Exam 2

• Production function


  • Q = F(K,L)
  • Q is quantity of output produced
  • K is capital input
  • L is labor input
  • F is a functional form relating the inputs to output
• Short-Run vs. Long-Run Decisions


  • Fixed vs. variable Inputs
  • At least one factor (usually capital) fixed in the short run
  • Q = F(K*,L)
• Total product (TP)


  Maximum level of output that can be produced with a given amount of inputs (essentially the production function)
• Average product (AP)


  Measure of the output produced per unit of input
• Marginal product (MP)


  • Change in total product (output) attributable to the last unit of an input
  • Marginal product of labor = ∂Q/∂L
  • Marginal product of capital = ∂Q/∂K
• Value Marginal Product (VMP)


  • Value of the output produced by the last unit of an input
  • VMPL = P·MPL
  • VMPK = P·MPK
• Law of diminishing returns: Marginal product of additional unit of output will at some point be lower than the marginal product of the previous unit
• Profit-Maximization input usage


  • Use input levels at which marginal benefit equals marginal cost
  • When cost of additional unit of labor is w, continue to employ labor up to the point where VMPL = w in the range of diminishing marginal product
  • If capital varies in the short run, to maximize profit hire capital until the value of marginal product of capital equals the rental rate: VMPK = r
• Linear production function


  Q = aK + bL, where a and b are constants
• Leontief production function


  Q = min{bK, cL}, where b and c are constants
• Cobb-Douglas production function


  Q = K^a * L^b, where a and b are constants
• Marginal products for linear, Leontief, and Cobb-Douglas production functions
• Average products for linear, Leontief, and Cobb-Douglas production functions
• Isoquant


  Illustrates the long-run combinations of inputs (K, L) that yield the producer the same level of output
• Marginal Rate of Technical Substitution (MRTS)


  The rate at which two inputs are substituted while maintaining the same output level
• Linear isoquants


  Capital and labor are perfect substitutes
• Leontief isoquants


  Capital and labor are perfect complements, used in fixed-proportions
• Cobb-Douglas isoquants


  Inputs are not perfectly substitutable, diminishing marginal rate of technical substitution
• Isocost


  The combinations of inputs that produce a given level of output at the same cost: wL + rK = C
• Changes in input prices

  Change the slope of the isocost line
• Cost-Minimization Input Rule


  Marginal product per dollar spent should be equal for all inputs: MPL/w = MPK/r
• If MPL/w > MPK/r, the firm is too capital-intensive and should substitute more labor for capital
• Short-run costs


  • Fixed costs: do not change with changes in output; include the costs of fixed inputs used in production
  • Variable costs: costs that change with changes in outputs; include the costs of inputs that vary with output
  • Total costs = Fixed costs + Variable costs
• Long-run costs


  All costs are variable, no fixed costs
• Fixed costs


  Cost that does not change with output
• Sunk cost


  Cost that is forever lost after it has been paid
• Irrelevance of Sunk Costs: A decision maker should ignore sunk costs to maximize profits or minimize losses
• Average fixed cost


  Fixed costs / Output
• Average variable costs


  Variable costs / Output
• Average costs


  Total costs / Output
• Minimum cost


  Derived through optimization, not a given like a budget constraint
• Wage (w0) falls to w1


  Isocost curve rotates counterclockwise
• Producing the same level of output, Q0

  Firm will produce on a lower isocost line (C1) at a point B
• Slope of the new isocost line

  Represents the lower wage relative to the rental rate of capital
• Optimal Input Substitution


  • To minimize the cost of producing a given level of output, the firm should use less of an input and more of other inputs when that input's price rises
• Cost Function


  Mathematical relationship that relates cost to the cost-minimizing output associated with an isoquant
• Short-run costs


  • Fixed costs: do not change with changes in output; include the costs of fixed inputs used in production
  • Variable costs: costs that change with changes in outputs; include the costs of inputs that vary with output
• Total costs


  Sum of fixed and variable costs
• Irrelevance of Sunk Costs

  A decision maker should ignore sunk costs to maximize profits or minimize loses
• Average costs


  Average fixed cost, Average variable costs, Average total cost