Cost Curves. Molly W. Dahl Georgetown University Econ 101 Spring 2009

Transcription

1 Cost Curves Moll W. Dahl Georgetown Universit Econ 101 Spring

2 Tpes of Cost Curves Total Cost Curve: graph of a firm s total cost function. Variable Cost Curve: graph of a firm s variable cost function. Average Total Cost Curve: graph of a firm s average total cost function. 2

3 Tpes of Cost Curves Average Variable Cost Curve: graph of a firm s average variable cost function. Average Fixed Cost Curve: graph of a firm s average fixed cost function. Marginal Cost Curve: graph of a firm s marginal cost function. 3

4 Tpes of Cost Curves How are these cost curves related to each other? How are a firm s long-run and short-run cost curves related? 4

5 Fixed, Variable & Total Cost Functions Fixed Costs: F = c(0) Total cost to a firm of its fixed inputs. Does not var with the firm s output level. Variable Costs: c v () = c() F Total cost to a firm of its variable inputs when producing output units. Total Costs: c() = c v () + F Total cost of all inputs, fixed and variable, when producing output units. 5

6 $ c() c ( ) = F+ c ( ) v c v () F F 6

7 AFC, AVC & ATC Curves The firm s total cost function is c ( ) = F+ cv ( ). For > 0, the firm s average total cost function is F cv ( ) AC( ) = + = AFC( ) + AVC( ). 7

8 AFC, AVC & ATC Curves What does an average fixed cost curve look like? AFC( ) = AFC() is a rectangular hperbola so its graph looks like... F 8

9 $/output unit AFC() 0 as AFC() 0 9

10 AFC, AVC & ATC Curves In a short-run with a fixed amount of at least one input, the Law of Diminishing (Marginal) Returns must appl, causing the firm s average variable cost of production to increase eventuall. 10

11 $/output unit AVC() 0 11

12 $/output unit AVC() AFC() 0 12

13 AFC, AVC & ATC Curves And ATC() = AFC() + AVC() 13

14 $/output unit ATC() = AFC() + AVC() ATC() AVC() AFC() 0 14

15 $/output unit AFC() = ATC() - AVC() ATC() AFC AVC() AFC() 0 15

16 $/output unit Since AFC() 0 as, ATC() AVC() as. ATC() AFC AVC() AFC() 0 16

17 $/output unit Since AFC() 0 as, ATC() AVC() as. And since short-run AVC() must eventuall increase, ATC() must eventuall increase in a short-run. ATC() AVC() AFC() 0 17

18 Marginal Cost Function Marginal cost is the rate-of-change of variable production cost as the output level changes. That is, cv MC( ) = ( ). 18

19 Marginal Cost Function The firm s total cost function is c ( ) = F+ cv ( ) and the fixed cost F does not change with the output level, so cv c MC( ) = ( ) = ( ). MC is the slope of both the variable cost and the total cost functions. 19

20 Marginal & Average Cost Functions How is marginal cost related to average variable cost? 20

21 $/output unit MC() AVC() 21

22 $/output unit AVC( ) MC( ) < AVC( ) < 0 MC() AVC() 22

23 $/output unit AVC( ) MC( ) > AVC( ) > 0 MC() AVC() 23

24 $/output unit AVC( ) MC( ) = AVC( ) = 0 MC() AVC() 24

25 $/output unit AVC( ) MC( ) = AVC( ) = 0 The short-run MC curve intersects the short-run AVC curve from below at the AVC curve s minimum. MC() AVC() 25

26 Marginal & Average Cost Functions How is marginal cost related to average total cost? 26

27 $/output unit ATC( ) > = 0 < as > MC( ) = ATC( ) < MC() ATC() 27

28 Marginal & Average Cost Functions The short-run MC curve intersects the short-run AVC curve from below at the AVC curve s minimum. And, similarl, the short-run MC curve intersects the short-run ATC curve from below at the ATC curve s minimum. 28

29 $/output unit MC() ATC() AVC() 29

30 Short-Run & Long-Run TC Curves A firm has a different short-run total cost curve for each possible short-run circumstance. Suppose the firm can be in one of just three short-runs; x 2 = x 2 or x 2 = x 2 x 2 < x 2 < x 2. or x 2 = x 2. 30

31 $ F = w 2 x 2 F = w 2 x 2 F = w 2 x 2 c s (;x 2 ) c s (;x 2 ) F F F 0 c s (;x 2 ) 31

32 Short-Run & Long-Run TC Curves The firm has three short-run total cost curves. In the long-run the firm is free to choose amongst these three since it is free to select x 2 equal to an of x 2, x 2, or x 2. How does the firm make this choice? 32

33 $ For 0, choose x 2 = x 2. c s (;x 2 ) c s (;x 2 ) F F F 0 c s (;x 2 ) 33

34 $ For 0, choose x 2 = x 2. c s (;x 2 ) For, choose x 2 = x 2. c s (;x 2 ) F F F 0 c s (;x 2 ) 34

35 $ For 0, choose x 2 = x 2. c s (;x 2 ) For, choose x 2 = x 2. For <, choose x 2 = x 2. c s (;x 2 ) F F F 0 c s (;x 2 ) 35

36 $ For 0, choose x 2 = x 2. c s (;x 2 ) For, choose x 2 = x 2. For <, choose x 2 = x 2. c s (;x 2 ) F F F 0 c s (;x 2 ) c(), the firm s longrun total cost curve. 36

37 Short-Run & Long-Run TC Curves The firm s long-run total cost curve consists of the lowest parts of the shortrun total cost curves. The long-run total cost curve is the lower envelope of the short-run total cost curves. 37

38 Short-Run & Long-Run ATC Curves For an output level, the long-run total cost curve alwas gives the lowest possible total production cost. Therefore, the long-run av. total cost curve must alwas give the lowest possible av. total production cost. The long-run av. total cost curve must be the lower envelope of all of the firm s short-run av. total cost curves. 38

39 Short-Run & Long-Run ATC Curves E.g. suppose again that the firm can be in one of just three short-runs; x 2 = x 2 or x 2 = x 2 (x 2 < x 2 < x 2 ) or x 2 = x 2 then the firm s three short-run average total cost curves are... 39

40 $/output unit AC s (;x 2 ) AC s (;x 2 ) AC s (;x 2 ) 40

41 Short-Run & Long-Run ATC Curves The firm s long-run average total cost curve is the lower envelope of the shortrun average total cost curves... 41

42 $/output unit AC s (;x 2 ) AC s (;x 2 ) AC s (;x 2 ) The long-run av. total cost AC() curve is the lower envelope of the short-run av. total cost curves. 42