Economic Principles (Micro) - Producer Theory

Neoclassical Consumer Theory Recap

• Rational consumer consumes where the slope of the indifference curve equals the slope of the budget line.
• A decrease in the price of good X results in higher consumption due to:
  • Budget line toggling outwards.
  • Tangency with a higher indifference curve.
• Price-consumption curve reflects how demand changes with price.
• Change in consumption due to:
  • Income effect.
  • Substitution effect.

Producer Theory

• Explains what drives supply, focusing on the rational firm.
• Firms decide:
  • How to produce (production functions, marginal products, scale).
  • How much to produce (costs, economies of scale, profit maximization).
• Main assumption: Perfect competition.

The Production Function

• Mathematical relationship between output and inputs.
• $TPP = f(K, L)$
  • TPP: Total physical product.
  • K: Capital input.
  • L: Labour input.
  • f(·) describes how output changes with K and/or L.

The Marginal Product of Labour and Capital

• Marginal Product of Labour (MPL): Change in output from a unit increase in labour.
• Marginal Product of Capital (MPK): Change in output from a unit increase in capital.
• $MPL = \frac{\partial f(K, L)}{\partial L}$, $MPK = \frac{\partial f(K, L)}{\partial K}$
• Marginal products are partial derivatives of the production function.
• Law of diminishing marginal returns: Increasing one input (holding others constant) leads to decreasing gains in output.

Cobb-Douglas Production Function

• $TPP = K^{\alpha} \cdot L^{\beta}$
  • TPP: Total physical product.
  • K: Capital input.
  • L: Labour input.
  • $\alpha, \beta$: Output elasticities.
• Respects diminishing marginal returns; allows input substitution.
• Marginal Products:
  • $MPL = \frac{\partial TPP}{\partial L} = \beta K^{\alpha}L^{\beta-1}$
  • $MPK = \frac{\partial TPP}{\partial K} = \alpha K^{\alpha-1}L^{\beta}$
• Returns to Scale:
  • Constant: $\alpha + \beta = 1$
  • Increasing: $\alpha + \beta > 1$
  • Decreasing: $\alpha + \beta < 1$
• Production Isoquant: Shows combinations of K and L yielding same output level.
• Marginal Rate of Technical Substitution: Rate at which a producer can substitute labour for capital, keeping output constant.
• Cost-minimizing combination: Where isoquant and isocost line slopes are equal.

Costs

• Short-run: Period where some inputs are fixed.
• Long-run: Period where all inputs are variable.
• Variable costs: Change in the short-run with production.
• Fixed costs: Can change in the long-run; do not vary with production.
• Cost structure:
  • Total Costs (TC) = Fixed Costs (FC) + Variable Costs (VC)
  • Average Costs (AC) = TC per unit of output
  • Average Variable Costs (AVC) = VC per unit of output
  • Average Fixed Costs (AFC) = FC per unit of output
  • Marginal Cost (MC) = Cost of producing one more unit
• Short Run Curves:
  • MC is positive, decreases initially, then increases.
  • AVC decreases until AVC = MC.
  • AC decreases until AC = MC.
  • AFC decreases as more units are produced.

Economies of Scale

• If costs per unit decrease as output expands, a firm experiences economies of scale.
• Sources:
  • Specialization/division of labour.
  • Lumpy inputs.
  • Large machines.
  • By-products.
• If costs per unit increase as output expands, a firm experiences diseconomies of scale.
• Sources:
  • Management and coordination issues.
  • Worker alienation.
  • Marketing costs.
• LRMC: Long Run Marginal Cost
• LRAC: Long Run Average Cost
  • Economies of scale: LRMC < LRAC (Decreasing LRMC and LRAC)
  • Diseconomies of scale: LRMC > LRAC (Increasing LRMC and LRAC)