EXPLORING ECON.-W/ACCESS (LL) >CUSTOM<
EXPLORING ECON.-W/ACCESS (LL) >CUSTOM<
7th Edition
ISBN: 9781305757448
Author: Sexton
Publisher: CENGAGE C
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Chapter 20, Problem 1P
To determine

(a)

To compute:

The years taken by a country to double its output.

Expert Solution
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Answer to Problem 1P

The years taken by a country to double its output is shown in the table below:

    0.5 percent140 years
    1 percent140 years
    1.4 percent140 years
    2 percent140 years
    2.8 percent140 years
    3.5 percent140 years
    7 percent140 years

Explanation of Solution

The calculation for years taken to double the annual growth rate:

By applying Rule 70,

The number of years is calculated by dividing 70 with the growth rate.

1. If the growth rate is 0.5%, then 140 years will be required to double the output. (70÷0.5=140 years)

2. If the growth rate is 1%, then 70 years will be required to double the output. (70÷1=70 years)

3. If the growth rate is 1.4%, then 50 years will be required to double the output. (70÷1.4=50 years)

4. If the growth rate is 2%, then 35 years will be required to double the output. (70÷2=35 years)

5. If the growth rate is 2.8%, then 25 years will be required to double the output. (70÷2.8=25 years)

6. If the growth rate is 3.5%, then 20 years will be required to double the output. (70÷3.5=20 years)

7. If the growth rate is 7%, then 10 years will be required to double the output. (70÷7=10 years)

Economics Concept Introduction

Annual growth rate:

Annual growth rate refers to the rate at which the value of an investment changes over a particular timeperiod.

Ruleof 70:

The years needed by a country to double its output at a given growth rate is calculated by the rule of 70. It is calculated or estimated by dividing 70 with the given growth rate.

To determine

(b)

To compute:

The value of real GDP in 50 years at the given annual growth rate.

Expert Solution
Check Mark

Answer to Problem 1P

The real GDP in 50 years when the annual growth rate is 1.4% is $200.40, for annual growth rate of 2.8% is $397.79 and for annual growth rate of 7% is $2,945.70.

Explanation of Solution

The country's real GDP is $100 billion.

Calculation for real GDP is shown below for different growth rates:

Using the compound interest formula,

Real GDP in 50years when the annual growth rate is 1.4percent :

  Real GDP in 50 years= Present GDP×(1+0.014 )50=100(1+0.014)50=$200.40

Real GDP in 50years when the annual growth rate is 2.8percent :

  Real GDP in 50 years=Present GDP×(1+0.028 )50=100(1+0.028)50=$397.79

Real GDP in 50years when the annual growth rate is 7percent :

  Real GDP in 50 years=Present GDP×(1+0.07 )50=100(1+0.07)50=$2,945.70

Economics Concept Introduction

Annual growth rate:

Annual growth rate refers to the rate at which the value of an investment changes over a particular timeperiod.

Real GDP:

Real gross domestic product is defined as a measure of economic output with respect to changes in prices.It is a macro-economic measure.

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