Microeconomics Lecture Outline

Lecture 4: Producer Theory: Costs and Profits

  1. Business types:
    • Sole proprietorship ¡]¿W¸ê¡^: unlimited liability
    • Partnership ¡]¦X¹Ù¡^: unlimited liability
    • Corporation ¡]¤½¥q¡^: limited liability, stock holders, double taxation
  2. Single input, single output:
    • Production of output y, using factor input x (eg, labor) (Fig. 4-1a)
      • Production function: y = f(x)
      • Marginal product (MP): f'(x) is decreasing
      • Input requirement function: x = g(y)
      • marginal input requirement: g'(y) is increasing
    • "Profit":
      • Profit is market revenues net of production costs
      • Profit(y) = py - C(y)
      Cost function: C(y)
      • Fixed costs: F (Fig. 4-1b)
      • Variable costs: wx = w*g(y) (Fig. 4-2a)
      • Total costs: C(y) = F + w*g(y)
    • Average costs:
      • Average fixed costs: AFC(y) = F/y is decreasing
      • Average variable costs: AVC(y) = w*g(y) / y
        • If VC(0+) = 0: AVC is increasing
        • If VC(0+) > 0: AVC is first decreasing, then increasing [minimum input requirement] (Fig. 4-2d)
      • Average total costs: ATC(y) = C(y)/y = [F+w*g(y)]/y is U-shaped (Fig. 4-2b)
    • Marginal costs: MC(y) = C'(y) = w*g'(y)
      • MC(y) is increasing
      • MC(y) is first decreasing, then increasing [economy of scale, specialization of labor] (Fig. 4-2c)
    • SR profit-max firm will set price=MC: p=C'(y) (Fig. 4-3a)
    • SR/LR profit condition: given market price P (Fig. 4-3b)

      PriceSR profitLR profit
      P < P1--
      P1 < P < P2+-
      P > P2++

    • SR v. LR costs: long-run is lower envelope of short-run curves (Fig. 4-4)
    • Economies/diseconomies of scale
  3. Multiple inputs (x1, x2), single output (y): y = f(x1,x2)
    • Factor input prices: (w1, w2)
    • Marginal product (MP): MP1=dy/dx1, MP2=dy/dx2 is decreasing
    • Isoquant curves: on x1-x2 space
      • y = f(x1,x2) = constant (Fig. 4-5)
      • (Ex.1) Substitutes (male v. female labor): y = x1 + x2
      • (Ex.2) Complements (1 worker for 1 machine): y = min{x1, x2}, fixed proportion
      • (Ex.3) Cobb-Douglas: y = x1 * x2, both inputs are essential
      • Technical rate of substitution (TRS): slope of isoquant
      • TRS1,2 = MP1 / MP2
    • Iso-cost curves: on x1-x2 space
      • w1*x1 + w2*x2 = constant (Fig. 4-6)
      • Slope is: dx2/dx1 = -w1/w2
    • Cost-min production of output y: Choose (x1,x2)
      • min w1x1+w2x2 st f(x1,x2)=y
      • TRS(1,2) = MP1 / MP2 = w1/w2 (price ratio)
      • [Comparative statics] Price effects of Cobb-Douglas technology:
        • If w1 goes up, firm will use less x1, and more x2.
        • If w2 goes up, firm will use less x2, and more x1.
    • Firm profit maximization: Choose (x1,x2)
      • max p*y(x1,x2) - [w1x1+w2x2]
      • Marginal value product (MVP): MVP1 = p*dy/dx1, MVP2 = p*dy/dx2
      • Optimal input choice: MVP1=w1, MVP2=w2
  4. Multiple outputs (y1, y2):
    • Market output prices: (p1, p2)
    • Production possibility frontier (PPF) (Fig. 4-7)
    • Iso-profit line: p1y1 + p2y2 = constant
    • Tangency Optimality: Marginal rate of transformation (MRT) = p1/p2 (price ratio)
    • [Comparative statics] Price effects:
      • If p1 rises, firm will produce more y1, and less y2.
      • If p2 rises, firm will produce more y2, and less y1.