Economics:
Economics:
10th Edition
ISBN: 9781285859460
Author: BOYES, William
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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Exercise 6 Imagine that you head production of a multinational food processing company. The ongoing uncer- tainty about costs means that you are unsure of the future cost of one of your inputs, x2. Your firm's production function is y = f(x1, x2) = x²x²² The output price p is 1000, x1 = 27, and wx₁ = 60. 1. Suppose the current input price is Wx2 = 50. Solve for the optimal choice of x2. 2. Now suppose that the probability the input price remains 50 is 0.65 and the probability that Wx2 60 is 0.35. Solve for the optimal choice of x2. Round down to the nearest integer. = 3. Finally, suppose the costs do actually rise, i.e., Wx2 = 60. Calculate the difference in profit from the uncertainty in (2) vs. the certainty in (1).
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