Explanation Given : The national average income A = T N where N is the total number of households and T is the total income earned by the entire population of a country r has a value such that 0 ≤ r ≤ 1 . Calculation : Step 1: The number of households in the bottom rth part is r N Step 2: The total income among the households in the bottom rth part is F ( r ) T . Hence the average income in this part of the population is F ( r ) T r N = F ( r ) r ... To determine (b) The reason how the average income among households in the interval [ r , r + Δ r ] is equal to ( F ( r + Δ r ) − F ( r ) Δ r ) A where A is the national average income of a country. To determine (c) The derivation for the interpretation that says a household in the 100rth percentile has income F'(r)A when passing F ( r + Δ r ) − F ( r ) Δ r A to the limit Δ r → 0 To determine (d) The percentage of households that have above - average income from the Lorenz curves L 1 and L 2

Applied Calculus (with Infotrac) 3rd Edition By Waner, Stefan; Costenoble, Steven Published By Brooks Cole Hardcover

3rd Edition

ISBN: 9781319048518

Author: Colin Adams Jon Rogawski

Publisher: Macmillan Higher Education

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Question

Chapter 3.4, Problem 49E

To determine

(a)

The reason how the average income among households in the bottom rth part is equal to $\frac{F (r)}{r} A$ where A is the national average income of a country.

To determine

(b)

The reason how the average income among households in the interval $[r, r + Δ r]$ is equal to $(\frac{F (r + Δ r) - F (r)}{Δ r}) A$ where A is the national average income of a country.

To determine

(c)

The derivation for the interpretation that says a household in the 100rth percentile has income F'(r)A when passing $\frac{F (r + Δ r) - F (r)}{Δ r} A$ to the limit $Δ r \to 0$

To determine

(d)

The percentage of households that have above - average income from the Lorenz curves L₁ and L₂

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Chapter 3.4, Problem 48E

Chapter 3.4, Problem 50E

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Chapter 3 Solutions

Applied Calculus (with Infotrac) 3rd Edition By Waner, Stefan; Costenoble, Steven Published By Brooks Cole Hardcover

Ch. 3.1 - Prob. 1PQ Ch. 3.1 - Prob. 2PQ Ch. 3.1 - Prob. 3PQ Ch. 3.1 - Prob. 4PQ Ch. 3.1 - Prob. 5PQ Ch. 3.1 - Prob. 1E Ch. 3.1 - Prob. 2E Ch. 3.1 - Prob. 3E Ch. 3.1 - Prob. 4E Ch. 3.1 - Prob. 5E

Ch. 3.1 - Prob. 6E Ch. 3.1 - Prob. 7E Ch. 3.1 - Prob. 8E Ch. 3.1 - Prob. 9E Ch. 3.1 - Prob. 10E Ch. 3.1 - Prob. 11E Ch. 3.1 - Prob. 12E Ch. 3.1 - Prob. 13E Ch. 3.1 - Prob. 14E Ch. 3.1 - Prob. 15E Ch. 3.1 - Prob. 16E Ch. 3.1 - Prob. 17E Ch. 3.1 - Prob. 18E Ch. 3.1 - Prob. 19E Ch. 3.1 - Prob. 20E Ch. 3.1 - Prob. 21E Ch. 3.1 - Prob. 22E Ch. 3.1 - Prob. 23E Ch. 3.1 - Prob. 24E Ch. 3.1 - Prob. 25E Ch. 3.1 - Prob. 26E Ch. 3.1 - Prob. 27E Ch. 3.1 - Prob. 28E Ch. 3.1 - Prob. 29E Ch. 3.1 - Prob. 30E Ch. 3.1 - Prob. 31E Ch. 3.1 - Prob. 32E Ch. 3.1 - Prob. 33E Ch. 3.1 - Prob. 34E Ch. 3.1 - Prob. 35E Ch. 3.1 - Prob. 36E Ch. 3.1 - Prob. 37E Ch. 3.1 - Prob. 38E Ch. 3.1 - Prob. 39E Ch. 3.1 - Prob. 40E Ch. 3.1 - Prob. 41E Ch. 3.1 - Prob. 42E Ch. 3.1 - Prob. 43E Ch. 3.1 - Prob. 44E Ch. 3.1 - Prob. 45E Ch. 3.1 - Prob. 46E Ch. 3.1 - Prob. 47E Ch. 3.1 - Prob. 48E Ch. 3.1 - Prob. 49E Ch. 3.1 - Prob. 50E Ch. 3.1 - Prob. 51E Ch. 3.1 - Prob. 52E Ch. 3.1 - Prob. 53E Ch. 3.1 - Prob. 54E Ch. 3.1 - Prob. 55E Ch. 3.1 - 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(a) The reason how the average income among households in the bottom rth part is equal to F ( r ) r A where A is the national average income of a country.

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(a) The reason how the average income among households in the bottom rth part is equal to F(r)rA where A is the national average income of a country.

(b) The reason how the average income among households in the interval [r,r+Δr] is equal to (F(r+Δr)−F(r)Δr)A where A is the national average income of a country.

(c) The derivation for the interpretation that says a household in the 100rth percentile has income F'(r)A when passing F(r+Δr)−F(r)ΔrA to the limit Δr→0

(d) The percentage of households that have above - average income from the Lorenz curves L1 and L2

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(a)

The reason how the average income among households in the bottom rth part is equal to $\frac{F (r)}{r} A$ where A is the national average income of a country.

(b)

The reason how the average income among households in the interval $[r, r + Δ r]$ is equal to $(\frac{F (r + Δ r) - F (r)}{Δ r}) A$ where A is the national average income of a country.

(c)

The derivation for the interpretation that says a household in the 100rth percentile has income F'(r)A when passing $\frac{F (r + Δ r) - F (r)}{Δ r} A$ to the limit $Δ r \to 0$

(d)

The percentage of households that have above - average income from the Lorenz curves L₁ and L₂