Upcoming SlideShare
×

# simba nyakdee nyakudanga presentation on isoquants

1,009 views

Published on

Published in: Education, News & Politics
1 Like
Statistics
Notes
• Full Name
Comment goes here.

Are you sure you want to Yes No
• Be the first to comment

Views
Total views
1,009
On SlideShare
0
From Embeds
0
Number of Embeds
2
Actions
Shares
0
80
0
Likes
1
Embeds 0
No embeds

No notes for slide

### simba nyakdee nyakudanga presentation on isoquants

1. 1. Chapter 5 The Firm And the Isoquant Map
2. 2. ISOQUANT- ISOCOST ANALYSISISOQUANT- ISOCOST ANALYSIS • Isoquant • A line indicating the level of inputs required to produce a given level of output • Iso- meaning - ‘Equal’ • -’Quant’ as in quantity • Isoquant – a line of equal quantity
3. 3. Units of K 40 20 10 6 4 Units of L 5 12 20 30 50 Point on diagram a b c d e a Units of labour (L) Unitsofcapital(K) An isoquant yielding output (TPP) of 5000 unitsAn isoquant yielding output (TPP) of 5000 units 0 5 10 15 20 25 30 35 40 45 0 5 10 15 20 25 30 35 40 45 50
4. 4. Units of K 40 20 10 6 4 Units of L 5 12 20 30 50 Point on diagram a b c d e a b Units of labour (L) Unitsofcapital(K) 0 5 10 15 20 25 30 35 40 45 0 5 10 15 20 25 30 35 40 45 50 An isoquant yielding output (TPP) of 5000 unitsAn isoquant yielding output (TPP) of 5000 units
5. 5. Units of K 40 20 10 6 4 Units of L 5 12 20 30 50 Point on diagram a b c d e a b c d e Units of labour (L) Unitsofcapital(K) 0 5 10 15 20 25 30 35 40 45 0 5 10 15 20 25 30 35 40 45 50 An isoquant yielding output (TPP) of 5000 unitsAn isoquant yielding output (TPP) of 5000 units
6. 6. ISOQUANT- ISOCOST ANALYSISISOQUANT- ISOCOST ANALYSIS • Isoquants – their shape – diminishing marginal rate of (technical) substitution – Rate at which we can substitute capital for labour and still maintain output at the given level. MRTS = ∆K / ∆L Sometimes just called Marginal rate of Substitution (MRS)
7. 7. 0 2 4 6 8 10 12 14 0 2 4 6 8 10 12 14 16 18 20 Unitsofcapital(K) Units of labour (L) g h ∆K = -2 ∆L = 1 isoquant MRTS = -2 MRTS = ∆K / ∆L Diminishing marginal rate of tech. substitutionDiminishing marginal rate of tech. substitution
8. 8. 0 2 4 6 8 10 12 14 0 2 4 6 8 10 12 14 16 18 20 Unitsofcapital(K) Units of labour (L) g h j k ∆K = -2 ∆L = 1 ∆K = -1 ∆L = 1 Diminishing marginal rate of factor substitutionDiminishing marginal rate of factor substitution isoquant MRTS = -2 MRTS = -1 MRTS = ∆K / ∆L
9. 9. 0 10 20 30 0 10 20 An isoquant mapAn isoquant mapUnitsofcapital(K) Units of labour (L) Q1=5000
10. 10. 0 10 20 30 0 10 20 Q2=7000 Unitsofcapital(K) Units of labour (L) An isoquant mapAn isoquant map Q1
11. 11. 0 10 20 30 0 10 20 Unitsofcapital(K) Units of labour (L) An isoquant mapAn isoquant map Q1 Q2 Q3
12. 12. 0 10 20 30 0 10 20 Unitsofcapital(K) Units of labour (L) An isoquant mapAn isoquant map Q1 Q2 Q3 Q4
13. 13. 0 10 20 30 0 10 20 Q1 Q2 Q3 Q4 Q5 Unitsofcapital(K) Units of labour (L) An isoquant mapAn isoquant map
14. 14. ISOQUANT- ISOCOST ANALYSISISOQUANT- ISOCOST ANALYSIS • Isoquants • E.g: Cobb-Douglas Production Function Q=K1/2 L1/2 • We now turn to an important aspect of production, namely returns to scale.
15. 15. 0 10 20 30 0 10 20 Unitsofcapital(K) Units of labour (L) Q1=5000 5 Suppose producing 5000 units with 10 units of capital and 5 units of labour What happens now if we double the amount of capital and labour?
16. 16. 0 10 20 30 0 10 20 Unitsofcapital(K) Units of labour (L) Q1=5000 5 Suppose producing 5000 units with 10 units of capital and 5 units of labour What happens now if we double the amount of capital and labour?
