Macroeconomics — Capital Formation Statement and Nominal/Real GDP

💰 Private savings (Sp):
Sp = Yd − C
= Disposable income − Consumption

What households do not consume from their disposable income.

💡 Yd = disposable income (after taxes)

🏢 Business savings (Sb):
Sb = undistributed profits
Profits the firm did not distribute to owners — retained for investment.

💡 Distributed profit = dividend (goes to owners); Undistributed profit = business savings

🏛️ Public savings (Sg):
Sg = T − G
= Taxes − Government consumption
• Sg > 0 → government is saving (surplus)
• Sg < 0 → government is "dis-saving" (deficit)

💵 Disposable income (Yd):
Yd = Y − T − Sb
= Output − Taxes − Undistributed profits
The income remaining for individuals to consume or save.

💡 Also: Yd = C + Sp (disposable income = consumption + private savings)

⚖️ In a closed economy: S = I
Total savings in the economy = total investment.
S = Sp + Sb + Sg = I

💡 What is not consumed → is saved → finances investment. No "leakage" abroad in a closed economy.

🌍 In an open economy:
S + (Im − Ex) = I
• If Im > Ex (import surplus) → abroad "finances" part of investments
• If Ex > Im (export surplus) → we "finance" abroad

💡 (Im − Ex) = "loan" from abroad

🔢 Calculation:
Step 1: Yd = Y − T − Sb = 1,000 − 200 − 50 = 750
Step 2: Sp = Yd − C = 750 − 600 = 150

🔢 Calculation:
Sg = T − G = 300 − 350 = −50

💡 Negative public savings = deficit. The government spends more than it collects.

📊 Nominal output:
Output at current prices (this year's prices).
⚠️ Problem: if prices rose, nominal output rises even if nothing more is produced!
💡 Does not reflect a true change in output volume

📈 Real output:
Output at constant prices (base year).
✅ Reflects a true change in the quantity of output; unaffected by price changes.

💡 Used for comparisons across years

🔢 The relationship:
Nominal output = real output × P
or: Real output = nominal output ÷ P
where P = price index

💡 By removing the effect of prices, we obtain real output

🔢 Calculation:
Real output = nominal output ÷ price index = 1,100 ÷ 1.1 = 1,000

💡 Prices rose by 10%, so the "true" output is lower

📈 Approximate calculation:
Real growth ≈ nominal growth − inflation ≈ 8% − 3% = 5%

💡 This is the "true" growth in output!
⚠️ Exact formula: (1.08/1.03) − 1 = 4.85%

📊 Consumer Price Index (CPI):
An index that tracks the price of a representative basket of goods that an average family consumes.
Includes: food, housing, health, clothing, transport, entertainment.

💡 A change in the index = inflation/deflation

👤 Output per capita = output ÷ number of residents
Uses: a measure of average standard of living; comparison between countries.

💡 Real output per capita is used for comparisons across years!

🔢 Calculation:
In a closed economy: S = I
S = Sp + Sb + Sg = 100 + 50 + (−30) = 120
Therefore: I = 120

🔢 Calculation:
S + (Im − Ex) = I
200 + (Im − Ex) = 250
Im − Ex = 250 − 200 = 50

💡 Import surplus of 50 = the economy "borrows" from abroad to finance investments

💡 Analysis:
Real growth ≈ nominal growth − inflation = 10% − 10% = 0%

💡 The entire rise in nominal output was due to rising prices! There was no true change in output.

📊 For comparing across years: real output per capita
✅ Why? "Real" — neutralises the effect of inflation; "per capita" — accounts for population growth.

💡 This shows whether the standard of living truly improved!

📝 S = I — the meaning:
In a closed economy, everything not consumed → is saved → finances investment.

Process: households save → firms retain profits → government may collect more than it spends → all this saving → finances new investment.

💡 No "leakage" — everything stays in the economy!