Assume that in our fictional country GDP is $6,000, personal disposable income is $5,100,and the government budget deficit is $200. Consumption is $3,800 and the trade deficitis $100. How large is saving (S)?How large is investment (I)?How large is government spending (G)?

Expert Answers

An illustration of the letter 'A' in a speech bubbles

Since the fictional country has a trade deficit, it's an open economy. In an open economy, the savings (S) are equal to the government savings (GS) plus the private savings (PS):

S = GS + PS

However, we don't have the value for PS, so we have to find it. Luckily, private savings (PS) can be defined if we have the figures for disposable income (DI) and Consumption (C). Disposable income is the extra earnings you get after consuming and saving, its formula is as follows:

DI = PS + C

But in this case, the value of C and DI are known, while PS is unknown; therefore, we flip the equation and make PS the dependent variable:

PS = DI - C = 5100 - 3800

Hence, private savings (PS) becomes $1300.

Government Savings (GS) is what remains after the government has spent money on various public projects. It depends on the total revenue or taxes collected (T) and government expenditure (G). In this scenario, the fictional country has a budget deficit $200, meaning that the government spent more than it earned and saved nothing. Hence the GS value becomes -200.

Substituting the values in the equation:

S = GS + PS = -200 + 1300

Hence, savings (S) becomes $1100.

In an open economy, net exports (X-M) is a function of savings (S) and investment (I):

X-M = S - I

Since the fictional country has a trade deficit, imports (M) were more than exports (X), thus the value of net exports will be negative, (X-M = -100). Therefore, to find the value of Investment (I), the equation becomes:

I = S - (X-M)

Substituting the values in the equation:

I = 1100 - (-100)

The value for Investment (I) becomes $1200.

So far, we have discovered how large both the investment and saving are, the only remaining value is government spending (G). Using the expenditure formula:

GDP = C + I + G + (X-M)

Since G is the only unknown, it becomes the dependent variable in the equation:

Hence, G = GDP - C - I - (X-M)

Substituting the letter with the figures, we get:

G = 6000 - 3800 - 1200 - (-100) = 1100

Thus, government expenditure (G) is equal to $1100.

Approved by eNotes Editorial Team
An illustration of the letter 'A' in a speech bubbles

We need to keep in mind the following formulae in order to solve the question:

1. GDP = Y = C + I + G + NX
2. Savings = S = Y - C - G
3. Budget Deficit = T - G

Where, C = Consumption, I = Investment, G = Goverment Spending, T = Taxes and NX = Trade Deficit.

We know that GDP = Y = Aggregate Income = $6000 and Disposable Income = $ 5100. Because Disposable Income is the income after taxes, T = Taxes = $6000 - $5100 = $900.
We also know that the Budget Deficit = $200, so we can use Formula 3 to calculate Government. So, G = $200 + $900 = $1100.
It is also given that Consumption = C = $3800. We can use Formula 2 and calculate Savings, which is S = $6000 - $3800 - $1100 = $1100.
Finally, we know that Trade Deficit = NX is -$100. We can use Formula 1 to find Investment. Therefore, I = $6000 - $3800 - $1100 - (-$100) = $1200.

Therefore, the answers are:

Savings = S = $1100

Investment = I= $1200

Government Spending = G = $1100

Approved by eNotes Editorial Team
An illustration of the letter 'A' in a speech bubbles

GDP = Y = C + I + G + NX
Savings = S = Y - C - G
Budget Deficit = T - G
NX = Trade deficit = -100
Explanation:
GDP = Y = Aggregate Income = 6000
Disposable Income = 5100, which is income after taxes, so T = taxes = 900.

With a budget deficit of 200, G (Government spending) must be 1100 if taxes are 900.

You now know G, C, and Y are given, so S must be 1100. (6000 - 3800 - 1100 = 1100)

You also know Y, C, G and NX, so you can solve for I.
I=Y-C-G-NX = 6000 - 3800 - 1100 + 100 = 1200

Approved by eNotes Editorial Team
An illustration of the letter 'A' in a speech bubbles

First, we can use the definition of disposable income to find the level of taxes.  Disposable income is income after taxes.  If we remember that gross domestic product (GDP) is the same as aggregate income, then we know the figure for income before taxes.  If income before taxes is $6,000 and income after taxes is $5,100, then taxes must be $900.  If we know the figure for taxes and we know the amount of the government deficit, then we can determine the level of government spending.  The government took in $900 in taxes and had a budget deficit of $200, which means that it spend $200 more than it took in.  By adding the taxes ($900) to the amount of deficit spending ($200) we find that the government spent $1100.

Now that we know how much the government spent, we can find savings.  We know that the formula to find savings is Savings = GDP – Consumption – Government spending.  In this example, Savings = $6,000 - $3,800 - $1,100 = $1,100.  So our figure for savings is $1100.

With all this information, we can now find the level of investment.  The relevant formula is GDP = Consumption + Investment + Government spending + Net Exports.  Plugging in our numbers,

$6,000 = $3,800 + I + $1100 - $100. 

$6,000 = I + $4800

I = $1200

So, our answers are:

Savings = $1100

Investment = $1200

Government spending = $1100

Approved by eNotes Editorial Team