Question

A developing country has determined that each additional $1$billion of net investment in capital goods adds $0.01$percentage point to its long-run average annual rate of growth of per capita real GDP.

a. Domestic entrepreneurs recently began to seek official approval to open a range of businesses employing capital resources valued at $20$billion. If the entrepreneurs undertake these investments, by what fraction of a percentage point will the nation's long-run average annual rate of growth of per capita real GDP increase, other things being equal?

b. After weeks of effort trying to complete the first of $15$stages of bureaucratic red tape necessary to obtain authorization to start their businesses, a number of entrepreneurs decide to drop their investment plans completely, and the amount of official investment that actually takes place turns out to be $10$billion. Other things being equal, by what fraction of a percentage point will this decision reduce the nation's long-run average annual rate of growth of per capita real GDP from what it would have been if investment had been $20$billion?

Short answer

(a) The Average annual rate of growth of per capita real GDP businesses employing capital resources valued at $20$billion is $0.2\%$

(b) The Average annual rate of growth of per capital real GDP reduces to $0.1\%$if investment had been$20$billion.

Step-by-step solution

Given Information (part a).

The Following are the information to find the Average annual rate of growth of per capita real GDP is as follows:

Employing capital resources valued$=20$billion.

A$1$billion investment for$0.01\%$

Find the Annual rate of growth of per capita real GDP (part a).

A $1$billion increase in capital goods investment translates in a $0.01$percent annual increase in per capita real GDP.

Calculation of the country's long-run average yearly rate of real GDP growth per capital:

Using capital resources worth $20$billion, the nation's long-run average yearly rate of real GDP growth per capita is,

$$\begin{gathered} =20\times 0.01\% \\ =0.2\% \end{gathered}$$

Given information (part b).

The information are used to find the Average annual rate of growth of per capital real GDP:

Amount of Investment$=20$billion to$10$billion.

Find the reduction of average annual rate of growth of per capital real GDP (part b). 

If the investment plan is scrapped and capital resources are reduced to $10$billion, the nation's long-run average annual rate of real GDP growth per capita will fall to,

$$\begin{gathered} =10\times 0.01\% \\ =0.1\% \end{gathered}$$