Explanation Given: An Australian study found that, if other factors are constant, taller people receive higher wages for the same work. The study reported a “height premium” for men of 3% of the hourly wages for a 10 cm increase in height; for women the height premium reported was 2%. We assume that hourly wages are a linear function of height, with slope given by the height premium at the average hourly wages for that gender. The average hourly wage of an Australian man as a function of his height, x cm Calculation: The study reported a “height premium” for men of 3% of the hourly wages for a 10 cm increase in height. We are given the wages of men was $29.40 at height of 178 cm. If height increases by 10 cm then wages will be 3% hike. New Height = 178+10 = 188 cm Wages for 188 cm = 29.40 + 3% of 29.40 = $30.282 The average hourly wage of an Australian man as a function of his height, x cm Height will be independent variable and wages will be depends on height. From above we get two points (178,29.4) and (188,30.282) Using two point formula to find the equation of line. y − y 1 x − x 1 = y 2 − y 1 x 2 − x 1 Where, x 1 → 178 , x 2 → 188 , y 1 → 29 To determine (b) The average hourly wage of an Australian women as a function of his height, x cm To determine (c) The difference of average hourly wage of men and women for height 178 cm. To determine (d) To find the height when men and women predict same wages.

Applied Calculus, 6e WileyPLUS + Loose-leaf

6th Edition

ISBN: 9781119408901

Author: Deborah Hughes-Hallett, Andrew M. Gleason, Patti Frazer Lock, Daniel E. Flath

Publisher: Wiley (WileyPLUS Products)

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Question

Chapter 1.2, Problem 43P

To determine

(a)

The average hourly wage of an Australian man as a function of his height, x cm

To determine

(b)

The average hourly wage of an Australian women as a function of his height, x cm

To determine

(c)

The difference of average hourly wage of men and women for height 178 cm.

To determine

(d)

To find the height when men and women predict same wages.

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Chapter 1.2, Problem 42P

Chapter 1.3, Problem 1P

Chapter 1 Solutions

Applied Calculus, 6e WileyPLUS + Loose-leaf

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(a) The average hourly wage of an Australian man as a function of his height, x cm

Solution Summary: The author calculates the average hourly wage of an Australian man as a function of his height.

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(a) The average hourly wage of an Australian man as a function of his height, x cm

(b) The average hourly wage of an Australian women as a function of his height, x cm

(c) The difference of average hourly wage of men and women for height 178 cm.

(d) To find the height when men and women predict same wages.

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Chapter 1 Solutions

(a)

The average hourly wage of an Australian man as a function of his height, x cm

(b)

The average hourly wage of an Australian women as a function of his height, x cm

(c)

The difference of average hourly wage of men and women for height 178 cm.

(d)

To find the height when men and women predict same wages.