Question

The following macroeconomic data corresponds to a closed economy (all values are in € billion):

Private Consumption 35,000
Public Spending 12,500
Taxes 10,000
Gross Domestic Product 50,000
Moreover, the investment function is estimated to be the following: I=4,500 -200r

1) Write down the GDP identity [Y=C+I+G] stating the value in € of each component. Explain your answer.

2) Calculate Total Savings, Total Investment, Private Savings, Public Savings and the equilibrium interest rate.

3) Suppose that the government increases its level of expenditure to 14,000. What happens to private savings, public savings and total savings? Which new values do they take? What are the new equilibrium values for investment and the interest rate? Explain your answer and comment on the results

Answer 1

1) Y=C+I+G; Y is total output i.e. GDP, C is consumer spending (private consumption), I is country's investment and G is government spending (public spending).

We have Y=€50,000 (GDP)

C= €35,000

G= €12,500

I= Y-G-C.

=> I=50000-35000-12500

=€2,500

So, GDP identity is:

Y=C+I+G

€: 50,000= 35,000+12,500+2,500;

A country's GDP is its total output which is equal to what people spend in the year plus what government spends in the year and the total investment made (fixed capital formation). This is expenditure method of calculating GDP.

2) Public Savings: This is the saving of government after its expenditures. Simply it is equal to difference of its revenue(taxes being the major source) and expenditure.

S_g=T-G (taxes - government spending)

=10,000-12,500

= €-2,500 (negative savings; government debt)

Private savings: This is the saving of people of nation after consumption and payment of taxes. It is equal to: Y-T-C

=> S_p =National income - taxes - consumptiom

=50000-10000-35000

=€5,000.

Total savings: It is the sum of public and private savings. Here, it will be equal to: (-2,500)+5,000

=> S_t =€2,500.

Equilibrium interest rate: At equilibrium, total savings is equal to investment!

=> S_t=I

We are given the investment function as I=4500 - 200r

=> 2500=4500 - 200r

=> 200r = 2000

=> r=10%

3) If government increases its expenditure (to 14,000);

●Public savings= T-G= 10,000-14,000

=€-4,000 (more negative, more debted)

So public savings decrease, government is indebted more.

●Private savings= Y-T-C.

So, private savings remain unaffected (short-run) =€5,000.

●Total saving= governmemt savings + private savings.

Total savings will decrease as public savings decrease.

= (-4000)+5000

=€1,000

● New investment value, usind GDP identity will be:

Y= C+I+G

=> I= Y-C-G

=> I= 50000-35000-14000

=> I=€1,000.

● New value of equilibrium intetest rate using I=4,500 - 200r:

1000=4500 - 200r

=> 200r= 3500

=> r= 17.5%.

Commentary:

This tells us, if government increases its spendings, total savings go down (in short-run). This increases the interest rate, which acts as a force to restore the investments as now people tend to invest more at higher interest rate.