Question

Assume that the capital/output ratio is \(2 .\) From a present level of \(\$ 600\) million, GNP increases in the coming 10 years, by \(2,6,4,5,6,6,3,5,2\), and 0 percent, in the respective years. How could the investments be expected to behave in those 10 years?

Short answer

The expected investments for the 10 years are: Year 1: 24 million dollars, Year 2: 73.44 million dollars, Year 3: 51.8976 million dollars, Year 4: 67.46688 million dollars, Year 5: 85.008268 million dollars, Year 6: 90.108764 million dollars, Year 7: 47.757644 million dollars, Year 8: 81.983958 million dollars, Year 9: 34.433262 million dollars, and Year 10: 0 million dollars.

Step-by-step solution

Calculate Yearly GNP

To find the change in GNP for each year, we will multiply the given percentage increase with the GNP of the previous year and then add the result to the previous year's GNP. For example, for the 1st year: Change_in_GNP_1 = (600 * 2%) + 600 Step 2: Calculate Expected Investments for each year

Calculate Expected Investments

To find the expected investment for each year, we will use the formula: Investment = Capital/Output Ratio * Change in GNP For example, for the 1st year: Investment_1 = 2 * Change_in_GNP_1 Now, let's calculate the investments for each of the 10 years: Year 1: Change_in_GNP_1 = (600 * 2%) + 600 Investment_1 = 2 * (12) = 24 million dollars Year 2: Change_in_GNP_2 = (612 * 6%) + 612 Investment_2 = 2 * (36.72) = 73.44 million dollars Year 3: Change_in_GNP_3 = (648.72 * 4%) + 648.72 Investment_3 = 2 * (25.9488) = 51.8976 million dollars Year 4: Change_in_GNP_4 = (674.6688 * 5%) + 674.6688 Investment_4 = 2 * (33.73344) = 67.46688 million dollars Year 5: Change_in_GNP_5 = (708.40224 * 6%) + 708.40224 Investment_5 = 2 * (42.504134) = 85.008268 million dollars Year 6: Change_in_GNP_6 = (750.906374 * 6%) + 750.906374 Investment_6 = 2 * (45.054382) = 90.108764 million dollars Year 7: Change_in_GNP_7 = (795.960756 * 3%) + 795.960756 Investment_7 = 2 * (23.878822) = 47.757644 million dollars Year 8: Change_in_GNP_8 = (819.839578 * 5%) + 819.839578 Investment_8 = 2 * (40.991979) = 81.983958 million dollars Year 9: Change_in_GNP_9 = (860.831557 * 2%) + 860.831557 Investment_9 = 2 * (17.216631) = 34.433262 million dollars Year 10: Change_in_GNP_10 = (878.048188 * 0%) + 878.048188 Investment_10 = 2 * (0) = 0 million dollars In conclusion, the expected investments for the 10 years are as follows: Year 1: 24 million dollars Year 2: 73.44 million dollars Year 3: 51.8976 million dollars Year 4: 67.46688 million dollars Year 5: 85.008268 million dollars Year 6: 90.108764 million dollars Year 7: 47.757644 million dollars Year 8: 81.983958 million dollars Year 9: 34.433262 million dollars Year 10: 0 million dollars

Key concepts

Understanding Capital/Output Ratio

The capital/output ratio is a fundamental concept in investment analysis. It represents the amount of capital needed to produce an additional unit of output. In simpler terms, it shows how much investment is required to generate a certain level of increased output in the economy. This ratio is crucial for businesses and economies as it helps in planning and predicting future investment needs.

In our exercise, the capital/output ratio is given as 2. This means for every dollar increase in output, 2 dollars of investment is needed. This ratio helps in calculating expected investments over time. It allows companies and governments to anticipate how much they need to invest to achieve their growth targets.

Understanding and using the capital/output ratio effectively allows for better resource allocation, more accurate financial forecasting, and strategic economic planning.

Exploring the Gross National Product

Gross National Product (GNP) is a key economic indicator that measures the total value of all goods and services produced by a country's residents over a specific period. GNP accounts for the aggregate economic output of a nation, including activities beyond its borders. This is slightly different from Gross Domestic Product (GDP), which only considers output within the country's physical boundaries.

In our example, we began with a GNP of $600 million. Over a decade, the GNP changes based on percentages provided for each year. These changes are crucial as they indicate the health and growth of an economy.

• GNP growth suggests a healthy, expanding economy.
• Stagnant or negative GNP indicates minimal to no growth, affecting investment and planning.

By analyzing the GNP changes, we gain insights into economic prosperity and can decide how best to manage resources and investments.

Simplifying Investment Calculation

Investment calculation in this context involves using the capital/output ratio to predict investment trends based on changes in GNP. The formula used is:
Investment = Capital/Output Ratio × Change in GNP.

This calculation framework allows for estimating how much should be invested to sustain or further economic growth. As GNP changes annually, so does the investment need. For example:

• If GNP grows by 2% in the first year, the necessary investment is calculated as:
  Investment = 2 × (Change_in_GNP_1), where Change_in_GNP_1 is a 2% increase of the initial GNP.
• This same logic applies each year, adjusting for different percentage changes in GNP.

As shown in the solution, the calculated investments vary annually based on these percentage changes. This keeps investments aligned with economic growth requirements. Understanding this logic ensures effective financial strategizing and supports economic stability.