CHAPTER 4: UNPACKING SUPPLY – FROM FACTORY TO SHELF

 

CHAPTER 4: UNPACKING SUPPLY – FROM FACTORY TO SHELF

Objective:

To analytically reconstruct the supply function using variables such as cost, time, logistics, inventory behavior, perishability, and policy disruptions. This chapter aims to understand how supply functions respond dynamically to internal and external shocks.

 

4.1 Understanding the Nature of Supply

In economics, the supply function denotes the relationship between the quantity of goods a producer is willing to supply and various influencing factors, primarily the market price. However, in a real-world framework, supply is far from linear or static. Modern supply chains are affected by cost structure, policy changes, inventory cycles, transportation delays, and demand unpredictability.

The basic supply function is often written as:
Qs = a + bP – cC + dT + eL – fS
Where:

·         Qs: Quantity supplied

·         P: Price of the product

·         C: Production cost

·         T: Technology index or time efficiency

·         L: Logistics infrastructure

·         S: Seasonality or perishability

·         a, b, c, d, e, f: Sensitivity coefficients

This function tells us that supply increases with price and technological improvements, while it decreases with higher costs, poor logistics, and perishability risks.

 

4.2 Components Influencing Supply

1. Production Costs (C)

Cost remains the most sensitive determinant. Higher input prices, especially for raw materials, fuel, and labor, decrease the margin and thus reduce willingness to supply.
For example, during the global oil shock, production costs surged, leading to a leftward shift in the supply curve.

Equation Insight:
If Qs = 50 + 4P – 2C, and cost increases from ₹10 to ₹20 while P = ₹15,
Then Qs changes from 50 + 4(15) – 2(10) = 100
To Qs = 50 + 4(15) – 2(20) = 80
Interpretation: A ₹10 increase in cost reduced supply by 20 units.

2. Lead Time (T)

The time lag between initiating production and delivery affects supply elasticity. In industries like automotive or electronics, long lead times reduce the ability to respond quickly to market signals.
Companies now use Just-in-Time (JIT) systems to reduce inventory holding costs but risk greater disruption sensitivity.

3. Perishability (S)

For sectors such as agriculture or dairy, perishability restricts storage and affects seasonal supply availability. Supply here depends on storage tech, weather, and consumer behavior.
E.g., tomato supply in monsoon drops drastically due to spoilage risks.

4. Government Policy & Regulation

Subsidies, taxes, and quotas impact supply. A favorable GST regime for textiles has enhanced supply, while regulatory bottlenecks in pharma often curtail it.

5. Logistics & Inventory Behavior (L)

A strong logistics chain—cold storage, container trucks, last-mile delivery—enhances market reach. Inventory behavior like safety stock or economic order quantity (EOQ) models affect short-term availability.

 

4.3 Supply Curve Shifts – Graphical Interpretation

Supply curves shift based on non-price determinants like cost changes, policy revisions, or logistics bottlenecks.

Graph Concept:

Plot Quantity Supplied (Qs) on the X-axis and Price (P) on the Y-axis.

·         Initial supply curve: S₀

·         After increase in input costs or logistics disruption: Curve shifts left to S₁

·         After technology improvement or subsidy: Curve shifts right to S₂

🟩 Graphical Summary:

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CopyEdit

       Price

         |

         |        S₁     S₀       S₂

         |         \      \       \

         |          \      \       \

         |           \      \       \

         |            \      \       \

         |-------------------------------> Quantity Supplied

 

4.4 Case Study: Supply Chain Shock in Pharma During COVID-19

Background

India is a major producer of generic drugs, but 70% of its active pharmaceutical ingredients (APIs) are imported from China. During the first wave of COVID-19, lockdowns in Wuhan disrupted API supply chains.

Impact

·         Lead time extended from 3 weeks to over 8 weeks.

·         Inventory backlogs and hoarding occurred.

·         Prices of common drugs increased by 30–50%.

·         Government introduced temporary export bans to secure domestic supply.

Supply Curve Effect

The supply curve of pharma products shifted left, reflecting reduced availability despite rising prices.

Learning Point: The pandemic highlighted the fragility of global supply networks and the importance of supply chain resilience.

  4.5 Supply Theories Integrated with Functional Equations

This section explains the most influential supply theories, aligned with the analytical supply function discussed earlier in the chapter:

Qs = a + bP – cC + dT + eL – fS

Where:

·         Qs = Quantity supplied

·         P = Price of the product

·         C = Cost of production

·         T = Time efficiency (or technological capability)

·         L = Logistics infrastructure

·         S = Seasonality/perishability

·         a, b, c, d, e, f = positive or negative coefficients depending on sensitivity

 

1. Law of Supply

This classical theory states that if all other factors remain constant, quantity supplied increases as the price increases. Mathematically, when Qs = a + bP, with b > 0, the slope of the curve is positive. For instance, if Qs = 20 + 4P and price increases from ₹10 to ₹12, supply increases from 60 to 68 units. This supports the upward-sloping nature of the supply curve.

 

2. Short-run vs Long-run Supply

In the short run, some factors like capital (K) remain fixed, making the supply less responsive. If we modify the function as:
Qs = a + bP – cC, then c is high, showing high cost impact due to limited flexibility.

In the long run, firms can adjust all inputs, and dT becomes significant in the function Qs = a + bP – cC + dT. For example, technological advancements (like automation) increase T, thereby raising Qs over time.

 

3. Marginal Cost Theory of Supply

According to this theory, producers supply additional units until marginal cost equals price. If marginal cost (MC) = 2 + 0.5Q and market price is ₹12, then setting MC = P:
2 + 0.5Q = 12 ⇒ Q = 20 units.
This value of Q becomes the firm's optimal supply at that price point.

This aligns with our supply function where cost is a component:
Qs = a + bP – cC. When C increases due to rising MC, the total supply Qs decreases.

 

4. Elasticity of Supply

Supply elasticity measures responsiveness to price changes.
The elasticity formula is:
Es = (% change in Qs) / (% change in P)

From Qs = 50 + 3P, if P increases from ₹10 to ₹12, Qs changes from 80 to 86.
So:
Es = [(86 – 80)/80] ÷ [(12 – 10)/10] = 0.075 / 0.2 = 0.375 (Inelastic supply)

This shows that when b is small in Qs = a + bP, elasticity is low.

 

5. Cobb-Douglas Production Function (Supply Base)

The production function:
Q = A × L^α × K^β
Where L is labor, K is capital, and A is total factor productivity.

Assuming A = 1, α = 0.6, β = 0.4, and input values L = 100, K = 64,
then Q = 1 × (100)^0.6 × (64)^0.4 ≈ 1 × 15.85 × 6.35 ≈ 100.7 units

This production-based output can be used in the supply function, i.e.,
Qs = Q = a + bP – cC + dT, where T includes technological or factor efficiency improvements derived from Cobb-Douglas parameters.

 

6. Agricultural Supply Response Theory

In agriculture, the supply function often includes lag effects. A simplified form is:
Qsₜ = a + bPₜ₋₁ – cS + eL
Here, supply in period t depends on price in period (t–1) due to seasonal production. If prices for wheat rose in the last year, farmers respond with increased supply this year.

Example:
Qsₜ = 40 + 2(Priceₜ₋₁) – 3(Perishability Index) + 4(Logistics Index)

 

7. Behavioral Supply Theory

Behavioral economics introduces psychological constraints and risk aversion. Firms may avoid scaling up supply even if P increases, due to fear of regulation or uncertainty.

This may flatten or distort the standard supply function. In such cases, b (price coefficient) becomes smaller, and f (risk or seasonal sensitivity) becomes larger in:
Qs = a + bP – cC + dT – fR

For example, during COVID-19, hoarding and fear caused supply to drop despite price incentives.

 

8. Inventory-Based Supply Models

Supply is also shaped by inventory strategies. If firms use Just-in-Time (JIT) systems, the function becomes highly sensitive to logistics delays, represented in:
Qs = a + bP – cC + dT + eL – fD

Where D = Disruption delay factor.
If logistics quality L falls or delays D increase, the available Qs declines regardless of price.

 

9. Leontief Production Function and Fixed Inputs

Here, inputs are used in fixed proportions. The production function is:
Q = min (L/α, K/β)
Where output depends on whichever input is the limiting factor.

This makes the supply function extremely rigid. For example, if 1 worker is needed per 1 machine, and machines are limited, increasing labor will not increase Qs.

Hence, in such cases, supply is perfectly inelastic:
Qs = constant, regardless of price changes.

 

10. Resource-Based Supply Theory

Firms with unique internal capabilities (e.g., patents, exclusive suppliers) are less influenced by market price and more by strategic factors.

A modified function could be:
Qs = a + bP – cC + dT + gR,
where R = proprietary resource index (like access to lithium or AI tech).

This theory applies well to companies like Tesla, which control supply via exclusive contracts rather than price-based market incentives.

 

All these theories enrich our understanding of the reconstructed supply function:
Qs = a + bP – cC + dT + eL – fS

·         Price (P) explains traditional supply behavior.

·         Cost (C) and Time (T) explain operational constraints.

·         Logistics (L), Seasonality (S), Risk (R), and Disruption (D) explain modern realities.

·         The elasticity, production, and inventory theories help quantify and forecast changes in Qs.

4.6 Numerical Problem Set

Problem 1: Basic Calculation

Given Qs = 40 + 3P – 2C + T
Where P = ₹20, C = ₹5, T = 10
Calculate Qs.

Solution:
Qs = 40 + 3(20) – 2(5) + 10 = 40 + 60 – 10 + 10 = 100 units

 

Problem 2: Interpreting Shocks

If cost (C) rises by ₹5 and T drops to 5, what’s the new Qs?

New Qs = 40 + 60 – 2(10) + 5 = 40 + 60 – 20 + 5 = 85 units
Interpretation: A ₹5 increase in cost and 5-unit drop in time efficiency led to a reduction of 15 units in supply.

 

Problem 3: Comparative Industry Analysis

Sector	Base Price (P)	Cost (C)	Tech (T)	Qs Equation
Electronics	₹30	₹12	8	Qs = 60 + 5P – 3C + 2T
Textiles	₹25	₹8	6	Qs = 55 + 4P – 2C + T

Calculate Qs for both sectors.

Electronics
Qs = 60 + 5(30) – 3(12) + 2(8) = 60 + 150 – 36 + 16 = 190

Textiles
Qs = 55 + 4(25) – 2(8) + 6 = 55 + 100 – 16 + 6 = 145

Interpretation: Despite a lower base price, electronics have higher Qs due to superior tech influence and sensitivity to price.

 

4.7 Summary and Policy Insights

·         Supply is more than price: Non-price determinants like cost, time, perishability, and policy disruptions critically shape supply.

·         Technology boosts elasticity: Tech investment reduces delay and perishability risks.

·         Global dependence is a risk: The COVID-19 case teaches that domestic sourcing and buffer inventory can reduce shocks.

·         Policy design must consider logistics: Merely increasing MSP or subsidies won't work unless logistics infrastructure is upgraded

 

Appendix –

📊 Table 1: Comparative Supply Function Across Industries

Industry	Qs Equation	Interpretation
Electronics	Qs = 60 + 5P – 3C + 2T	High responsiveness to price and tech, but sensitive to cost increases
Textiles	Qs = 55 + 4P – 2C + T	Moderate elasticity, benefits from low cost and average tech dependence
Agriculture	Qs = 45 + 3P – 4C – 2S + L	Highly perishable; logistics play a critical role in supply quantity
Pharmaceuticals	Qs = 70 + 4P – 5C + T – D	Vulnerable to disruption (D); strong regulatory and input cost dependency
Fast Food Chains	Qs = 50 + 3P – 2C + L – S	Seasonal variation affects fresh inventory; local logistics boost supply reliability

 

📦 Table 2: Inventory Behavior & Supply Resilience

Inventory Type	Used By	Supply Impact	Advantages	Disadvantages
Just-in-Time (JIT)	Electronics, Automotive	Fast turnaround, reduced holding cost	Cost-efficient, agile	Disruption-prone, less buffer
Safety Stock	Pharma, FMCG	Buffer against unexpected demand/supply delays	Ensures availability	Ties up capital
Economic Order Quantity (EOQ)	Retail Chains	Optimal ordering to minimize total cost	Efficient use of resources	Needs accurate demand forecasting
Seasonal Stock	Agriculture, Apparel	Preparedness for peak demand cycles	Satisfies demand surges	Risk of overstock or spoilage
Bulk Inventory	Hardware, Furniture	High volume production, economies of scale	Cost-effective in long run	Higher storage & insurance costs

 

📉 Table 3: Disruptions and Delays – COVID-19 Supply Chain Case

Sector	Dependency Type	Disruption Source	Impact on Supply Curve	Government/Industry Response
Pharma	Raw Material (APIs)	Lockdown in China (Wuhan)	Leftward shift due to input scarcity	Export bans, domestic API push
Automotive	Global Components	Border closures, chip shortage	Long-run supply curve flattening	Local sourcing, chip plant investments
Agriculture	Seasonal Labor	Migration & lockdown	Supply dip, wastage of perishables	Special trains, farmgate procurement
Retail Grocery	Logistics & Warehousing	Movement restrictions	Stockout of essentials	E-pass systems, last-mile delivery innovations
Textiles	Export Dependency	Port closures	Delayed shipments, idle inventory	Shift to domestic e-commerce channels