Question

Given the following information about the closed economy of Brittania, what is the level of investment spending and private savings, and what is the budget balance? What is the relationship among the three? Is national savings equal to investment spending? There are no government transfers. \(\mathrm{GDP}=\$ 1,000\) million \(\quad T=\$ 50\) million \(C=\$ 850\) million \(\quad G=\$ 100\) million

Short answer

Answer: Yes, in the closed economy of Brittania, national savings is equal to investment spending. The levels of investment spending (I), private savings (PS), and budget balance are as follows: - Investment Spending (I): \(50\) million - Private Savings (PS): \(100\) million - Budget Balance: \(-50\) million

Step-by-step solution

Identify the given variables

The problem provides us with the following values: - GDP = \(1,000\) million - Taxes (T) = \(50\) million - Consumption (C) = \(850\) million - Government spending (G) = \(100\) million

Calculate the level of investment spending (I)

Using the formula for GDP, we can find the level of investment spending. GDP = C + I + G \(1000 = 850 + I + 100\) Now, solve for I: I = \(1000 - 850 - 100\) I = \(50\) million

Calculate the private savings (PS)

Using the formula for private savings, we can find the level of private savings. PS = Y - T - C Where Y is GDP, PS = \(1000 - 50 - 850\) PS = \(100\) million

Calculate the budget balance

Using the formula for budget balance, we can find the level of budget balance. Budget Balance = T - G Budget Balance = \(50 - 100\) Budget Balance = \(-50\) million

Calculate the relationship among I, PS, and Budget Balance

In this step, we will analyze if national savings is equal to the investment spending. National Savings (NS) can be represented as the sum of private savings (PS) and budget balance. Using the National savings formula: NS = PS + Budget Balance NS = \(100 + (-50)\) NS = \(50\) million Since NS = \(50\) million and I = \(50\) million, we can conclude that national savings is equal to investment spending in this closed economy of Brittania.

Key concepts

Understanding Private Savings

Private savings refer to the portion of household income that is not consumed in goods and services nor paid as taxes. In simple terms, private savings is the amount left after individuals have covered their consumption expenditures and tax obligations. This savings can be channeled into investments, creating funds for businesses and the economy to grow. In the case of Brittania, private savings are calculated using the formula:

• Private Savings (PS) = Y - T - C

Here, Y is the Gross Domestic Product (GDP), T represents taxes, and C stands for consumption. So for Brittania: PS = 1000 million - 50 million - 850 million = 100 million. This indicates that after accounting for their expenditures and taxes, the households in Brittania save a total of 100 million. This amount of savings plays a vital role in funding investment spending.

Decoding Budget Balance

Budget balance is a measurement of the government's fiscal position, calculated as the difference between government revenues and expenditures. Essentially, it shows whether the government is running a surplus, balanced budget, or a deficit. The formula used is:

• Budget Balance = T - G

Where T is taxes collected, and G is government spending. For Brittania, the budget balance is: 50 million - 100 million = -50 million. This negative result ( -50 million) indicates a budget deficit. Such a deficit occurs when government spending exceeds the revenue collected, meaning the government may have to borrow money or reduce savings to fund its operations.

National Savings Simplified

National savings represents the total savings within an economy, including both private savings and the government's budget surplus or deficit. It forms a crucial part of a country’s financial health and its ability to fund investments. The formula to find national savings is as follows:

• National Savings (NS) = Private Savings (PS) + Budget Balance

For the economy of Brittania, using the data provided: NS = 100 million + (-50 million) = 50 million. This means that the national savings is 50 million. Interestingly, this sum in a closed economy like Brittania directly funds investment spending. Therefore, the national savings must equal the investment spending.

Defining a Closed Economy

A closed economy is one that does not engage in trade with other countries, meaning it neither imports goods and services nor exports them. In this scenario, all financial activities revolve within its boundaries, such as consumption, government spending, and investments. Brittania is a closed economy, influencing how national savings and investments operate: - All outputs must be either consumed, saved, or invested domestically. - National savings directly equate to domestic investment due to the lack of foreign interactions. In Brittania’s case, we see that the national savings do indeed match investment spending, both at 50 million. This illustrates the classic economic model where in a closed economy, the country's savings are fully utilized for domestic investments.