Consumption, Saving, Investment: Functions, Graphs & Equilibrium

Key Definitions and Relationships

1. Consumption Function

The consumption function shows how household spending ($C$) depends on disposable income ($Y_d$): $$C=c_0+c_1{Y}_d$$

• $c_0$: Autonomous consumption (spending even if income = 0, e.g., basic needs).
• $c_1$: Marginal Propensity to Consume (MPC): $\Delta C/\Delta Y_d$ (how much extra income is spent).
• Average Propensity to Consume (APC): $C/Y_d$.

---

In the Real World

1. eSewa & Khalti Apps

   • Idea: Marginal Propensity to Consume (MPC).
   • How: When Nepalis receive remittances (e.g., Rs. 50,000/month), they spend ~60% on essentials (food, rent) and save 40%. The MPC ≈ 0.6 drives demand for digital payments, increasing app usage.

2. Daraz’s Inventory Investment

   • Idea: Investment Function ($I=I_0+bY$).
   • How: Daraz invests in stock (e.g., Rs. 2 billion/year) based on expected sales growth. If GDP grows 5%, Daraz’s inventory investment rises by $b\times 5\%$, boosting warehouse jobs.

3. Nepal Rastra Bank (NRB) Loan Interest

   • Idea: Saving-Investment Equilibrium.
   • How: If households save more (e.g., due to inflation fears), banks reduce loan rates to stimulate investment (e.g., NRB’s 2023 policy cut from 8% to 6% to boost business loans).

---

2. Saving Function

Derived from the consumption function: $$S=Y_d-C=-c_0+(1-c_1)Y_d$$

• Marginal Propensity to Save (MPS): $1-c_1$ (how much extra income is saved).
• Average Propensity to Save (APS): $S/Y_d$.

WORKED EXAMPLE: Nepal’s Remittance Savings Assume:

• Disposable income ($Y_d$): Rs. 1,000 billion (2023 estimate).
• Autonomous consumption ($c_0$): Rs. 200 billion (basic needs).
• MPC ($c_1$): 0.7 (typical for Nepal).

Calculations:

INSIGHT: As income rises, APS increases (richer households save more).

---

3. Investment Function

Investment ($I$) depends on:

• Autonomous investment ($I_0$): Business spending regardless of income (e.g., Daraz’s new warehouse).
• Induced investment ($bY$): Spending tied to income growth (e.g., Pathao’s bike purchases if ridership rises).

Equation: $$I=I_0+bY$$

• $b$: Sensitivity of investment to income (e.g., $b=0.1$ means Rs. 100bn income → Rs. 10bn more investment).

---

4. Equilibrium: Saving = Investment

In a closed economy, equilibrium occurs when: $$S=I$$ $$Y_d=C+S=C+I$$ Graphical Equilibrium:

WORKED EXAMPLE: Nepal’s 2023 Equilibrium Given:

• $C=100+0.8Y_d$
• $I=200+0.1Y$

Step 1: Find equilibrium $Y$ where $S=I$. $$S=Y-C=Y-(100+0.8Y)=0.2Y-100$$ Set $S=I$: $$0.2Y-100=200+0.1Y$$ $$0.1Y=300⟹Y=3,000\text{ billion Rs.}$$

Step 2: Calculate $C$ and $S$ at $Y=3,000$: $$C=100+0.8(3,000)=2,500\text{ bn Rs.}$$ $$S=3,000-2,500=500\text{ bn Rs.}$$

REAL TIE-IN: Nepal’s GDP in 2023 was ~Rs. 3,500 bn, but this simplified model ignores taxes/imports. The equilibrium shows how saving drives investment (e.g., NRB’s push for Rs. 500bn savings to fund infrastructure).

---

5. Determinants of Consumption, Saving, and Investment

Consumption Function Determinants

Saving Function Determinants

Investment Function Determinants

---

6. Graphical Analysis: 3 Propositions of Psychological Law of Consumption

Keynes’ psychological law states:

1. APC declines as income rises (poor spend almost all; rich save more).
2. MPC is positive but < 1 (people spend less than extra income).
3. MPS rises with income (rich save a larger % of extra income).

• APC curve: Starts high (near 1), slopes downward.
• MPC: Horizontal line at $c_1$ (e.g., 0.7).
• MPS: Horizontal line at $1-c_1$ (e.g., 0.3).

WORKED EXAMPLE: Kathmandu Traffic vs. Income

• Low-income driver (Rs. 20,000/month):
  • Spends Rs. 18,000 on fuel/food → APC = 0.9.
• High-income driver (Rs. 200,000/month):
  • Spends Rs. 150,000 → APC = 0.75. Why? Richer drivers save for electric cars (↓APC).

---

7. Multiplier Effect (Preview for Unit 5)

A change in autonomous investment ($I_0$) triggers a multiplier effect: $$\text{Multiplier}=\frac{1}{1-c_1}=\frac{1}{\text{MPS}}$$ Example: If $c_1=0.8$ (MPS = 0.2), a Rs. 100bn increase in $I_0$ leads to: $$\Delta Y=\frac{1}{0.2}\times 100=500\text{ bn Rs. GDP growth}$$ Real-world: NRB’s Rs. 100bn infrastructure push (2023) could generate Rs. 500bn GDP if MPC = 0.8.

---

Exam Tip

1. Graphs are 50% of marks: Always draw:
   • Consumption curve (45° line + C = c₀ + c₁Y_d).
   • Saving curve (below 45° line).
   • Investment curve (intersecting saving at equilibrium).
2. Memorize formulas:
   • $C=c_0+c_1{Y}_d$
   • $S=-c_0+(1-c_1)Y_d$
   • Equilibrium: $S=I$ → $Y=\frac{I_0-c_0}{c_1-b}$
3. Determinants: Link to Nepal’s context (e.g., remittances ↑$C$, NRB policy ↑$I$).
4. Numerical questions: Show all steps (e.g., solving for $Y$ in equilibrium).
5. Avoid common mistakes:
   • Confusing MPC and MPS (MPC + MPS = 1).
   • Forgetting autonomous terms ($c_0$, $I_0$) in equations.

---

KEY VISUAL SUMMARY