Question

A small economy starts the year with 1 million dollars in capital. During the course of the year, gross investment is 150,000 dollars and depreciation is 50,000 dollars . How big is the economy's stock of capital at the end of the year? a. $$ 1,150,000\( b. $$ 1,100,000\) c. $$ 1,000,000\( d. $$ 850,000\) e. $$ 800,000$

Short answer

Option b: 1,100,000 dollars.

Step-by-step solution

Identify Initial Capital

The problem states the economy starts with 1 million dollars in capital at the beginning of the year. Let's denote this initial capital as \( C_0 = 1,000,000 \) dollars.

Calculate Additions to Capital from Investment

The gross investment over the year adds to the current stock of capital. The problem tells us gross investment is 150,000 dollars. Thus, the increase in capital is \( I = 150,000 \) dollars.

Account for Depreciation

Depreciation reduces the capital stock. The depreciation provided in the problem is 50,000 dollars. So, the decrease in capital due to depreciation is \( D = 50,000 \) dollars.

Compute End-of-Year Capital

To find the end-of-year capital stock, start with the initial capital, add gross investment, and subtract depreciation: \[ C_1 = C_0 + I - D = 1,000,000 + 150,000 - 50,000 = 1,100,000 \].

Choose the Correct Option

The calculated end-of-year capital is 1,100,000 dollars. Among the given options, this corresponds to option b. Therefore, the correct answer is option b: 1,100,000 dollars.

Key concepts

Gross Investment

Gross investment is a key term when discussing capital and economic growth. It refers to the total amount of money that is spent on acquiring new assets or improving existing ones over a period. In this exercise, the economy's gross investment is $150,000. This amount is critical because it reflects the actual spending on capital goods, which are essential for enhancing productive capabilities and achieving economic growth.

Consider these points about gross investment:

• It simply indicates the total investment without accounting for any depreciation.
• This amount is used to purchase or upgrade capital goods, such as machinery or technology.
• The higher the gross investment, the more potential an economy has for growth, as it can imply increased productivity.

The gross investment boosts the economy’s initial capital stock, forming a part of the total resources available for generating goods and services. It's essential to remember that gross investment is always calculated before subtracting depreciation, which will be covered next.

Depreciation

Depreciation is the reduction in the value of assets over time, often due to wear and tear or obsolescence. For the small economy in our exercise, depreciation is $50,000. This figure is an estimate of how much the economy's capital stock has decreased over the year due to usage and natural decline in value.

Depreciation is crucial for the following reasons:

• It shows the ongoing cost of maintaining assets in use.
• Knowing the depreciation amount helps in estimating the net value of investments.
• It ensures more accurate financial reporting by reflecting the true value of assets.

We subtract the depreciation from the gross investment to understand how much of the initial capital has actually increased. It is an important step to finding out the net investment, which is a true indicator of capital growth after accounting for loss.

End-of-Year Capital

The end-of-year capital figure represents the total capital the economy has after accounting for new investments and depreciation. It provides a snapshot of the available economic resources at the end of the year. In our scenario, the end-of-year capital calculation is as follows:
Starting with the initial capital of \(1,000,000, add the gross investment of \)150,000, and then subtract the depreciation of \(50,000:\[C_1 = C_0 + I - D = 1,000,000 + 150,000 - 50,000 = 1,100,000\]
This simple calculation gives us the end-of-year capital of \)1,100,000, which is option b from the choices given in the exercise. This figure is essential for understanding an economy's financial health and planning future investments. Knowing the end-of-year capital allows economists and decision-makers to assess past performance and prepare for future resource allocation.