smith. This could be expressed as Professor = Adam Smith. Or Friends = Bob + Shawn + Margaret.

Often in economics, functions describe cause and effect. The variable on the left-hand side is what is being explained (“the effect”). On the right-hand side is what is doing the explaining (“the causes”). For example, suppose your GPA was determined as follows:

This equation states that your GPA depends on three things: your combined SAT score, your class attendance, and the number of hours you spend studying. It also says that study time is twice as important (0.50) as either combined_SAT score (0.25) or class_attendance (0.25). If this relationship is true, how could you raise your GPA? By not skipping class and studying more. Note that you cannot do anything about your SAT score, since if you are in college, you have (presumably) already taken the SATs.

please suggest me topic for research, about following issues 1. labor migration & economic growth 2. terrorism and trade 3. religious pessimism and trad
state the law of diminishing returns.
the law diminishing returns states that as more and more units of variable factors of production(such as capital, labour) are combined with a fixed factor (such as land) after a certain point, the marginal product diminishes or declines
Vanessa
I would like to add one more point In the above statement. The addition of more variable factors of production will only leads to diminishing returns if the existing fixed capacity is fully utilised.
Ankit
what is diminishing marginal utility
with more units of consumption of a same commodity you will feel less satisfied with every next commodity. if you are thirsty you purchase a bottle of Coca-Cola and drink it, you will be satisfied at the same time again you drink another bottle of Cola you will be less satisfied in comparison.
Ankit
utility nothing it is just a measurement of your satisfaction.
Ankit
and diminishes as long as you consume same commodity continuously
Ankit
what is taxation
levy paid by eligible individuals and companies to the government
Kingt
tax
Raji
A means by which governments finance their expenditure by imposing charges on citizens and corporate entities. Governments use taxation to encourage or discourage certain economic decisions.
Raji
a source of economic revenue in which working citizens pay levy which varies from one individual to the other.
Vanessa
monies paid by residents of a country to the government in which the residents benefit indirectly
Kotey
it's the government, looking for funding to create public goods and services so that everyone can be happy.
Sinethemba
why does the demand curve slop downward
Ronaxic
thanks
Ronaxic
why does the demand curve slop downward?
Ronaxic
the demand curve is nothing but a line which shows willingness to purchase a commodity or a thing.For example, if you want to purchase a Pepsi can you are willing to purchase 5 Pepsi cans if they are of $3 each. but if they are of$5 each you want to purchase only three of them.
Ankit
so at Higher prices you like to purchase less quantity that's why demand curve falls down words. but please note demand curve does not fall downwards always for inferior goods the rise up parts like a supply curve because at Higher prices you tend to purchase those goods more
Ankit
and at lower prices of inferior goods you tend to avoid them and relocate your Limited money to other goods.
Ankit
what is taxation?
In simple term. Taxation can be defined as compulsory payment levy on company or individual by the government. It can be direct or indirect.
salawu
what is capital
K.visor
its nice
Belaisan
it's nice
Abdulwali
capital , it is a investment of money or assets which is invested before starting up of the business
its nice
Belaisan
it won't let you sleep
Ankit
Please any Ghanaian schooling at KNUST?
combining factors of production is the role of
the situation in economic where by a more valuable good is sold at a low price while less valuable good is sold at a higher price .how can we describe this situation in economic
Fung
price discrimination
Fayaz
deman and supply
Samim
price discrimination
Citizen
enterlrenure
Fayaz
you can take example of water and daimond. you can ask someone to choose anyone from above 1. to a person in a Sahara desert and 2. a girl in London. you will get your answer
Ankit
it depends upon the buyer's preference what he wants why he wants and what is the necessity of that product at current time.
Ankit
causes of high elasticity of demand
causes of high elasticity of supply
Onyango
what is optimazation
lepekola
lepekola
A trade-off  is a situational decision that involves diminishing one quality, or property of a design in return for gains in other aspects.
what is indifference curve ?
abdullah
its represnted by the loops of points and gives same level of satisfaction
hisham
what is enterpreneurship
Kukoyi
Entrepreneurship is the talent, knowledge and willingness individual has to engage in an activity that can result in new kind of firm
what is the short run industry supply curves?
james
I think there' s a mistake. P = - 0.4 + 0.2Qs is the supply curve and not the demand curve. Am I correct?
Qs is quantity supplied
The
This is what I think
The
this eaquation is supply curve Qs=P-0.4 the relationship is positive when the price increase the Qs increase....
mukhtaar
since Qs is quantity supplied P= -0.4 + 0.2Qs =>P +0.4=0.2Qs =>P/0.2 + 0.4=Qs I made Qs the subject of the formula or equation. So your answer is correct
The
P = -0.4 + 0.2Qs is the same as P/0.2+0.4=Qs Price has a direct relationship with the quantity supplied i.e the higher the price the higher the quantity supplied. that is why it is +0.4(this is the quantity and it is postive) and P/O.2(is the price and it is positive).
The
For the demand equation let me give an example 0.2P-0.4=Qd. Here the P is postive(+0.2) and the quantity which is -O.4 is negative( because of the negative sign(-) there is an inverse relationship between price and quantity. For quantity demanded the higher the price the lower the quantuty.
The
It's how I understand it
The
0.2P-0.4=Qd. the equation is wrong because the price have direct ralationship Quantity demanded but the correct equation is-0.2P -0.4=Qd so the higher price the lower Quantity
mukhtaar
I think the relationship is inverse because of the negative sign(-)
The
ok You mean the price and quantity demanded should be negative(inverse relationship) for Qd and the price and quantity supplied should be postive(direct relationship) for Qs
The
thank you for the correction
The
yes because it got a positive gradient of +0.2
Michael
This is the mistake I found: "Since P is on the vertical axis, it is easiest if you solve each equation for P. The demand curve is then P = 8 – 0.5Qd and the demand curve is P = –0.4 + 0.2Qs. Note that the vertical intercepts are 8 and –0.4, and the slopes are –0.5 for demand and 0.2 for supply."
Valeria
dear price do not depend on quantity. rather quantity depends on price. so the equation should be Qty=0.2Px-0.4
Michael
please can someone generate supply equation for me
ok
Detto
Qs=f(P,Pr,G,E,Z,Pf,)
The
where p is price, Pr is price of related goods, G is goals of a firm E is supplier's future expectation of prices,Z is other related factors, Pf is cost of factors of production.
The
I think it's wrong
The
if Qd=90-p Qs=90+p
The
the coefficient of price must be positive since supply curve is positively slopping
Kotey
yes
The
it's true. thank you
The
welcome
Kotey
ok
The
OK, thank you
David
no one can do that, you must determine the the key factors for the commodity, like price, income, prices of alternative commodity, and other factors, if you want the main equation, you must have 4 values, 2 values for each quantity and price, for one commodity
Chief
What is the acceptable definition of economic?
The economics is the optimal use for the resources, this is general definition, but from my point view it is the production,
Chief
diagram of perfectly inelastic
this platform is okay
K.visor
chi-square test is used to test A. Analysis of variance B. Association between the qualitative variables C. Difference between means of two distribution drawn from the same population D. Difference between the means of two distribution drawn from different population
Amanuel
Confirm?
Syk
A
Satyanarayana
Lawrence
Thank you
Syk
What is economic?
bilya
is the system that study the difference between resources and the growth population
Messi
Economics studies humanbehaviour as a relation between ends and scarce means which have alternative uses
Kotey
rigth .....but economic has different concepts
Messi
yes
Kotey
what is equilibrium
it is that point where price is equal to output or rather a point where demand is equal to supply
Fung
it is a point where consumer get maximum satisfaction and producers maximise profit or minimise loss
Imtiyaz
thanks
Obed
supply equal demand in one point
Messi
it's a point where supply and demand meets/equal whether profit or loss
deany