Chapter 21: Cost Minimisation

COST MINIMISATION

  • If a firm is not minimising costs, it is not maximising profit

Formula: see formula page

  • the solution to the cost minimising problem (the min costs to produce the desired level of output) will depend on the cost function c(w1,w2,y), which measures the minimal costs of producing y units of output when the factor prices are w1 & w2

CONDITIONAL FACTOR DEMAND FUNCTION

ISOCOST LINES

  • Lines which show all combinations of inputs that have some level of cost, C
  • C = w1x1 + w2x2
  • When we change level of C (cost) we get a family of isocost lines
    .
  • Every point on the isocost line has the same cost & Higher isocost lines have higher costs
  • The higher the C, the higher the isocost line

TANGENCY CONDITION

  • Point of tangency on isocost line is the optimal choice isoquant, where costs are minimised
  • "Point where you can use the isocost line to produce 'isoquant formula' of output"
  • The choices of inputs that yield minimal costs for the firm will in general depend on the input prices and the level of output the firm wants to produce. This is called the conditional factor demand function or derived factor demand: π‘₯1 (𝑀1,𝑀2,𝑦) and π‘₯2 (𝑀1,𝑀2,𝑦).
    .
  • Separates optimal level of output from cost effective method of production

COSTS

SHORT RUN

LONG RUN

  • Remember short run is period where one factor of production must be fixed
  • Short run cost function is the minimum cost to produce a given level of output, only adjusting the variable factors of production
  • period where all factors of production can be changed
  • Long run cost function is the minimum cost of producing a given level of output

see formula page for calc!

RELATIONSHIP BETWEEN SHORT RUN & LONG RUN COST FUNCTIONS

  • The minimum costs when all factors are variable is the minimum cost when factor 2 is fixed at the minimised long run cost level
    .
  • The cost minimising amount of the variable factor in the long run is the amount the firm would choose in the short run
    see slide 11 and formula page

RETURNS TO SCALE

see slide 12

COSTS

FIXED COSTS

  • costs associated with fixed factors (independent of output) and must be paid regardless of whether there is output or not. (e.g office rent)

QUASI FIXED COSTS

  • costs also independent of output but only need to be paid if the firm produces a positive amount of output (e.g electricity usage per unit produced)


  • there are no fixed costs in the long run but there can be quasi fixed costs in the long run

  • if it is necessary to spend a fixed amount of money before you can produce any output then quasi costs are present

SUNK COSTS

  • costs that are not recoverable
  • e.g when you paint your office building, your sunk cost is the paint as you can't get it back