Factor Markets: Labour & Capital – Demand, Supply, and Productivity

TAKEAWAYS:

• Factor demand depends on marginal productivity (MP) and factor prices: firms hire until MP_L = W (wage) and MP_K = r (rental rate).
• Labour supply shifts due to population, education, migration, and wage expectations—Nepal’s remittance-driven labour migration is a key example.
• Capital supply depends on savings, interest rates, and expected returns—NTC’s reliance on loans for grid expansion shows this.
• Elasticity of factor demand determines how sensitive firms are to price changes (e.g., Daraz’s response to driver wages vs. warehouse automation costs).
• Monopsony power (single buyer, like Ncell hiring call-center workers) lets firms pay wages below competitive levels.
• Profit maximization in factor markets requires balancing marginal revenue product (MRP) with factor costs—critical for TU/PU exam calculations.

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1. Factor Demand: How Firms Choose Labour and Capital

Firms demand factors of production (labour, capital) based on their contribution to revenue. The core principle:

A firm hires a factor until its Marginal Revenue Product (MRP) equals its price.

Key Concepts

• Marginal Product (MP): Additional output from one more unit of input.
  • For labour: $M{P}_L=\frac{\Delta Q}{\Delta L}$
  • For capital: $M{P}_K=\frac{\Delta Q}{\Delta K}$
• Value of Marginal Product (VMP): $VMP=P\times MP$ (where $P$ = product price).
• Marginal Revenue Product (MRP): In perfect competition, $MRP=VMP$. In monopoly, $MRP=MR\times MP$.

Worked Example: Ncell’s Call-Center Hiring

Scenario: Ncell wants to hire telemarketers. The production function is $Q=100L^{1/2}$, product price $P=\text{Rs }25$, and wage $W=\text{Rs }25$. How many workers should Ncell hire?

Steps:

1. Find $M{P}_L$: $M{P}_L=\frac{dQ}{dL}=\frac{100}{2\sqrt{L}}=50/\sqrt{L}$.
2. $VM{P}_L=P\times M{P}_L=25\times (50/\sqrt{L})=1250/\sqrt{L}$.
3. Hire until $VM{P}_L=W$: $1250/\sqrt{L}=25⟹\sqrt{L}=50⟹L=2500$.

Output: $Q=100\times \sqrt{2500}=100\times 50=5000$ calls/day.

Ncell’s telemarketers: Labour as a variable input (Image: Department of Defense. American Forces Information Service. , Public domain, via Wikimedia Commons)

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2. Labour Supply: Why Workers Work

Labour supply depends on:

• Wage rate (higher wages = more supply, but with diminishing returns).
• Non-pecuniary factors (job satisfaction, safety, location).
• Population and demographics (Nepal’s youth bulge increases supply).
• Migration (remittance workers leave Nepal, reducing domestic supply).

Shift in Labour Supply Curve

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3. Capital Demand and Supply

Capital includes physical assets (machines, buildings) and financial capital (loans, equity). Firms demand capital if its MP_K > rental rate (r).

Capital Supply in Nepal: NTC’s Grid Expansion

• Problem: NTC needs Rs 500 billion to upgrade transmission lines (2023 data).
• Sources:
  • Domestic savings (low due to high consumption).
  • Foreign loans (e.g., World Bank’s Rs 20B grant for hydropower).
  • Private equity (e.g., Butwal Power Company’s IPO on NEPSE).
• Supply curve shifts:
  • Higher interest rates → Leftward shift (costly borrowing).
  • Tax incentives → Rightward shift (e.g., 10-year tax holiday for renewable energy).

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4. Elasticity of Factor Demand

Measures how sensitive firms are to price changes of factors.

Worked Example: Pathao’s Driver Wages

• Scenario: Pathao raises driver wages from Rs 300/day to Rs 350/day.
• Data: Initially, 500 drivers work. After hike, 450 drivers quit.
• Elasticity Calculation: $E_L=\frac{\%\Delta L}{\%\Delta W}=\frac{(450-500)/500}{(350-300)/300}=\frac{-10\%}{16.67\%}=-0.6$. Interpretation: Inelastic demand (|E| < 1). Pathao cannot easily reduce driver numbers.

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5. Monopsony in Factor Markets

A monopsony is a single buyer of labour/capital (e.g., Ncell hiring call-center workers in Kathmandu).

Key Differences: Competitive vs. Monopsony Market

Example: NTC’s Labour Monopsony

• NTC is the sole employer for high-voltage line technicians in remote areas.
• Result: Pays wages below competitive levels, reducing labour supply.
• Government intervention: Minimum wage laws (e.g., Rs 22,000/month for skilled workers) counteract this.

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6. Profit Maximization with Two Factors

When a firm uses both labour (L) and capital (K), it must satisfy: $$\frac{M{P}_L}{W}=\frac{M{P}_K}{r}$$ (Equal marginal productivity per rupee spent.)

Worked Example: Daraz’s Warehouse

Production function: $Q=100K^{1/2}{L}^{1/2}$ Costs: $W=\text{Rs }25$, $r=\text{Rs }40$, Budget $C=\text{Rs }1100$.

Steps:

1. Optimal condition: $\frac{M{P}_L}{W}=\frac{M{P}_K}{r}$.
   • $M{P}_L=50/\sqrt{L}$, $M{P}_K=50/\sqrt{K}$.
   • $\frac{50/\sqrt{L}}{25}=\frac{50/\sqrt{K}}{40}⟹\frac{2}{\sqrt{L}}=\frac{1.25}{\sqrt{K}}⟹\sqrt{K}=0.625\sqrt{L}$.
2. Budget constraint: $25L+40K=1100$. Substitute $K=(0.625\sqrt{L}{)}^2=0.39L$: $25L+40(0.39L)=1100⟹25L+15.6L=1100⟹L=28.57$, $K=11.2$.
3. Output: $Q=100\times \sqrt{11.2}\times \sqrt{28.57}\approx 100\times 3.35\times 5.34\approx 1794$ units.

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In the Real World

1. Ncell’s Hiring (Labour Demand):

   • Ncell uses marginal productivity theory to hire call-center agents. If an agent handles 50 calls/day at Rs 25/call revenue, their $VMP=50\times 25=\text{Rs }1250$. Ncell pays wages below this (e.g., Rs 800–1000) due to monopsony power in Kathmandu.

2. NTC’s Grid Expansion (Capital Supply):

   • NTC’s Rs 500B capital demand is met via:
     • Foreign loans (World Bank, ADB) shifting the supply curve right.
     • High interest rates (10–12%) making domestic savings expensive.
   • Elasticity impact: A 1% rise in interest rates reduces capital projects by 0.5% (inelastic supply).

3. Pathao’s Driver Wages (Labour Supply Elasticity):

   • Pathao’s Rs 300–350/day wage attracts drivers from informal transport (e-rickshaws, buses).
   • Short-run: Drivers have few alternatives → inelastic supply.
   • Long-run: More drivers enter the market as Pathao grows → elastic supply.

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Exam Tip

1. Always check units: In calculations, ensure $M{P}_L$ is in "units per worker" and $VMP$ is in "rupees per worker."
2. Graph shifts: For labour supply shifts, ask:
   • Is it population (right) or migration (left)?
   • Are wages expected to rise (right) or fall (left)?
3. Monopsony trap: If the question mentions a single buyer (e.g., NTC, Ncell), use $MRP=MC$, not $MRP=W$.
4. Two-factor problems: Use the equal marginal productivity per rupee rule and budget constraint together.
5. Real-world links: TU/PU often test Nepal-specific examples (NTC, Ncell, Daraz). Relate theory to these in answers.

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Visual Summary: