In macroeconomic investment analysis, if depreciation of capital exceeds gross investment in a given year, what happens to the stock of capital in the economy?

Introduction / Context:
In macroeconomics, it is important to distinguish between gross investment, depreciation, and net investment. Gross investment measures total spending on new capital goods, while depreciation represents the wearing out or obsolescence of existing capital. Net investment indicates whether the capital stock is expanding or contracting. This question asks what happens when depreciation exceeds gross investment.

Given Data / Assumptions:

• Gross investment is the total expenditure on new capital goods in a given period.
• Depreciation is the estimated value of capital stock that has been used up or has worn out during the same period.
• Net investment is defined as gross investment minus depreciation.
• The capital stock is the total quantity of plant, machinery, and other productive equipment in the economy.
• We assume that the only factors affecting the capital stock are gross investment additions and depreciation losses.

Concept / Approach:
The relationship between gross investment, depreciation, and net investment is given by the formula net investment = gross investment minus depreciation. If gross investment equals depreciation, net investment is zero and the capital stock remains unchanged. If gross investment is greater than depreciation, net investment is positive and the capital stock grows. If depreciation is greater than gross investment, net investment becomes negative, which means that more capital is wearing out than is being added, so the total stock of capital shrinks.

Step-by-Step Solution:
Step 1: Write the basic formula: net investment = gross investment - depreciation.Step 2: Consider the case where depreciation exceeds gross investment, so depreciation is larger than gross investment.Step 3: Subtract a larger number (depreciation) from a smaller number (gross investment); the result is negative net investment.Step 4: Interpret negative net investment as a reduction in the capital stock, because the economy is not replacing all of the capital that is wearing out.Step 5: Conclude that when depreciation exceeds gross investment, the capital stock is shrinking.

Verification / Alternative check:
Take a numerical example. Suppose gross investment is 100 units and depreciation is 120 units in a year. Then net investment equals 100 minus 120, which is minus 20. This means the economy has 20 units less capital at the end of the year than at the beginning. In contrast, if gross investment had been 120 and depreciation 100, net investment would be plus 20 and the capital stock would grow. This numerical reasoning supports the conclusion that depreciation greater than gross investment implies a shrinking capital stock.

Why Other Options Are Wrong:
Option a claims that the capital stock is growing, which would require positive net investment, not negative. Option b says the capital stock may be either growing or shrinking, but when depreciation clearly exceeds gross investment, the outcome is unambiguously negative net investment, so the stock must be shrinking. Option c states that net investment is zero, which is true only when depreciation equals gross investment, not when it exceeds it. Option e makes an incorrect statement about capital doubling because depreciation allowances do not automatically expand the capital stock.

Common Pitfalls:
Some students confuse gross investment with net investment and think that any positive gross investment means the capital stock is growing. They forget to subtract depreciation, which can be large in an economy with a big existing capital base. Another error is to misread questions and treat depreciation equal to gross investment as the same as depreciation greater than gross investment. To avoid such mistakes, it is useful to always apply the formula net investment = gross investment minus depreciation carefully.

Final Answer:
If depreciation exceeds gross investment, net investment is negative and the stock of capital in the economy is shrinking.