1. Economics 10 1 2017 September Lecture 4 Chapter 1A Math for Economics
2017 Economics 101 CCC

2. Content Show me the math General: Graphs & Equations Equations
Demand & Supply Equations
Equilibrium Equations
Graphing

3. General: Graphs & Equations

4. Graphs used in Economic Models

5. Graphs used in Economic Models

6. Graphs used in Economic Models

7. The Slope of a Relationship
The slope of a relationship is the change in the value of the variable measured on the y-axis divided by the change in the value of the variable measured on the x-axis.
We use the Greek letter  (capital delta) to represent “change in.”
So y means the change in the value of the variable measured on the y-axis and x means the change in the value of the variable measured on the x-axis.
Slope equals y/x.

8. The Slope of a Relationship
The Slope of a Straight Line
The slope of a straight line is constant.
Graphically, the slope is calculated as the “rise” over the “run.”
The slope is positive if the line is upward sloping.

9. The Slope of a Relationship
The slope is negative if the line is downward sloping.

10. Equations demand and supply

11. In math graphs and equations
Y = mX + b
slope intercept format
Slope = ?? Rise/Run
Intercept = ??
Y = 5X + 10
So if X = 0 then Y = ? Y X

12. Demand Curve Demand curves follow this general equation.. QD = c – dP
c = intercept
Given QD = 10-2P
If P = 2 then Qd = ?
If P = 3 then Qd = ?
If P = 5 then Qd = ?
Quantity
Price

13. Demand Curve Given QD = 10-2P
Expresses Qd as a function of Price and in economics that is fine.
In Graphing – need to rearrange demand equation
Inverse Demand Curve used for graphing!
Price
Quantity

14. Demand Curve Given QD = 10-2P P = 5- 1/2Qd Intercept = 5 Slope = ½
If Q = 0 then P = 5
Inverse Demand Curve used for graphing!
Price
Quantity 5

15. Supply Curve All supply curves follow this general equation..
Qs = a + bP
a = intercept
if P =0 how many supplied to the market by firm?
b = inverse slope of curve
Quantity
Price

16. Supply Curve
Qs = P-4 2
Rearrange and get
Quantity
Price

17. Supply Curve Qs = P-4 2 Rearrange and get P = 2Q + 4
If Q = 0 then P = 4
Quantity
Price 4

18. Market equilibrium

19. Market Equilibrium Qd= Qs Find Price
no product in excess and no product in shortage
not everyone is happy

20. Market Equilibrium

21. Example 1 Given QD= 8 – P QS = ½ P-1 Find market equilibrium
Set Qd = Q s
Solve for P value or equilibrium price
Solve for Q by inputting this price into either equation!
Please graph this problem labeling all lines, axes, and the equilibrium, price, slope, intercept and quantity

22. Example continued : Same equations
The government institutes a price support program where the support price is $4.
Calculate the resulting shortage or a surplus value

23. Example 2 Qd = 80-3P Qs = -20+ 2P Find the market equilibrium
Please graph this problem labeling all lines, axes, and the equilibrium, price, slope, intercept and quantity

24. Watch your
Ps & Qs

25. WATCH YOUR P’s AND Q’s
Given QD= a - bP .. Demand Curve Conceptually correct! P defines Qd Graphically – not so much! Why? Because it is the equation for graph like this .. This equation provides info for Quantity vertical axis Price horizontal axis meaning that Qd defines price ..not in economics !

26. WATCH YOUR P’s AND Q’s In economics … Price defines Qd
And we use the graph where
Price vertical axis
Quantity horizontal axis

27. WATCH YOUR P’s AND Q’s Thus - if we want to graph this equation
QD= a - bP
And want a graph where
P is on the vertical axis
Q is on the horizontal axis
Find the slope and intercept for that graph and curve
Need to rearrange things..
All that means is to put P on the left hand of the equation!

28. WATCH YOUR P’s AND Q’s P = a/b -1/b QD Intercept Slope
QD = a - bP QD + bP = a then bP = a- QD
P = a/b -1/b QD
Now the intercept & slope are correct for these axis
Intercept
Slope

29. Example Given Qd= (16-P)/4 4Qd = 16-P 4Qd – 16 = -P -4Qd + 16 = P
Multiply both sides by 4
4Qd = 16-P
Subtract 16 from both sides
4Qd – 16 = -P
Multiply both side by -1
-4Qd + 16 = P
rearranged to P = 16-4Qd
So slope (rise/run) is 4 and intercept is 16 on a graph where P vertical axis and Q horizontal axis

30. example
Supply Qs= (P-4)/2
rearranged
P = 2Q + 4

31. WATCH YOUR P’s AND Q’s Slope Defined:
slope is always equal to rise/run..
So the slope depends upon the axis. In this graph …
Rise is change in price and Run is change in quantity

32. WATCH YOUR P’s AND Q’s Watch the Sign of the SLOPES
Be careful with your + and - and remember the use of a + bP does not imply that the a and b are always positive.
These are generalized equation forms where a is the intercept and b is the slope.
Slope (b value) in a demand curve will be negative
Slope (b value) in a supply curve will be negative

33. Example Given a SUPPLY curve of
Qs= (P-4)/2 then you need to place it into this generalized format Qs = P-4 2Q+4 = P or
P = 2Q so here the intercept = 4 and slope is equal to positive 2

34. Example Given a DEMAND curve of Qd= (16-P)/4
Rearrange to find the slope b and intercept a as follows:
4Qd= 16-P
4Qd - 16 =- P
Rearrange to make P positive
P = 16-4Qd
So intercept is 16 and slope is negative 4

35. And to find equilibrium??? What do you do?
Does it matter which of these you use??
Demand Qd= (16-P)/4 or rearranged to P = Qd
Supply Qs= (P-4)/2 or rearranged to P = 2Q + 4

36. End of slides