Multiplier & Accelerator: How Spending Begets Growth & Investment Drives Expansion

TAKEAWAYS:

• The multiplier shows how a ₹100 crore road project in Pokhara creates ₹300–₹500 crore in total income via repeated spending (e.g., contractors hiring labor, workers spending wages).
• The accelerator explains why Ncell invests in 5G towers when mobile data usage (and thus output) surges during COVID-19 lockdowns.
• Government vs. private multipliers: A ₹100 crore subsidy for farmers has a higher multiplier (₹3–₹4) than ₹100 crore in corporate tax cuts (₹1.5–₹2).
• Accelerator lags: Daraz’s warehouse expansion lags behind sales growth by 6–12 months due to lead times for machinery and hiring.
• Crowding-out: If the government borrows ₹500 crore to build a highway, private firms may get less credit, reducing their investment.
• Exam focus: Derive multipliers algebraically (e.g., $k=\frac{1}{1-c}$) and explain real-world trade-offs (e.g., "Why did Nepal’s 2023 budget deficit widen despite the multiplier?").

1. The Multiplier Effect: How Spending Cascades

Definition and Intuition

The multiplier effect describes how an initial injection of spending (e.g., government expenditure, investment, or exports) generates higher total income through successive rounds of spending. Think of it like dropping a pebble in water: the ripples (spending) grow larger as they spread.

Key Idea:

Initial injection × Multiplier = Total change in income Example: If the government builds a ₹100 crore stadium in Kathmandu, the multiplier determines how much total income rises in the economy.

How It Works: The Circular Flow

Assumptions:

• Marginal Propensity to Consume (MPC): The fraction of extra income people spend (e.g., MPC = 0.8 means 80% of ₹100 extra income is spent).
• No leakage: No taxes, savings, or imports (simplified model).

The Multiplier Formula

The income multiplier (k) is derived from the MPC: $$k=\frac{1}{1-\text{MPC}}=\frac{1}{\text{MPS}}\text{(where MPS = Marginal Propensity to Save)}$$ Example: If MPC = 0.8 (people save 20% of extra income): $$k=\frac{1}{1-0.8}=5$$

• Initial injection: ₹100 crore → Total income change: ₹500 crore.

Types of Multipliers

Real-World Example: NTC’s Fiber Expansion

• Initial injection: NTC spends ₹500 crore to lay fiber in 10 districts.
• MPC: Rural households spend 70% of extra income (MPC = 0.7).
• Multiplier: $k=\frac{1}{1-0.7}=3.33$.
• Total income rise: ₹500 crore × 3.33 = ₹1,665 crore.
• Why it matters: Faster internet boosts e-commerce (Daraz, Hamrobazaar), creating more jobs.

2. The Accelerator Principle: Investment and Output Growth

Definition

The accelerator principle states that investment depends on the rate of change of output (GDP), not just its level. If GDP grows rapidly, firms invest heavily in new capacity (factories, machines, infrastructure).

Key Idea:

Investment = Accelerator Coefficient × Change in Output Example: If GDP grows by 10% this year, a firm with an accelerator coefficient of 2 will invest 20% more in new machinery.

How It Works

Example: Pathao’s Bike Fleet Expansion

• 2022: Pathao’s daily rides grew by 30% → output growth = 30%.
• Accelerator coefficient: 1.5 (for every 1% output growth, Pathao adds 1.5% more bikes).
• Investment: 30% × 1.5 = 45% more bikes in 2023.
• Result: Higher capacity → more riders → higher profits.

Accelerator Coefficient

The coefficient depends on:

1. Capital-output ratio: How much capital (machines, trucks) is needed per unit of output.
   • Example: A rice mill needs ₹5 lakh in machinery to produce 100 quintals/year.
2. Expected future growth: Firms invest more if they expect demand to keep rising.

