mat 125 – applied calculus 6.7 - applications of the definite integral to business and economics
TRANSCRIPT
MAT 125 – Applied Calculus6.7 - Applications of the Definite Integral to Business and Economics
6.7 - Applications of the Definite Integral to Business and Economics
2 Today’s Class We will be learning the following concepts today:
Consumers’ and Producers’ Surplus
The Future and Present Value of an Income Stream
Lorenz Curves and Income Distributions
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6.7 - Applications of the Definite Integral to Business and Economics
3 Introduction In this section, we will be considering several applications of the
definite integral in the fields of business and economics.
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6.7 - Applications of the Definite Integral to Business and Economics
4 Consumers’ Surplus
The consumers’ surplus is the difference between what the consumers would be willing to pay for a commodity and what they actually pay for them.
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6.7 - Applications of the Definite Integral to Business and Economics
5 Producers’ Surplus
The producers’ surplus is the difference between what the suppliers actually receive and what they would be willing to receive.
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6.7 - Applications of the Definite Integral to Business and Economics
6 Example 1
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6.7 - Applications of the Definite Integral to Business and Economics
7 Example 2
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6.7 - Applications of the Definite Integral to Business and Economics
8 Example 3
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6.7 - Applications of the Definite Integral to Business and Economics
9 Annuities The amount of an annuity is the sum of the payments plus the
interest earned.
Where P = size of each payment in the annuity
r = interest rate compounded continuously
T = term of the annuity in years
m = number of payments per yearDr. Erickson
6.7 - Applications of the Definite Integral to Business and Economics
10 Annuities
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6.7 - Applications of the Definite Integral to Business and Economics
11 Example 4
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6.7 - Applications of the Definite Integral to Business and Economics
12 Example 5
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6.7 - Applications of the Definite Integral to Business and Economics
13 Lorenz Curve
Let f (x) denote the proportion of the total income received by the poorest 100x% of the population for 0 ≤ x ≤ 1.
Using this terminology, f (0.3) = 0.1 simply states that the lowest 30% of the income recipients receive 10% of the total income.
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6.7 - Applications of the Definite Integral to Business and Economics
14 Lorenz Curve The function f has the following properties:
1. The domain of f is [0, 1].
2. The range of f is [0, 1].
3. f (0) = 0 and f (1) = 1.
4. f (x) ≤ x for every x in [0, 1].
5. f is increasing on [0, 1].
Dr. Erickson
6.7 - Applications of the Definite Integral to Business and Economics
15 Lorenz Curve
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6.7 - Applications of the Definite Integral to Business and Economics
16 Example 6
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6.7 - Applications of the Definite Integral to Business and Economics
17 Example 7
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6.7 - Applications of the Definite Integral to Business and Economics
18 Next Class Review/Make-up/Final Exam
THE END!
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