Marginal Productivity and Production Cost Principles
Marginal Productivity & Production Costs
Law of Diminishing Marginal Productivity
Law of Diminishing Marginal Productivity: Extra output per worker eventually decreases as more workers are added to fixed capital.
Short Run and Long Run
Short Run: Some inputs (like labor) can be changed, but others (like capital or factory size) are fixed.
Long Run: All inputs can be changed; the firm can adjust labor, capital, etc., to optimize production.
Production Function and Products
Production Function: Maximum output possible from given inputs (labor, capital, etc.).
Marginal Product (Labor): Extra output from one more worker.
Total Product (TP) Curve:
- Slopes up → TP increasing → MP positive.
- Slopes down → TP decreasing → MP negative.
MP = ΔTP / ΔLabor Units (L) AP = TP / L
Increasing MP → TP rises faster. AP rises while MP > AP.
Decreasing MP → TP rises slower. AP falls when MP < AP.
MP = 0 → TP at maximum. ATC = TC ÷ Q
MP negative → TP falling. ↑ MP ⇒ ↑ AP.
MP decreases when the TP slope flattens.
Diminishing marginal product begins as soon as MP starts to fall. Diminishing marginal product begins when MP first starts to fall.
Costs: Fixed, Variable, and Averages
Explicit cost: Actual money paid for inputs.
Implicit costs: Value of forgone alternatives.
Total Cost (TC) = Fixed Cost (FC) + Variable Cost (VC)
Total Fixed Cost (TFC) = constant; does not change with output.
Total Variable Cost (TVC) = TC − TFC.
Average Total Cost (ATC) = TC ÷ Q
Average Variable Cost (AVC) = TVC ÷ Q
Average Fixed Cost (AFC) = FC ÷ Q
AVC = TVC / TP AFC = FC / TP ATC = TC / TP
↑ Output → FC spread over more units → ↓ AFC.
High setup costs → when spread over more units → average cost drops as output rises.
Variable inputs → change with output (materials, labor, ingredients).
Fixed inputs → stay the same regardless of output (rent, taxes, insurance).
Marginal Cost and Its Relations
Marginal Cost (MC) = Cost of producing one more unit of output.
MC = ΔTC / ΔQ (MC equals the change in total cost divided by the change in quantity).
When marginal productivity falls → marginal cost rises. ↓ MP → ↑ MC.
MC intersects AVC and ATC at their minimums.
MC < ATC → ATC falling. MC = ATC → ATC at minimum. MC > ATC → ATC rising.
MC < AVC → AVC falls. MC = AVC → AVC at its minimum. MC > AVC → AVC rises.
AVC rises when AP starts falling.
MP < AP → AP falls; AVC tends to rise. MP > AP → AP rises → AVC tends to fall.
Revenue, Profit, and Firm Decisions
Total Revenue (TR) = Price per person × Number of people
Accounting Profit (AP) = TR − Explicit Costs
Economic Profit = TR − (Explicit + Implicit)
Economic Profit = Revenue − Costs (explicit + implicit)
Profit-Maximizing Output
- Produce if P > AVC.
- Stop increasing output when MC > P.
- A firm maximizes profit where MR = MC. If MR < MC, producing more reduces profit.
- Produce up to the quantity where MC = P (or just below it).
Total economic profit = (P − ATC) × Q
If firm operates: Loss = (P − ATC) × Q.
If firm shuts down: Loss = TFC.
Operate if P ≥ AVC. Shut down if P < AVC.
Profit = (Price − ATC) × Quantity.
Loss = −TFC.
Scale, Scope, and Efficiency
Economies of scale: as output increases in the long run, the long-run average total cost (LRATC) can fall and the LRATC curve slopes downward.
Diseconomies of scale → ATC rises → LRATC slopes upward.
LRAC (long-run average cost) shape reflects economies and diseconomies of scale.
Multiple products produced more cheaply together → economies of scope.
Technology that makes multiple products efficiently → reduces indivisible setup costs.
Economic efficiency = lowest cost for a given output; pick the least-cost method.
Abundant resource = used more efficiently.
Japan: lots of capital → production is capital intensive.
Cambodia: labor abundant → production is labor intensive.
Formulas and Key Identities
- TC = TFC + TVC
- TFC = constant; does not change with output.
- TVC = TC − TFC
- MC = ΔTC / ΔQ
- AVC = TVC / Q
- ATC = TC / Q
Other Notes
When MP falls → MC rises. High setup costs, when spread over more units, cause average cost to drop as output rises.
Bigger firm = harder to monitor.