Macroeconomics (MindTap Course List)
Macroeconomics (MindTap Course List)
10th Edition
ISBN: 9781285859477
Author: William Boyes, Michael Melvin
Publisher: Cengage Learning
Question
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Chapter 16, Problem 2E
To determine

Calculate the level of output after four years if initial output equals $1,000 and the economy grows at a rate of 8% a year.

Expert Solution & Answer
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Explanation of Solution

Calculate the output for 4 years with a growth rate of 8% by multiplying the initial output with growth rate per year then add obtained value with growth rate.

Given,

Initial output as 8% as $1,000

Growth rate:

  8%=8100=0.08

Now,

Multiply initial year output with growth of rate per year

Then,

Add previous year output with growth rate of current year.

That is,

    GrowthAmount
    Initial output  $1,000
    Growth rate at the end of First year
      (Initialoutput×growthrateperyear)
      1,000×0.08=80
    Level of output at the end of first year
      (Initialoutput+Growthattheendoftheyear)
      1000+80=1080
    Growth rate at the end of second year
      (Firstyearoutput×growthrateperyear)
      1,080×0.08=86.40
    Level of output at the end of second year
      (Firstyearoutput+Growthattheendofthesecondyear)
      1080+86.4=1,166.4
    Growth rate at the end of third year
      (Second yearoutput×growthrateperyear)
      1,166.4×0.08=93.312
    Level of output at the end of third year
      (Second yearoutput+Growthattheendofthethirdyear)
      1,166.4+93.3=1,259.71
    Growth rate at the end of fourth year
      (Third yearoutput×growthrateperyear)
      1,259.71×0.08=100.77
    Level of output at the end of fourth year
      (third yearoutput+Growthattheendofthefourthyear)
      1,259.71+93.3=1,360.49

Therefore, the level of output at the end of fourth year is $1,360.49

Economics Concept Introduction

To calculate the value of growth at the end of first year:

Multiply initial year output with growth of rate per year.

That is,

  Growthattheendoffirstyear=Intialoutput×growthrateatendoftheyear=1000×0.08=80

Growth at the end of the year is $80

  Level of output at the end of first year=1,000+80=1,080

Similarly

Calculate the level of output for 4 years with a growth rate of 8% and add obtained value with growth rate.

Therefore, the level of output at the end of fourth year is $1,360.49

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