mba index

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Basic Idea

 A graph enables us to visualize the relationship between

two variables.

To make a graph, set two lines perpendicular to each

other:

• The horizontal line is called the x -axis.• The vertical line is called the y -axis.

•  The common zero point is called the origin.

APPENDIX: MAKING AND USING GRAPHS

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APPENDIX: MAKING AND USING GRAPHS

$rend is a general tendenc& +or the value o+ a variable

to rise or +all.

&r'ss%secti'n !ra" is a graph that shows thevalues o+ an economic variable +or di++erent groups in a

population at a point in time.

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APPENDIX: MAKING AND USING GRAPHS

Figure A.*!a" shows ascatter diagram.

The data +or to*%% show that asincome increases,expenditure increases.

n *%%$ !marked %$",income per person was*(,% andexpenditure per personwas */,$%%.

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APPENDIX: MAKING AND USING GRAPHS

Figure A.*!b" showsanother scatter diagram.

The data show that as themonthl& bill +ell, morepeople became cell phonesubscribers.

n / !marked /", *%percent o+ 0.1. cell-phonesubscribers had a monthl&cell phone bill o+ '%.

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APPENDIX: MAKING AND USING GRAPHS

Figure A.*!c" shows atimes-series graph.

• 2ow or high.

• 3ising or +alling.

• 4hanging 5uickl& orslowl&.

The graph shows whenthe price o+ co++ee was:

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APPENDIX: MAKING AND USING GRAPHS

Figure A.*!d" shows across-section graph.

The graph shows thepercentage o+ peoplewho participate invarious sports activities.

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APPENDIX: MAKING AND USING GRAPHS

Interretin! Gra"s Used in Ec'n'#ic

M'de(s

P'siti)e re(ati'ns"i or  direct re(ati'ns"i is arelationship between two variables that move in thesame direction.

*inear re(ati'ns"i is a relationship that graphs as astraight line.

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APPENDIX: MAKING AND USING GRAPHS

Figure A.6!a" shows apositive !direct" relationship.

 As the speed increases, thedistance traveled in ' hoursincreases proportionatel&.

 At a speed o+ $% 7#8, &ou

travel *%% miles in ' hours9point A.

 At a speed o+ % 7#8, &outravel 6%% miles in ' hours9

point B.

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APPENDIX: MAKING AND USING GRAPHS

Figure A.6!b" shows a

positive !direct" relationship.

 As the distance sprintedincreases, recover& timeincreases.

;ut sprint twice as +ar andit takes more than twice aslong to recover9the curvegets steeper.

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APPENDIX: MAKING AND USING GRAPHS

Figure A.6!c" shows apositive !direct" relationship.

 As stud& time increases,the number o+ problemsworked increases.

;ut stud& twice as long

and the number o+problems &ou work less than double9the curvegets less steep.

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APPENDIX: MAKING AND USING GRAPHS

Ne!ati)e re(ati'ns"i or  in)erse re(ati'ns"i is a

relationship between two variables that move in

opposite directions.

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APPENDIX: MAKING AND USING GRAPHS

Figure A.$!a" shows anegative !inverse" relationship.

 As the time pla&ing tennisincreases, the time pla&ings5uash decreases.

;ecause one more hour o+

tennis means one hour less o+s5uash, the relationshipbetween these two variablesis described b& a straight line.

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APPENDIX: MAKING AND USING GRAPHS

Figure A.$!b" shows anegative !inverse" relationship.

 As the )ourne& length increases,the cost per mile o+ the trip +alls.

;ut there is a limit to how

much the cost per mile can+all, so the curve becomesless steep as )ourne& lengthincreases.

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APPENDIX: MAKING AND USING GRAPHS

Figure A.$!c" shows anegative !inverse" relationship.

 As leisure time increases,

the number o+ problemsworked decreases.

;ut during the tenth hour o+leisure !the +irst hour o+

work" the decrease in thenumber o+ problems workedis largest, so the curvebecomes steeper as leisure

time increases.

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APPENDIX: MAKING AND USING GRAPHS

Figure A.'!a" shows amaximum point.

1. The curve slopes upward asthe &ield rises.

2. The curve is +lat at point A,the maximum &ield.

3. Then slopes downward asthe &ield +alls.

 As the rain+all increases:

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APPENDIX: MAKING AND USING GRAPHS

Figure A.'!a" shows aminimum point.

1. The curve slopes downwardas the cost per mile +alls.

2. The curve is +lat at point B,the minimum cost per mile.

3. The curve slopes upwardas the cost per mile rises.

 As the speed increases:

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APPENDIX: MAKING AND USING GRAPHS

Figure A.!a" showsvariables that are unrelated.

 As the price o+ bananasincreases, the student<sgrade in economicsremains at /' percent.

 The curve is horizontal.

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APPENDIX: MAKING AND USING GRAPHS

Figure A.!b" showsvariables that are unrelated.

 As rain+all in 4ali+orniaincreases, the output o+French vine&ards remainsat 6 billion gallons.

 The curve is vertical.

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APPENDIX: MAKING AND USING GRAPHS

$"e S('e '+ a Re(ati'ns"i

S('e e5uals the change in the value o+ the variable

measured on the y -axis divided b& the change the valueo+ the variable measured on the x -axis.

1lope = ∆y  > ∆ x .

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APPENDIX: MAKING AND USING GRAPHS

Figure A./!a" shows apositive slope.

1.  ?hen @ x  is $,

2.  @y  is 6.

3.  1lope !@y @ x " is 6$.

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APPENDIX: MAKING AND USING GRAPHS

Figure A./!b" shows anegative slope.

1.  ?hen @ x  is $,

2.  @y  is B6.

3.  1lope !@y @ x " is B6$.

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APPENDIX: MAKING AND USING GRAPHS

Figure A./!c" shows theslope o+ a curve at a point.

 1.  ?hen @ x  is $,2.  @y  is 6.

3.  1lope !@y @ x " is 6$.

1lope o+ the curve at Ae5uals the slope o+ the redline tangent to the curve at A.

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APPENDIX: MAKING AND USING GRAPHS

Re(ati'ns"is A#'n! M're $"an $,'

-aria(es

To graph a relationship that involves more than twovariables, we use the ceteris paribus assumption.

Ceteris Paribus

Cother things remaining the same.DFigure A.( shows the relationships between ice cream

consumed, the temperature, and the price o+ ice cream.

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APPENDIX: MAKING AND USING GRAPHS

Figure !a" shows the relationship between price andconsumption, temperature remaining the same.

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Figure !b" shows the relationship between temperature andconsumption, price remaining the same.

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APPENDIX: MAKING AND USING GRAPHS

Figure !c" shows the relationship between price andtemperature, consumption remaining the same.