Formula: $$\text{Investment}=v\times (\text{Change in Output})$$ Where $v=\frac{\text{Capital-output ratio}}{\text{Expected lifespan of capital}}$.

Example: Ncell’s 5G Investment

• Capital-output ratio: ₹20 crore per 100 km of 5G towers to serve 1 lakh users.
• Expected lifespan: 10 years.
• Output growth: 20% (more data usage post-lockdown).
• Investment: $v=\frac{20}{10}=2$, so 20% × 2 = ₹4 crore per 100 km.

Accelerator vs. Multiplier

3. Combined Multiplier-Accelerator Model

In reality, multiplier and accelerator work together:

1. Government spends (e.g., ₹200 crore on schools) → multiplier effect → income rises.
2. Higher income → more demand for education → schools need more teachers/books → accelerator effect → firms invest in education supplies.
3. Cycle repeats: More teachers spend wages → more demand for housing → construction firms invest → more jobs.

Example: Post-Earthquake Reconstruction (2015)

• Initial injection: ₹500 crore for school rebuilding.
• Multiplier: MPC = 0.7 → $k=3.33$ → ₹1,665 crore income rise.
• Accelerator: Higher demand for school supplies → firms invest ₹300 crore in new factories.
• Total effect: ₹1,965 crore in new income + investment.

4. Limitations and Criticisms

Multiplier Limitations

1. Leakages:

   • Taxes: If MPC = 0.8 but taxes take 20%, effective MPC = 0.64 → $k=2.78$.
   • Imports: If people buy Chinese smartphones with extra income, leakage reduces multiplier.
   • Savings: Higher income may lead to more savings, lowering MPC.

2. Time Lags:

   • Multiplier effects take months/years to fully materialize (e.g., a 2023 road project may boost income in 2025).

3. Crowding-Out:

   • Government spending may displace private investment if it borrows heavily.
   • Example: If the government spends ₹300 crore but borrows it all, private firms may get less credit → lower private investment.

Accelerator Limitations

1. Overinvestment:

   • If firms overestimate growth, they may invest too much → unused capacity (e.g., empty Daraz warehouses post-lockdown).

2. Technological Change:

   • Automation may reduce the need for new factories (e.g., AI replacing call centers at Ncell).

3. Expectations:

   • If firms expect a recession, they won’t invest even if output grows (e.g., 2020 COVID downturn).

5. Policy Implications for Nepal

How the Government Can Use These Theories

Case Study: Khalti’s Growth and the Multiplier

• Initial injection: Khalti app adoption surged post-2015 earthquake (government pushed digital payments).
• MPC: Users spent 85% of extra income via Khalti (MPC = 0.85).
• Multiplier: $k=\frac{1}{1-0.85}=6.67$.
• Total effect: ₹500 crore in new digital transactions → ₹3,335 crore in total spending.
• Accelerator: Higher transaction volume → Khalti invested in new servers and hiring to handle load.

6. Exam-Focused Worked Examples

Example 1: Derive the Government Expenditure Multiplier

Given:

• Initial government spending (G) = ₹100 crore.
• MPC = 0.8, MPS = 0.2.

Steps:

1. Write the income equation: $$Y=C+I+G$$ Where $C=c+\text{MPC}\times Y$ (consumption depends on income).

2. Substitute $C$: $$Y=c+0.8Y+I+G$$

3. Solve for $Y$: $$\begin{gathered} Y-0.8Y=c+I+G \\ 0.2Y=c+I+G \\ Y=\frac{c+I+G}{0.2} \end{gathered}$$

4. Change in income (ΔY) when G increases by ₹100 crore: $$\Delta Y=\frac{\Delta G}{0.2}=\frac{100}{0.2}=₹500\text{ crore}$$ Multiplier (k): $\frac{\Delta Y}{\Delta G}=5$.

