Question

Refer to Figure 8.2 and assume that the values for points a, b, and c are \(10 billion, \)20 billion, and $18 billion, respectively. If the economy moves from point a to point b over a 10-year period, what must have been its annual rate of economic growth? If, instead, the economy was at point c at the end of the 10-year period, by what percentage did it fall short of its production capacity?

Short answer

• If the economy moves from point ‘a’ to point ‘b,’ the economic growth must be 7 percent.
• The economy experienced a fall of 20 percent in its production capacity when it moved from point ‘a’ to point ‘c.’

Step-by-step solution

Step 1. Calculating the annual rate of economic growth

The real GDP of the economy increases from $10 billion to $20 billion when it moves from point ‘a’ to point ‘b.’ The movement from economy doubles the size of the economy. The annual economic growth can be determined using the ‘rule of 70’. The formula for ‘rule of 70’ is:

$Annualpercentagerateofgrowth=\frac{70}{ApproximatenumberofyearsrequiredtodoubletherealGDP}$

The economy doubles its real GDP size over a period of 10 years. The required annual percentage rate of growth is calculated by putting the value of the period in the above expression.

$$\begin{gathered} Annualpercentagerateofgrowth=\frac{70}{10} \\ =7percent \end{gathered}$$

Thus, the economy requires an annual rate of growth of 7 percent in order to move from point ‘a’ to point ‘b.’

Step 2. Calculating the percentage fall in the economy's production capacity

The economy's production capacity is $20 billion, but it can produce only $18 billion.The difference between the production capacity and actual production is the shortage in the economy that prevents it from reaching its full production potential.

When the economy moves from point ‘a’ to point ‘c’ instead of ‘b,’ it increases its size of real GDP from $10 billion to $18 billion. It shows that the economy falls short of $2 billion from doublings its size of real GDP. The percentage fall in production capacity that resulted in a fall of $2 billion in real GDP can be calculated by dividing the short in real GDP with the initial size of GDP and multiplying it by 100.

$$\begin{gathered} Fallinproductioncapacity\left(percentage\right)=\frac{\left(\$20billion-\$18billion\right)}{\$10billion}\times 100 \\ =\frac{\$2billion}{\$10billion}\times 100 \\ =20percent \end{gathered}$$

The economy falls short of its production capacity by 20 percent.