Multiplier & Accelerator: How Spending Creates Jobs & Growth

TAKEAWAYS:

• The multiplier shows how an initial injection of spending (like a new road) creates more income through repeated spending cycles, boosting GDP more than the original amount.
• The accelerator explains why businesses invest more when demand (income) is growing fast, and cut investment when growth slows—linking investment to past income changes.
• The multiplier formula is $K=\frac{1}{1-MPC}$ (where MPC = Marginal Propensity to Consume), and the accelerator coefficient is $\frac{\Delta I}{\Delta Y}=\frac{1}{v}$ (where $v$ = capital-output ratio).
• Real-world uses: Governments use multipliers to decide how much to spend on infrastructure, and businesses use accelerators to plan investments.
• Limitations: The multiplier weakens if people save more (MPC falls) or if imports rise (leakages increase). The accelerator can cause boom-bust cycles if overreacted to.
• NEB focus: Expect numerical problems (calculate multiplier/accelerator), graph questions (shift in AD curve), and short-answer definitions of key terms like "induced investment."

What is the Multiplier Effect?

Imagine you win Rs. 10,000 and spend it all on groceries. The shopkeeper uses part of that money to buy new shelves (Rs. 4,000). The shelf supplier then spends Rs. 2,000 on raw materials, and so on. Your initial Rs. 10,000 has created more income for others in the economy. This is the multiplier effect: a small injection of spending leads to a larger increase in total income.

How Does It Work?

1. Initial Injection: Government spends Rs. 100 crore on building a bridge.
2. First Round: Bridge workers earn Rs. 100 crore and spend Rs. 70 crore (assuming they save Rs. 30 crore).
3. Second Round: Those who sold goods/services to workers now have Rs. 70 crore to spend, and so on.
4. Total Income Increase: The total income rises by more than Rs. 100 crore because of repeated spending.

Key Terms:

• Marginal Propensity to Consume (MPC): The fraction of extra income people spend. If MPC = 0.7, they spend 70% and save 30%.
• Marginal Propensity to Save (MPS): The fraction saved. $MPS=1-MPC$.
• Multiplier (K): Shows how much total income changes for every unit of initial spending. Formula: $$K=\frac{1}{MPS}\text{or}K=\frac{1}{1-MPC}$$

Example Calculation:

If MPC = 0.8 (people spend 80% of extra income), then: $$K=\frac{1}{1-0.8}=\frac{1}{0.2}=5$$ This means an initial Rs. 1 crore injection increases total income by Rs. 5 crore.

Graphical Representation of the Multiplier

The multiplier works because spending becomes income for someone else, who then spends again. Graphically, this looks like a geometric series where each round is smaller than the last (because people save some income).

graph TD
    A["Initial Injection\n(Rs. 100 crore)"] --> B["Round 1 Spending\n(Rs. 80 crore)\n(MPC=0.8)"]
    B --> C["Round 2 Spending\n(Rs. 64 crore)"]
    C --> D["Round 3 Spending\n(Rs. 51.2 crore)"]
    D --> E["... and so on"]

Total Income Change = Initial Injection × Multiplier = Rs. 100 crore × 5 = Rs. 500 crore

Types of Multipliers

Limitations of the Multiplier

While powerful, the multiplier isn’t perfect:

1. Assumes Full Employment: If factories are idle, the multiplier works well. But if everyone is already employed, extra spending may just cause inflation (prices rise, not output).
2. Leakages: Not all income is spent. If people save more or buy imports, the multiplier shrinks.
   • Example: If MPC drops to 0.5 (people save 50%), $K=\frac{1}{0.5}=2$. Now Rs. 1 crore only adds Rs. 2 crore to income.
3. Time Lags: It takes time for the multiplier to work. Delays can reduce its impact.
4. Psychological Factors: If people fear recession, they may save more, weakening the multiplier.

The Accelerator: How Investment Depends on Growth

The accelerator explains why businesses invest more when the economy is growing fast—and cut investment when growth slows. It links investment (I) to changes in income (ΔY).

How It Works:

• If income grows by 10%, businesses expect higher demand and invest in new machines/factories.
• If income falls, businesses reduce investment (they don’t need as much capacity).
• The accelerator is not about current income, but about how fast income is changing.

Formula:

$$\text{Accelerator Coefficient}=\frac{\Delta I}{\Delta Y}=\frac{1}{v}$$ Where:

• $\Delta I$ = Change in investment.
• $\Delta Y$ = Change in income.
• $v$ = Capital-output ratio (how much capital is needed per unit of output, e.g., Rs. 5 lakh per car).

Example:

If $v=2$ (Rs. 2 lakh of capital per unit of output), then: $$\frac{\Delta I}{\Delta Y}=\frac{1}{2}=0.5$$ This means if income rises by Rs. 100 crore, investment rises by Rs. 50 crore.

Accelerator vs. Multiplier: Key Differences

Combined Effect: Multiplier-Accelerator Interaction

In reality, both forces work together:

1. Government spends (multiplier kicks in) → Income rises.
2. Income rise triggers more investment (accelerator) → More factories, jobs, and growth.
3. But: If investment grows too fast, it can lead to overproduction and recession (boom-bust cycle).

Boom-Bust Cycle Example:

• Boom: Government spends → Income rises → Businesses invest heavily → Economy grows fast.
• Bust: Growth slows → Businesses cut investment → Income falls → Layoffs → Recession.
• This cycle can repeat unless managed by fiscal policy (government spending/taxes).

Real-World Applications

1. Government Policies:

   • During recessions, governments increase spending (e.g., road projects) to boost income via the multiplier.
   • Example: Nepal’s Budget Speech often highlights infrastructure projects to create jobs.

2. Business Decisions:

   • Companies use the accelerator to decide when to expand. If sales are rising fast, they invest in new machinery.
   • Example: A biscuit factory in Nepal may build a new oven if demand for biscuits is growing.

3. Economic Stability:

   • Central banks (like Nepal Rastra Bank) monitor these effects to prevent inflation (too much growth) or recession (too little growth).

Solved NEB-Style Problems

Problem 1: Calculate the Multiplier

If MPC = 0.9, what is the multiplier? How much will national income rise if the government injects Rs. 50 crore?

Solution:

1. MPC = 0.9 → MPS = 1 – 0.9 = 0.1.
2. Multiplier $K=\frac{1}{MPS}=\frac{1}{0.1}=10$.
3. Income rise = Initial injection × K = Rs. 50 crore × 10 = Rs. 500 crore.

Problem 2: Accelerator Calculation

If the capital-output ratio ($v$) is 4, how much will investment change if income rises by Rs. 200 crore?

Solution:

1. Accelerator coefficient = $\frac{1}{v}=\frac{1}{4}=0.25$.
2. $\Delta I=0.25\times \Delta Y=0.25\times 200=$ Rs. 50 crore.

Problem 3: Graph Interpretation

Draw a graph showing the AD (Aggregate Demand) curve shifting right due to a multiplier effect. Label the initial and final equilibrium points.

Solution:

• Initial AD: Economy at point A (lower income Y1, price P1).
• Government spends: AD shifts right (due to multiplier).
• New AD: Economy moves to point B (higher income Y2, price P2).

Common Mistakes to Avoid

1. Confusing Multiplier and Accelerator:

   • Multiplier = Spending → Income.
   • Accelerator = Income change → Investment.
   • Don’t mix them up!

2. Ignoring Leakages:

   • Always check if MPC/MPS is given. If not, assume typical values (e.g., MPC = 0.8).

3. Assuming Infinite Multiplier:

   • The multiplier works best when MPS is small (people spend most of extra income). If MPS is high, the multiplier shrinks.

4. Forgetting Units:

   • Multiplier is unitless (e.g., 5 means Rs. 1 crore → Rs. 5 crore).
   • Accelerator is a ratio (e.g., 0.5 means Rs. 1 crore income rise → Rs. 0.5 crore investment rise).

Exam Tip: How to Score Full Marks

1. Definitions:

   • Know these by heart:
     • Multiplier: The ratio of total change in income to initial change in spending.
     • Accelerator: The ratio of change in investment to change in income.

2. Formulas:

   • Write them clearly:
     • $K=\frac{1}{MPS}$ or $K=\frac{1}{1-MPC}$.
     • $\frac{\Delta I}{\Delta Y}=\frac{1}{v}$.

3. Graphs:

   • For multiplier: Draw a rightward shift in AD with labeled equilibrium points.
   • For accelerator: Draw a graph showing investment rising with income growth.

4. Numerical Problems:

   • Show all steps. Example:

     Given MPC = 0.75, calculate the multiplier. Solution: MPS = 1 – 0.75 = 0.25 → K = 1/0.25 = 4.

5. Real-World Links:

   • Connect to Nepal:
     • "Nepal’s budget focuses on infrastructure to use the multiplier effect and create jobs."
     • "Factories in Chitwan invest more when tourist income rises (accelerator)."

6. Limitations:

   • Always mention at least one limitation (e.g., "The multiplier assumes no inflation, but in Nepal, price rises can reduce its effect.").

NEB Board-Style Questions

Short Answer (5 marks)

1. Explain the multiplier effect with an example. What are its limitations?
2. Distinguish between the multiplier and the accelerator.
3. If MPS is 0.2, how much will national income rise from a Rs. 20 crore government spending?

Long Answer (10 marks)

1. "The multiplier and accelerator together can cause economic instability." Explain with the help of a diagram and real-world examples from Nepal.
2. Calculate the multiplier if:
   • MPC = 0.6
   • MPS = 0.3
   • Savings = Rs. 2 crore when income rises by Rs. 10 crore. Also, explain how leakage affects the multiplier.

Practical/Application (7 marks)

1. A factory in Biratnagar produces 1,000 units of output with capital worth Rs. 5 lakh. If demand rises by 20%, how much will the factory invest? Use the accelerator concept.
2. Suggest two policies Nepal can use to maximize the multiplier effect during a recession.

Final Note:

• Multiplier = Spending begets more spending → bigger income.
• Accelerator = Growth begets more investment → faster growth (or crashes).
• Both are tools to understand how economies expand or contract. Master the formulas, graphs, and real-world links to ace your NEB exam!