# 0.1 The use of mathematics in principles of economics  (Page 4/9)

 Page 4 / 9

where Qs is the amount of pizza producers will supply (i.e., quantity supplied).

Finally, suppose that the personal pizza market operates where supply equals demand, or

We now have a system of three equations and three unknowns (Qd, Qs, and P), which we can solve with algebra:

Since Qd = Qs, we can set the demand and supply equation equal to each other:

Subtracting 2 from both sides and adding 2P to both sides yields:

In other words, the price of each personal pizza will be $2. How much will consumers buy? Taking the price of$2, and plugging it into the demand equation, we get:

So if the price is $2 each, consumers will purchase 12. How much will producers supply? Taking the price of$2, and plugging it into the supply equation, we get:

So if the price is $2 each, producers will supply 12 personal pizzas. This means we did our math correctly, since Qd = Qs. Solving Models with Graphs If algebra is not your forte, you can get the same answer by using graphs. Take the equations for Qd and Qs and graph them on the same set of axes as shown in [link] . 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. If you draw the graphs carefully, you will see that where they cross (Qs = Qd), the price is$2 and the quantity is 12, just like the algebra predicted.

We will use graphs more frequently in this book than algebra, but now you know the math behind the graphs.

## Growth rates

Growth rates are frequently encountered in real world economics. A growth rate is simply the percentage change in some quantity. It could be your income. It could be a business’s sales. It could be a nation’s GDP. The formula for computing a growth rate is straightforward:

Suppose your job pays $10 per hour. Your boss, however, is so impressed with your work that he gives you a$2 per hour raise. The percentage change (or growth rate) in your pay is $2/$10 = 0.20 or 20%.

To compute the growth rate for data over an extended period of time, for example, the average annual growth in GDP over a decade or more, the denominator is commonly defined a little differently. In the previous example, we defined the quantity as the initial quantity—or the quantity when we started. This is fine for a one-time calculation, but when we compute the growth over and over, it makes more sense to define the quantity as the average quantity over the period in question, which is defined as the quantity halfway between the initial quantity and the next quantity. This is harder to explain in words than to show with an example. Suppose a nation’s GDP was $1 trillion in 2005 and$1.03 trillion in 2006. The growth rate between 2005 and 2006 would be the change in GDP ($1.03 trillion –$1.00 trillion) divided by the average GDP between 2005 and 2006 ($1.03 trillion +$1.00 trillion)/2. In other words:

#### Questions & Answers

how does one analyze a market where both demand and supply shift
Reymark Reply
explain and justify the effect of the event to the demand and supply for direction then apply the elasticity concepts for extent , support with diagrams
samantha
objective of macro economic
saroj Reply
give the characteristics of good money?
Chok Reply
suppose that there is a positive aggregate demand shock. what graph most accurately show how this would affect the aggregate demand-aggregate supply model?
Shielyn Reply
ppf and ad/as
jax
PPF , AD/AS
Shubham
Every Work must be done properly based on its Feasibility Studies duly prepared.
Pundato
why is it desirable for a country to have a large gdp? give an example of something that would raise gdp and yet be undesirable
JAWAD
if there is advance technology in the fishing industry, how will this change in supply and demand
El Reply
yes
Shehazahd
increase Supply, since technology in fishing will increase the efficiency of fishing , higher productivity and thus lower per unit cost of production, which incentive producers to increase their supply. demand wise, not so sure. depends on what exactly is the advancement in tech.
samantha
how many types of natural rate of unemployment
Trina Reply
what is macro economic
muniira Reply
in the year 1933, Ragnar Frisch used the term macro
Ammu
factors that determine the country material standard ?
Serena Reply
population divide by gdp in currency analysis
Aniyikayekenny
what is the important of studying economics
Akurugu Reply
economics teaches you how to think not what think
umer
in order to know how our country operates and corporate with other countries based on the international marketing and to know how our economy is doing regarding incomes going in and out through exchange of goods and services,we have to study more about economics to gain more and better understanding
Betty
important studying economic is make a choice under the condition of scarcity
cafifo
why is it desirable for a country to have a large gdp? give an example of something that would raise gdp and yet be undesirable
JAWAD
High GDP is good as it serves as an indicator of strong economic performance which would affect confidence in an economy, and affect living standards of citizens in the economy.
samantha
Me believes in GNP as an indicator bcoz no country tries to export products and services successfully. No government agrees of inter-regional jurisdiction to save guard investments.
Tan
I do agree with u on this. As far as I am aware of, theorically, both GDP and GNP are indicators of economic growth. but GNP is technically more accurate.
samantha
is labour a intermediate good or final good
umer Reply
what is economics
Mahamed Reply
Economic is science, which Studies human behaviour and who they are earn and spend
Ammu
economics is the science which shows how can use scare resources among society
umer
economic is a science which study human behavior as a result relationship between ends at scarce means which have more than one use
Jovert
simply, economics is a science which studies human wants,
Saeed
Economy is knowledge of choice
Omid
how to derive the equation for the equilibrium level of national income in an open economy with no taxes
loise Reply
what is inflation?
Herry Reply
when price goes up with some shottime
umer
Give me 5 example for Macro economics
Neha Reply
1. Markets 2. Market Failure 3. Competition 4. Price Stability 5. Efficiency
Luyando
please can you explain markets and markets failure ?
Timothy
When we talk about Markets as an example of macroeconomics, we look at demand and supply in labor market.
Luyando
Then for market failures, we focus on market inefficiencies and failures such as the destruction of common goods due to economic systems that provide no incentive for their preservation
Luyando
Who is a discourage worker.?
Timothy
a discourage worker is simply a worker who stop looking for a job because he/she believe no job is available for them..
Joseph
sloping curve normal
Mirasol Reply
A normal sloping curve
Mirasol
State what happen to the aggregate supply curve for beef. The price of beef decrease
Mirasol
i think there is positive relationship between price n supply so as the price decreases the supply curve so decreases and vice versa
Dharani
quantity supply will decrease,less.profit for firms in a perfectly competitive market i guess
Joseph
yaa
Dharani

### Read also:

#### Get the best Macroeconomics course in your pocket!

Source:  OpenStax, Macroeconomics. OpenStax CNX. Jun 16, 2014 Download for free at http://legacy.cnx.org/content/col11626/1.10
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Macroeconomics' conversation and receive update notifications?

 By By By OpenStax By Brooke Delaney By By Joli Julianna By Richley Crapo By OpenStax By Cath Yu By Yasser Ibrahim By OpenStax By OpenStax