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

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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

What is Budget constraint
Veena Reply
Budget constraints is when government expenditure is greater than government revenue or when revenue is less than expenditure.
Jeremiah
thanks
fuh
join you to microeconomic
fuh
what will happen to the budget constraints if the consumer income decline?
Maryam Reply
please what is the relationship between microeconomics and macroeconomics?
Maryam
Accordingly, Microeconomics focuses on the drivers of decision making, as well as the ways in which individuals' decisions affect the overall supply and demand and supply of particular goods and services, in an economy, and in turn their prices. Whereas Macroeconomics is the study of the big picture
Donia
Of the economy (retrieved from Google)
Donia
***quora.com/How-do-microeconomics-and-macroeconomics-interrelate
Donia
when consumer's income decline then purchasing power of consumer decreases .Budget line shifts inward.
Zeeshan
what is a deductive reasoning
tobi Reply
Deductive reasoning makes use of to arrive at the conclusion.That is, the premise must be real and put to rest .
Jeremiah
Deductive statement makes use of facts to arrive at the conclusion.That is ,the premise must be real and put to rest in order to produce the required results.
Jeremiah
price change in case of an inferior good
divya Reply
Search on Google
Harsh
what is frontier
Ebrima Reply
I want the answers
Gideon
What is the difference between microeconomics and macroeconomics?
Krysstel Reply
what is demand
Chidex Reply
demand Is the quantity of goods a consumer is willing and able to produce at a given price and at a particular period of time.
inioluwa
fixed and variable factors of production
muqtaar Reply
James' income declines, and as a result, he buys more spinach. Is spinach an inferior or a normal good? What happens to James' demand curve for spinach?
Alwyn Reply
When the price floor is implemented, the equilibrium quantity will decrease. Is it true or wrong?
naim Reply
it's true
Nathaniel
what is elasticity
Chibuzor Reply
calculate the price elasticity of demand for Mr chibuzor (y) using both arc and price elasticity formulae
Chibuzor
The best way to understand elasticity is just looking to your behavior as a consumer. Just think about the basic need like food. We all know without, one end up dying if could not eat for a couple of days. It is a reason we say the demand is inelastic. It's impossible to survive without food.
busywork
On the other hand, the demand for luxury goods is elastic because it's sensitive to price changes as it is possible to survive without such good like expensive car. We say demand for such goods is elastic because as consumers, we have an option of not buying as it's possible to survive without them.
busywork
pls how do u calculate for the opportunity cost of two commodities when giving two commodities in question, and one is measured in tons and the other is measured in units
DBA Reply
what are tge factors that causes change in demand
emy Reply
change in income change in price change in taste and preference
Wahida
Change in price, ,availability of substitutes ,change in consumer preferences, changes in economic situation.
busywork
Qd=f(Y, P ,Ps ,F, T ,W , Pop)
Zeeshan
substitute goods taste preference income
Hermina
income increase and decrease is the most important reason of demand changing
Taufiq
Price variable : price This leads to a same direction change for certain luxury goods, and to an opposite direction change for the ordinary, normal, inferior... that's the remaining types of goods. As a result, the is a movement along the demand curve. We also have non price variables like income,
Jonas
We also have non price variables like income, that increases the willingness to pay of the consumers and thus increase the demande at any price, leading to a shift of the demand curve to the right if income increases or to the left of income decreases. A change in income also leads to
Jonas
A same direction change in demand for the normal good and for the opposite direction change for inferior goods.
Jonas
We also have other non price variables like taste, time horizon,...
Jonas
what are the production function
Mohammed Reply
capital and land and labor that is called the function production
Mustafe
production is a function of capital and labor.
Zeeshan
land labor capital are the function of production
Mumin
yes
Mustafe
when we existing economic we classify in this action
Mustafe
the technical relationship b/w input and output
Neha
Neha can we say it is not technical relationship
Waseem
How u can say like that Waseem ji
Neha
as far I know it is physical and technical relationship because producer are rational
Neha
so they use physical inputs to get physical output by technical process
Neha
how to use price elasticity of demand for analysis water demand?
Pupu
The production function is the relation between inputs and outputs. It shows how a producer combines the sets of available inputs and resources to maximise his output and thus his turnover.
Jonas
What is indifference curve
JUMA
the are use price to get quality of good and service
Adamu
1. Interdepwndence 2. advertising, 3. group behaviour 4. Competition 5. barriers to entry of firm 6. lack of uniformity 7. Existence of price rigidity 8. No unique pattern of pricing behaviour 9. Indeterminatensess of demand curve
Shashan Reply

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Source:  OpenStax, Microeconomics. OpenStax CNX. Aug 03, 2014 Download for free at http://legacy.cnx.org/content/col11627/1.10
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