Question

What do you expect the rate of growth to be of an economy where, on average, the population saves \(15 \%\) of its income and marginal capital/output ratio is \(2.5\), i.e., an increase in output of \(\$ 100\) billion per year is produced by an increase in the capital stock of \(\$ 250\) billion.

Short answer

The rate of growth for this economy is expected to be \(6\%\).

Step-by-step solution

Identify the given values

We are given the following values: - Saving rate: \(15\%\) - Marginal capital/output ratio: \(2.5\)

Convert saving rate to decimal

To convert the saving rate to decimal, we can divide it by \(100\). Saving rate (decimal) = \(\frac{15}{100} = 0.15\)

Calculate the rate of growth using the given formula

We can calculate the rate of growth by dividing the saving rate (decimal) by the marginal capital/output ratio. Rate of growth = \(\frac{Saving \, rate}{Marginal \, capital/output \, ratio}\) Using the given values, we have: Rate of growth = \(\frac{0.15}{2.5}\)

Simplify the expression

Now, let's simplify the value of the rate of growth: Rate of growth = \(0.06\)

Convert the rate of growth to percentage

To express the rate of growth as a percentage, we can multiply it by \(100\): Rate of growth (percentage) = \(0.06 \times 100 = 6\%\) The rate of growth of this economy is expected to be \(6\%\).

Key concepts

The Importance of Saving Rate

When trying to determine the health and potential growth of an economy, the saving rate is a crucial indicator. It represents the proportion of income that households save rather than spend on consumption. A higher saving rate implies that more resources are being set aside for investment, which is essential for capital accumulation and, consequently, long-term economic growth.

The relationship between savings and growth is multifaceted. Savings provide the funds that banks and other financial institutions lend to businesses and entrepreneurs; these loans are then used to invest in new technologies, equipment, and other capital that increase productive capacity. Economically speaking, when a country has a high saving rate, it is often able to invest more in capital goods, which can boost productivity and growth.

In our exercise, a saving rate of 15% is considered. This means that for every dollar earned, 15 cents is saved for future investment. In simple terms, this is a relatively moderate saving rate, which can fuel moderate economic growth, assuming these savings are efficiently transformed into productive investments.

Marginal Capital-Output Ratio Explained

The marginal capital-output ratio (MCOR) is a measure of the additional amount of capital needed to produce an additional unit of output. It is a critical parameter in growth models as it indicates how effectively capital is being used in the economy. A lower MCOR is generally preferred because it means that less capital is needed to increase production, which can lead to higher economic efficiency and growth.

For instance, an MCOR of 2.5, as given in our exercise, suggests that an investment of \(250 billion is required to produce an additional \)100 billion in output. This value provides insight into the productivity of new capital investments. An MCOR of 2.5 can be considered high, which could mean that the economy is not using its capital as efficiently as possible. However, this number can vary greatly between industries and over time due to technological advances or changes in capital utilization.

Calculating Economic Growth

To calculate the economic growth rate using the saving rate and marginal capital-output ratio, a basic formula from growth theory can be utilized: Economic Growth Rate = (Saving Rate) / (Marginal Capital-Output Ratio). This formula encapsulates the idea that growth is driven by the amount of saving that is available to fund new investment, adjusted by the productivity of that investment (as indicated by the MCOR).

In our example, by dividing a saving rate of 0.15 by an MCOR of 2.5, we get 0.06, or 6% when converted to a percentage. This result suggests a moderate economic growth rate for the economy in question, assuming other factors such as technology and labor force growth remain constant.

The practical implication of this calculation is that policies aimed at increasing the saving rate or decreasing the marginal capital-output ratio could potentially increase a country's economic growth rate. However, it's always important to recognize that reality is more complex, and such direct relationships might be influenced by a multitude of other economic variables and policy considerations.