GRAPHS AND EQUATIONS

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Post by modi on Sun Oct 27, 2013 1:37 pm

GRAPHS AND EQUATIONS


1). a line or curve on a two dimensional (two variable graph) graph shows the relationship of

how an independent variable (x) “affects” a dependent variable (y), assuming all “outside”

variables that affect (y) (not x) are ceteris paribus (fixed, constant or frozen).


2). a two dimensional graph has a horizontal or (x) axis and a vertical or (y) axis. In

mathematics, the independent or (x) variable is always on the horizontal axis and the

dependent or (y) variable is always on the vertical axis. In economics this is not always the

case.

3). a line or curve on a graph therefore shows the relationship between an independent

variable (x) and a dependent variable (y), assuming ceteris paribus.

4). movement along a line/curve vs. shift in a line/curve

a). particular attention should be paid to the differences between MOVEMENT-ALONG-A-

LINE (or curve) vs. a SHIFT-IN-A -LINE (or curve) concepts. Understanding the

distinction between the two is crucial to understanding Economics.

Movement-Along-a-Line
• Ceteris paribus applies

• Shows the impact the independent variable has on a dependent variable assuming

outside variables are unchanged (ceteris paribus). Therefore movement-along-a line
shows the exact effect variable ( x ) has on variable (y) because we "assume" that all

other variables that affect (y) have not changed, i.e. are ceteris paribus and therefore

can not affect the value of (y).

Shift-In-A-Line
• Ceteris paribus does not apply.

• Shows the impact on the dependent variable (y) that a change in one or more of the
"outside variables" (not x) has on the dependent variable (y).

b) the difference between these two concepts is very important to grasp.

- for example, it seems logical to say that a buyer will buy less of a product, the higher
the price. This means that as price rises, the quantity demanded of the good will fall.
This is only true if we make the assumption that all other variables (other than price)
that affect quantity demanded are held constant or are ceteris paribus. If so, we can
show the exact relationship between price and quantity demanded of a product with
a line (or curve) on a graph.

But what happens if we assume that as the price of a good rises, the buyer's income
(one of the outside variables) rises? The relationship between price and quantity
demanded then changes or "shifts" because ceteris paribus did not apply! With a
rise in income, a buyer will buy more of the product at a higher price than they would
have before their income increased. So a shift in the line shows the effect that a
change in one or more of the "outside variables" has on the dependent variable (y).

SLOPE OF A LINE OR CURVE

- measures “rate of change” of the variable (y) with respect to a change in the variable
(x).

- slope = change in (y) divided by change in (x)

- steepness or flatness of a line or curve. The greater the steepness, the greater the
slope, i.e. the greater the rate of change in (y) with respect to a change in (x).
- rise (change in y) divided by run (change in x)

Slope is : 1). Constant along a straight line,
2). Changing along a curved line.

Infinite slope: vertical line
Zero slope: horizontal line

Linear vs. Nonlinear Relationships
Linear – straight line, constant slope
Non-linear – curved line, changing slope


VERTICAL OR Y INTERCEPT

1). the value of (y) at the intersection of a line or curve on a graph with the (y) axis.

2). the value of (y) when (x) = 0.

3). represents the constant of a linear or straight line equations.

4). represents the value of (y) that is determined by “outside” variables (not (x)) that are
fixed or frozen or assumed constant.


POSITIVE OR DIRECT RELATIONSHIP OF VARIABLES

1). both variables move in same direction: increase in (x) , (y) increases; decrease in (x), (y)
decreases.


NEGATIVE OR INDIRECT OR INVERSE RELATIONSHIP OF VARIABLES

1). variables move in opposite directions: increase in (x), (y) decreases; decrease in (x), (y)
increases.



MAXIMUM AND MINIMUM VALUES OF DEPENDENT VARIABLES

1). the maximum value of an “inverted U shaped ”curve is the highest value of (y) on the
curve.

2). the minimum value of a “ U shaped” curve is the lowest value of (y) on the curve.

SLOPE OF A NON-LINEAR (CURVED) LINE

1). the slope of a “specific point” on a non-linear curve is equal to the slope of a tangent line to
the curve at the specific point.

EQUATION OF A STRAIGHT LINE

1). the equation for any straight line is: y = a + bx.

2). it shows in algebraic terms:

a). the “effect” (x) has on (y) and
- the “effect” (x) has on (y) is the coefficient of (x) which is equivalent to the slope of
the equation’s line.

b). the “effect” all other variables have on (y).
- the “effect” of all other variables on (y) is the constant of the equation or Y
intercept.

3). in the equation for a straight line y = a + bx:

a). (x) = the independent variable
b). (y) = the dependent variable
c). (a) = constant or vertical intercept or the effect of outside variables on (y)
d). (b) = coefficient of (x) or slope or “the effect” (x) has on (y)

MARGINAL CHANGES

1). since economics is concerned with marginal changes, it is also important to note that the
SLOPE of a line or curve is equal to marginal changes in the dependent variable.
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