#### Transcript Math Review

```Micro Tools Review
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1. Plotting coordinates
2. Vertical intercept
3. Horizontal intercept
4. Slope
5. Ceteris paribus: how relates
6. Tangency
7. Independent variable
8. Dependent variable.
9. Solving equations.
Graph of a
Demand Curve
Demand for Concert
Tickets
Point on
Curve
a
Ticket Price Ticket
Demand
\$250
0
b
\$200
40
c
\$150
80
d
\$100
120
e
\$50
160
f
\$0
200
Relate to Demand
Theory
• Demand curve:
Shows quantity demanded as a function
of price so that Qd is the dependent
variable and P is the independent
variable.
Qd = fn(P).
• Ceteris Paribus Assumption:
“Other Things Equal” : graph is twodimensional and everything ELSE
related to quantity demanded OTHER
than price is held constant.
• Note:  c.p.factors, draw new line.
• Law of Demand:
Negative relationship between quantity
demanded and price.
Line slopes down.
Further Details
• For folks with math background:
with this graph, economists put the
independent variable (price) on the
vertical axis and the dependent
variable (quantity demanded) on the
horizontal axis. This is opposite to
what is done in math, and will affect
how you calculate the slope off of
the equation.
• The shape of the demand curve is
the SLOPE. Since the curve is
downward-sloping, we say the slope
is negative.
Calculating Slope of
Demand Curve
• Slope of Demand curve always
negative as curve is drawn
down to right.
• Calculate slope as movement
from one point to another.
Slope = rise/run
Slope = (P) / (Qd)
• Using previous graph drawn:
Slope = (200-150)/(40-80) =
50/-40 = 5/-4 = -1.25.
Slope using Algebraic
Expression
• Equation for a demand curve:
Qd = a – bP
Qd = 8 – 2P
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Qd = quantity demanded
P = price
See negative relationship
Slope of demand curve:
Need P/Q.
• See: -b = Q/P
Slope = -1/b = -1/2
Intercepts
• Intercepts are where the line hits
the vertical and horizontal axis.
question—what is price when
Qd=0? Can show on graph and
solve for using equation.
question—what is Qd when
P=0? Can show on graph and
solve for using equation.
Calculate Intercepts
Using Equation
• Use equation for demand curve:
Qd = a – bP
Qd = 8 – 2P
• Solve for vertical intercept:
Set Qd=0 and solve for price.
0 = 8-2P
2P=8
P=4 (see = a/b in general equation)
• Solve for horizontal intercept:
Set P=0 and solve for Qd.
Qd=8 – 2*0
Qd=8. (see = a in general equation)
Measuring Slope of
Nonlinear Curve
• Slope of a nonlinear curve is NOT
a constant, so slope will be different
at each different point along the
curve.
• To measure slope of nonlinear
curve:
– Pick a particular point;
– Draw line tangent to the curve at that
point;
– Calculate slope of that tangent line.
– Intercepts useful here.
• Note that tangent means touches at
one point.
Slope of Nonlinear
Curve
Solving Equations
• Two skills:
– 1) Given an equation and a price, solve
for quantity (example below).
– 2) Given two equations, solve for
equilibrium price and quantity (example
to come in later chapter).
• Example for # 1:
Qd = a – b P
15 = 20 – 1*P.
Solve for P.
In-Class Exercise
POINT
Video Price
Video Qd
a
\$60
0
b
50
3
c
40
6
d
30
9
e
20
12
f
10
15
g
0
18