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Mar 09, 2018

Marginal Analysis-simple exampleMath165: Business Calculus

Roy M. Lowman

Spring 2010, Week4 Lec3

Roy M. Lowman Marginal Analysis-simple example

Marginal Analysisexample

Given:

cost per unit: c = $6 per unit, cost to producer

Demand Relation: q = 100 2p,sometimes written D(p) = 100 2p. Note, as the price perunit increases, the demand decreases.

production level: q,assume that the number of units sold is the same as thenumber of units produced.

price per unit: p, selling price

Roy M. Lowman Marginal Analysis-simple example

Marginal Analysisexample

Given:

cost per unit: c = $6 per unit, cost to producer

Demand Relation: q = 100 2p,sometimes written D(p) = 100 2p. Note, as the price perunit increases, the demand decreases.

production level: q,assume that the number of units sold is the same as thenumber of units produced.

price per unit: p, selling price

Roy M. Lowman Marginal Analysis-simple example

Marginal Analysisexample

Given:

cost per unit: c = $6 per unit, cost to producer

Demand Relation: q = 100 2p,sometimes written D(p) = 100 2p. Note, as the price perunit increases, the demand decreases.

production level: q,assume that the number of units sold is the same as thenumber of units produced.

price per unit: p, selling price

Roy M. Lowman Marginal Analysis-simple example

Marginal Analysisexample

Given:

cost per unit: c = $6 per unit, cost to producer

production level: q,assume that the number of units sold is the same as thenumber of units produced.

price per unit: p, selling price

Roy M. Lowman Marginal Analysis-simple example

Marginal Analysisexample

Given:

cost per unit: c = $6 per unit, cost to producer

production level: q,assume that the number of units sold is the same as thenumber of units produced.

price per unit: p, selling price

Roy M. Lowman Marginal Analysis-simple example

Marginal Analysisexample

Given:

cost per unit: c = $6 per unit, cost to producer

production level: q,assume that the number of units sold is the same as thenumber of units produced.

price per unit: p, selling price

Roy M. Lowman Marginal Analysis-simple example

Marginal Analysisexample part 1

Find:

C(q), Cost function

R(q), Revenue function

P(q), Profit function

qmax production level to maximize profit

pmax the price to charge for each unit to maximize profit

maximum profit Pmax

Cavg =C(q)

q Average Cost function

break even point(s), set P(q) = 0 and solve for q

Roy M. Lowman Marginal Analysis-simple example

Marginal Analysisexample part 1

Find:

C(q), Cost function

R(q), Revenue function

P(q), Profit function

qmax production level to maximize profit

pmax the price to charge for each unit to maximize profit

maximum profit Pmax

Cavg =C(q)

q Average Cost function

break even point(s), set P(q) = 0 and solve for q

Roy M. Lowman Marginal Analysis-simple example

Marginal Analysisexample part 1

Find:

C(q), Cost function

R(q), Revenue function

P(q), Profit function

qmax production level to maximize profit

pmax the price to charge for each unit to maximize profit

maximum profit Pmax

Cavg =C(q)

q Average Cost function

break even point(s), set P(q) = 0 and solve for q

Roy M. Lowman Marginal Analysis-simple example

Marginal Analysisexample part 1

Find:

C(q), Cost function

R(q), Revenue function

P(q), Profit function

qmax production level to maximize profit

pmax the price to charge for each unit to maximize profit

maximum profit Pmax

Cavg =C(q)

q Average Cost function

break even point(s), set P(q) = 0 and solve for q

Roy M. Lowman Marginal Analysis-simple example

Marginal Analysisexample part 1

Find:

C(q), Cost function

R(q), Revenue function

P(q), Profit function

qmax production level to maximize profit

pmax the price to charge for each unit to maximize profit

maximum profit Pmax

Cavg =C(q)

q Average Cost function

break even point(s), set P(q) = 0 and solve for q

Roy M. Lowman Marginal Analysis-simple example

Marginal Analysisexample part 1

Find:

C(q), Cost function

R(q), Revenue function

P(q), Profit function

qmax production level to maximize profit

pmax the price to charge for each unit to maximize profit

maximum profit Pmax

Cavg =C(q)

q Average Cost function

break even point(s), set P(q) = 0 and solve for q

Roy M. Lowman Marginal Analysis-simple example

Marginal Analysisexample part 1

Find:

C(q), Cost function

R(q), Revenue function

P(q), Profit function

qmax production level to maximize profit

pmax the price to charge for each unit to maximize profit

maximum profit Pmax

Cavg =C(q)

q Average Cost function

break even point(s), set P(q) = 0 and solve for q

Roy M. Lowman Marginal Analysis-simple example

Marginal Analysisexample part 1

Find:

C(q), Cost function

R(q), Revenue function

P(q), Profit function

qmax production level to maximize profit

pmax the price to charge for each unit to maximize profit

maximum profit Pmax

Cavg =C(q)

q Average Cost function

break even point(s), set P(q) = 0 and solve for q

Roy M. Lowman Marginal Analysis-simple example

Marginal Analysisexample part 1

There are two standard ways to approach the problem offinding qmax1st solve MR = MC i.e. set R(q) = C(q) and solve for qmax.

Using this method you never need to actually find the profitfunction. Sometimes this is useful.

2nd solve MP = 0, i.e. set P(q) = 0 and solve for qmax. Hereyou must first find the profit function and its derivative.

This should be obvious from the graph:

-65 -60 -55 -50 -45 -40 -35 -30 -25 -20 -15 -10 -5 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 105 110 115 120 125 130 135 140 145 150 155 160 165 170 175 180 185 190 195

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5

10

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30

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40

45

50

55

60

65

70

75

80

85

90

95

100

105

110

Roy M. Lowman Marginal Analysis-simple example

Marginal Analysisexample part 1

There are two standard ways to approach the problem offinding qmax1st solve MR = MC i.e. set R(q) = C(q) and solve for qmax.

Using this method you never need to actually find the profitfunction. Sometimes this is useful.

2nd solve MP = 0, i.e. set P(q) = 0 and solve for qmax. Hereyou must first find the profit function and its derivative.

This should be obvious from the graph:

-65 -60 -55 -50 -45 -40 -35 -30 -25 -20 -15 -10 -5 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 105 110 115 120 125 130 135 140 145 150 155 160 165 170 175 180 185 190 195

-40

-35

-30

-25

-20

-15

-10

-5

5

10

15

20

25

30

35

40

45

50

55

60

65

70

75

80

85

90

95

100

105

110

Roy M. Lowman Marginal Analysis-simple example

Marginal Analysisexample part 1

There are two standard ways to approach the problem offinding qmax1st solve MR = MC i.e. set R(q) = C(q) and solve for qmax.

Using this method you never need to actually find the profitfunction. Sometimes this is useful.

2nd solve MP = 0, i.e. set P(q) = 0 and solve for qmax. Hereyou must first find the profit function and its derivative.

This should be obvious from the graph:

-65 -60 -55 -50 -45 -40 -35 -30 -25 -20 -15 -10 -5 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 105 110 115 120 125 130 135 140 145 150 155 160 165 170 175 180 185 190 195

-40

-35

-30

-25

-20

-15

-10

-5

5

10

15

20

25

30

35

40

45

50

55

60

65

70

75

80

85

90

95

100

105

110

Roy M. Lowman Marginal Analysis-simple example

Marginal Analysisexample part 1

Using this method you never need to actually find the profitfunction. Sometimes this is useful.

This should be obvious from the graph:

-40

-35

-30

-25

-20

-15

-10

-5

5

10

15

20

25

30

35

40

45

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