Econ Math Review

7/25/2019 Econ Math Review

1/9

Review of Demand Graphs

Demand: Qd= 1000 - 100P

Inverse Demand: P = 10 - (Qd/100)

P Qd0 1000

1 900

2 8003 700

4 600

5 500

6 400

7 300

8 200

9 100

10 0

Slope -1/100

x-axis intercept 1000y-axis intercept 10

Slope = Change in P / Change in Q

For any two points along this linear demand curve, the slope = -1/100.

The slope does not change along this linear demand curve.

If the demand equation is written in the inverse demand form: P = b - mQ, then the slope of the demand curve

is -m. Note that the slope is negative.

The x-axis intercept is the quantity demanded when price = 0.

The y-axis intercept is the price when quantity = 0.

0

2

4

6

8

10

12

0 500 1000 1500

Price

perburger

(y-axis)

Quantity Demanded (x-axis)

Graph 1: Linear Demand Curve for Burgers

D0

ECON 300 Page 1 of 9


2/9

Review of Demand GraphsChange in Slope of Linear Demand Curve (holding y-axis in tercept constant)

Demand: Qd1= 2000 - 200P

Inverse Demand: P = 10 - (Qd/200)

P Qd10 2000

1 18002 1600

3 1400

4 1200

5 1000

6 800

7 600

8 400

9 200

10 0

Slope -1/200x-axis intercept 2000

y-axis intercept 10

Change in Intercept of Linear Demand Curve

Demand: Qd2= 1450 - 100P

Inverse Demand: P = 14.5 - (Qd/100)

P Qd20 1450

1 1350

2 1250

3 1150

4 1050

5 950

6 850

7 750

8 650

9 550

10 450

11 350

12 250

13 150

14 50

14.5 0

Slope -1/100

x-axis intercept 1450

y-axis intercept 14.5

0

2

4

6

8

10

12

0 500 1000 1500 2000 2500

Price

perburger

Quantity Demanded

Graph 2: Change in Slope of Demand Curve

D0 D1

0

2

4

6

8

10

12

14

16

0 500 1000 1500 2000

Price

perburger

Quantity Demanded

Graph 3: Change in Intercept of Demand Curve

D0

D2



3/9

Review of Supply Graphs

Supply: Qs= -125 + 125P

Inverse Supply: P = 1 + (Qs/125)

P Qs0 -125

1 0

2 1253 250

4 375

5 500

6 625

7 750

8 875

9 1000

10 1125

Slope 1/125

y-axis intercept 1

Slope = Change in P / Change in Q

For any two points along this linear supply curve, the slope = 1/125.

The slope does not change along this linear supply curve.

If the supply equation is written in the inverse supply form: P = b + mQ, then the slope of the supply curve

is m. Note that the slope is positive.

The y-axis intercept is the price when quantity = 0.

0

2

4

6

8

10

12

0 200 400 600 800 1000 1200

Price

perburger

Quantity Supplied

Graph 4: Linear Supply Curve for Burgers

S0



4/9

Review of Supply Graphs

Change in Slope of Linear Supply Curve (holding y-intercept constant)

Supply: Qs1= -175 + 175P

Inverse Supply: P = 1 + (Qs/175)

P Qs1

0 -1751 0

2 175

3 350

4 525

5 700

6 875

7 1050

8 1225

9 1400

10 1575

Slope 1/175y-axis intercept 1

Change in Intercept of Linear Supply Curve

Supply: Qs2= -5 + 125P

Inverse Supply: P = (5/125) + (Qs/125)

P Qs20 -5

0.04 0

1 120

2 245

3 370

4 495

5 620

6 745

7 870

8 995

9 1120

10 1245

Slope 1/125

y-axis intercept 1/25

0

2

4

6

8

10

12

0 500 1000 1500 2000

Price

perburger

Quantity Supplied

Graph 5: Change in Slope of Supply Curve

S1S0

0

2

4

6

8

10

12

0 500 1000 1500

P

rice

perburger

Quantity Supplied

Graph 6: Change in Intercept of Supply Curve

S2

S0



5/9

Review of Market Equil ibr ium

Demand: Qd= 1000 - 100P

Supply: Qs= -125 + 125P

P Qd Qs Solve for Equili brium (Qd= Qs)

0 1000 -125 1000 - 100P = -125 + 125P

1 900 0 1125 = 225 P

2 800 125 P* = 53 700 250 Q* = 500

4 600 375

5 500 500

6 400 625

7 300 750

8 200 875

9 100 1000

10 0 1125

0

2

4

6

8

10

12

0 500 1000 1500

Price

perburger

Quantity

Graph 7: Market Equilibr ium for Burgers

D0

S0

P* = 5Q* = 500



6/9

Review of Market Equil ibr iumEffect of Demand Shift on Market Equilibr ium

Demand: Qd1= 1450 - 100P

Supply: Qs= -125 + 125P

P Qd1 Qs Solve for Equili brium (Qd= Qs)

0 1450 -125 1450 - 100P = -125 + 125P

1 1350 0 1575 = 225 P2 1250 125 P* = 7

3 1150 250 Q* = 750

4 1050 375

5 950 500

6 850 625

7 750 750

8 650 875

9 550 1000

10 450 1125

0

2

4

6

8

10

12

0 200 400 600 800 1000 1200 1400 1600

Price

perburg

er

Quantity

Graph 8: New Market Equilibrium for Burgers

D0

S0

P* = 7Q* = 750

D1



7/9

Review of Nonlinear Funct ions

Function: Y = -X2+ 10X

Y X

0 0

9 1

16 2

21 324 4

25 5

24 6

The shape of this function is concave (not linear). The slope is not the same at every point along this function.

The slope at a particular point can be defined as the slope of the straight line tangent to the function at that point.

Note that as X increases, the tangent lines get flatter - their slope gets smaller.

0

5

10

15

20

25

30

0 2 4 6 8

Y

X

Graph 9: Nonlinear Function

0

5

10

15

20

25

30

0 2 4 6

Y

X

Graph 10: Nonlinear Function with Tangent Lines

Slope of Tangent Lines =Change in Y / Change in X



8/9

Review of Nonlinear Functions with Contour Lines

Funct ion : Z = X*Y

Contour Line Z = 2 Contour Line Z = 6 Contour Line Z = 10

Z X Y Z X Y Z X Y

2 1 2.00 6 1 6.00 10 1 10.00

2 2 1.00 6 2 3.00 10 2 5.002 3 0.67 6 3 2.00 10 3 3.33

2 4 0.50 6 4 1.50 10 4 2.50

2 5 0.40 6 5 1.20 10 5 2.00

2 6 0.33 6 6 1.00 10 6 1.67

2 7 0.29 6 7 0.86 10 7 1.43

2 8 0.25 6 8 0.75 10 8 1.25

2 9 0.22 6 9 0.67 10 9 1.11

2 10 0.20 6 10 0.60 10 10 1.00

0.00

2.00

4.00

6.00

8.00

10.00

12.00

0 5 10 15

Y

X

Graph 11: Contour Lines for Z = X*Y

Contour Z = 2

Contour Z = 6

Contour Z = 10



9/9

Review of Nonlinear Functions with Contour Lines

Funct ion : Z = min(X,2Y)

Contour Line Z = 4 Contour Line Z = 6 Contour Line Z = 10

Z X Y Z X Y Z X Y

4 4 5.00 6 6 6.00 10 10 8.00

4 4 4.00 6 6 5.00 10 10 7.004 4 3.00 6 6 4.00 10 10 6.00

4 4 2.00 6 6 3.00 10 10 5.00

4 5 2.00 6 7 3.00 10 11 5.00

4 6 2.00 6 8 3.00 10 12 5.00

4 7 2.00 6 9 3.00 10 13 5.00

4 8 2.00 6 10 3.00 10 14 5.00

vertex = (4,2) vertex = (6,3) vertex = (10,5)

0.00

1.00

2.00

3.00

4.00

5.00

6.00

7.00

8.00

9.00

0 5 10 15

Y

X

Graph 12: Contour Lines for Z = MIN(X,2Y)

Contour Z = 4

Contour Z = 6

Contour Z = 10


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Econ Math Review