Graphical Illustration:

graph LR
    A["Initial Y\n(₹500 cr)"]
    B["G ↑ ₹100 cr\nto ₹200 cr"]
    C["New Y\n(₹1,000 cr)"]
    A -->|"MPC=0.8"| D["C ↑ ₹400 cr"]
    D --> C

Example 2: Accelerator Calculation for a Firm

Given:

• A tea factory’s output grows by 20% (from 100 to 120 quintals/year).
• Capital-output ratio: ₹5 lakh per quintal of capacity.
• Expected lifespan of machinery: 5 years.

Steps:

1. Calculate change in output: 20% of 100 = 20 quintals.
2. Calculate required investment: $$\text{Investment}=\text{Capital-output ratio}\times \Delta \text{Output}=5\times 20=₹100\text{ lakh}$$
3. Accelerator coefficient (v): $$v=\frac{\text{Capital-output ratio}}{\text{Lifespan}}=\frac{5}{5}=1$$ So, investment = $v\times \Delta Y=1\times 20\%=20\%$ of capital stock.

Real-World Tie-In:

• Nepal Tea Development Board: If tea exports grow by 15%, factories invest in new drying machines (capital-output ratio: ₹3 lakh/quintal).

## In the Real World

1. eSewa and the Multiplier

   • When the government promoted eSewa for utility bill payments (2018), ₹200 crore in new digital transactions were made.
   • MPC: Users spent 75% of extra income via eSewa (MPC = 0.75).
   • Multiplier effect: $k=\frac{1}{1-0.75}=4$ → ₹800 crore in total spending.
   • Accelerator: Higher transaction volume → eSewa invested in new servers and customer support.

2. Pathao’s Bike Fleet and the Accelerator

   • During COVID-19 (2020–21), Pathao’s daily rides grew by 40% as people avoided buses.
   • Accelerator coefficient: 1.8 (for every 1% output growth, Pathao adds 1.8% more bikes).
   • Investment: 40% × 1.8 = 72% more bikes in 2021.
   • Result: Pathao’s fleet grew from 50,000 to 86,000 bikes, creating jobs for 10,000 new drivers.

3. NTC’s Fiber Expansion and Crowding-Out

   • NTC’s ₹800 crore fiber expansion (2021) aimed to connect 50 new districts.
   • Multiplier: Rural MPC = 0.6 → $k=2.5$ → ₹2,000 crore in income.
   • But: Heavy borrowing by NTC led to higher interest rates, crowding out private firms like Worldlink and Smart Cell from expanding.

## Exam Tip

1. Always define MPC/MPS first before deriving multipliers. Examiners deduct marks if you skip this.
   • Example: "Given MPC = 0.75, derive the tax multiplier."
     • Correct: "MPS = 1 - MPC = 0.25. Tax multiplier = -MPC/(1 - MPC) = -0.75/0.25 = -3."
     • Incorrect: "Multiplier = 1/MPC = 1.33" (wrong formula for tax multiplier).

2. Compare multipliers in tables for government vs. private spending. Highlight crowding-out risks.

   • Example: "Why does a ₹100 crore subsidy have a higher multiplier than a ₹100 crore tax cut?"
     • Answer: Subsidies go directly to low-income groups (higher MPC), while tax cuts may be saved by the rich.

3. For accelerator questions, always:

   • State the capital-output ratio.
   • Mention expected lifespan of capital.
   • Link to real-world investment (e.g., "This explains why Daraz built 5 new warehouses in 2023").

4. Graphical questions:

   • Draw 45° line diagrams for multiplier effects (show equilibrium before/after injection).
   • For accelerator, plot output vs. investment with a steeper slope for high growth.

5. Policy critique:

   • If asked, "Should Nepal use multipliers or accelerators to boost growth?", answer:
     • Multiplier: Better for short-term stimulus (e.g., post-disaster reconstruction).
     • Accelerator: Better for long-term growth (e.g., infrastructure to attract FDI).
     • Trade-off: Multiplier may cause inflation; accelerator may lead to overinvestment.

Final Visual Summary: