Introduction
Production and cost analysis forms the supply side of economic analysis. This unit provides an integrated overview showing how the physical production function translates into cost curves when input prices are applied.
The Production-Cost Link
Production Function: Q = f(L, K)
Cost Function: C = wL + rK
Where: w = wage rate, r = rental rate of capital
Key Relationships
| Production Concept | Cost Concept | Relationship |
|---|---|---|
| Marginal Product (MP) | Marginal Cost (MC) | MC = w/MP (inversely related) |
| Average Product (AP) | Average Variable Cost (AVC) | AVC = w/AP (inversely related) |
| Returns to Scale | LAC Shape | IRS → Falling LAC; DRS → Rising LAC |
Short-Run Analysis
In the short run, at least one factor (typically capital) is fixed.
Short-Run Production
- Total Product (TP): Total output from all inputs
- Average Product (AP): Output per unit of variable input = TP/L
- Marginal Product (MP): Additional output from one more unit = ΔTP/ΔL
Law of Diminishing Returns
As more units of a variable input are added to fixed inputs, the marginal product eventually decreases.
Short-Run Costs
- Fixed Costs (FC): Don't vary with output
- Variable Costs (VC): Change with output
- Total Cost: TC = FC + VC
- Marginal Cost: MC = ΔTC/ΔQ
Example: Short-Run Cost Calculation
Given: FC = ₹10,000, VC = 20Q + 0.5Q²
At Q = 100:
- VC = 20(100) + 0.5(100)² = ₹7,000
- TC = ₹10,000 + ₹7,000 = ₹17,000
- ATC = ₹17,000/100 = ₹170
- MC = 20 + Q = 20 + 100 = ₹120
Long-Run Analysis
In the long run, all factors are variable. Firms can adjust plant size optimally.
Returns to Scale
| Type | Description | LAC Effect |
|---|---|---|
| Increasing Returns | Output rises more than proportionally | LAC falls |
| Constant Returns | Output rises proportionally | LAC constant |
| Decreasing Returns | Output rises less than proportionally | LAC rises |
Economies of Scale
- Technical: Larger equipment is more efficient
- Managerial: Specialization of management
- Financial: Better terms on financing
- Marketing: Spreading advertising costs
Finding Optimal Production
Profit Maximization
Profit = Total Revenue - Total Cost
π = TR - TC = PQ - TC
Optimal Condition: MR = MC
Cost Minimization
For a given output level, minimize cost by choosing inputs where:
MPL/w = MPK/r
Marginal product per rupee should be equal for all inputs
Conclusion
Key Takeaways
- Production and cost are two sides of the same coin
- MC is inversely related to MP: MC = w/MP
- Diminishing returns cause rising marginal costs
- Economies of scale cause falling long-run average costs
- Profit maximization occurs where MR = MC
- Cost minimization requires equalizing MP per rupee across inputs