17. 17. 0 10 20 30 0 10 20 Unitsofcapital(K) Units of labour (L) Q1=5000 5 What is the output level at this new isoquant?
18. 18. 0 10 20 30 0 10 20 Unitsofcapital(K) Units of labour (L) Q1=5000 5 Suppose 20 K and 10 L gives 10,000 units then we say there are constant returns to scale
19. 19. 0 10 20 30 0 10 20 Unitsofcapital(K) Units of labour (L) Q1=5000 5 If Q(K,L) =5000 Then Q(2K,2L) = 2Q(K,L) =10,000 Q2=10,000 Constant Returns to ScaleConstant Returns to Scale
20. 20. • For example the Cobb-Douglas ProductionFor example the Cobb-Douglas Production Function: Q(K,L)=Function: Q(K,L)= K1/2 L1/2 Q(2K,2L)= (2Q(2K,2L)= (2K)1/2 (2L)1/2 =2=2 K1/2 L1/2 =2Q(K,L)Q(K,L) A function such that Q(aK,aL)=aQ(K,L) for allA function such that Q(aK,aL)=aQ(K,L) for all a>0 (or a=0), is said to be HOMOGENOUSa>0 (or a=0), is said to be HOMOGENOUS OF DEGREE 1 (sometimes: LINEAROF DEGREE 1 (sometimes: LINEAR HOMOGENOUS)HOMOGENOUS) ≥
21. 21. 0 10 20 30 0 10 20 Unitsofcapital(K) Units of labour (L) Q1=5000 5 If Q(K,L) =5000 and Q(2K,2L)=15,000 >2Q(K,L)=10000 Then there is IRS Q2=15,000 Increasing returns to scale, IRS
22. 22. 0 10 20 30 0 10 20 Unitsofcapital(K) Units of labour (L) Q1=5000 5 Increasing returns to scale: “Isoquants get closer together” Q2=15,000 Q2=10,000
23. 23. 0 10 20 30 0 10 20 Unitsofcapital(K) Units of labour (L) Q1=5000 5 If Q(K,L) =5000 and Q(2K,2L)=7,000 < 2Q(K,L)=10000 Q2=7,000 Decreasing returns to scale, DRS
24. 24. 0 10 20 30 0 10 20 Unitsofcapital(K) Units of labour (L) Q1=5000 5 Q2=7,000 Q2=10,000 Decreasing returns to scale: “Isoquants get further apart”
25. 25. 0 10 20 30 0 10 20 Unitsofcapital(K) Units of labour (L) Q1=5000 5 Q2=7,000 Q2=10,000 If Decreasing returns to scale: “Isoquants get further apart”
26. 26. ISOQUANT- ISOCOST ANALYSISISOQUANT- ISOCOST ANALYSIS • Isoquants – isoquants and marginal returns: The Marginal Return measures the change in output when one variable is changed and the other is kept fixed. – To see this, suppose we examine the CRS diagram again, this time with 3 isoquants, – 5000, 10,000, and 15,000
27. 27. 0 10 20 30 0 10 20 Unitsofcapital(K) Units of labour (L) Q1=5000 5 15 Q2=10,000 Q3=15000
28. 28. ISOQUANT- ISOCOST ANALYSISISOQUANT- ISOCOST ANALYSIS • Next, holding capital constant at K=20 we examine the different amounts of labour required to produce • 5000, 10,000, and 15,000 units of output
29. 29. 0 10 20 30 0 10 20 Unitsofcapital(K) Units of labour (L) Q1=5000 5 15 Q1=10,000 Q3=15000 232
30. 30. 0 10 20 30 0 10 20 Unitsofcapital(K) Units of labour (L) Q1=5000 5 15 Q1=10,000 Q3=15000 With K Constant, Q1 to Q2 requires 8 L 232
31. 31. 0 10 20 30 0 10 20 Unitsofcapital(K) Units of labour (L) Q1=5000 5 15 Q1=10,000 Q3=15000 With K Constant, Q1 to Q2 requires 8 L With K Constant, Q2 to Q3 requires 13 L 2 23
32. 32. ISOQUANT- ISOCOST ANALYSISISOQUANT- ISOCOST ANALYSIS • So 5000 to 10,000 requires 8 extra L • 10,000 to 15,000 requires 13 extra L
33. 33. 0 10 20 30 0 10 20 Unitsofcapital(K) Units of labour (L) Q1=5000 5 15 Q1=10,000 Q3=15000 <- 8 L -> <- 13 L -> 2 23 What principle is this?
34. 34. ISOQUANT- ISOCOST ANALYSISISOQUANT- ISOCOST ANALYSIS • So 5000 to 10,000 requires 8 extra L • 10,000 to 15,000 requires 13 extra L • What principle is this? •Principle of Diminishing MARGINAL returns •Note: So CRS and diminishing marginal returns go well together
35. 35. ISOQUANT- ISOCOST ANALYSISISOQUANT- ISOCOST ANALYSIS • Isoquants – their shape – diminishing marginal rate of substitution – isoquants and returns to scale – isoquants and marginal returns
36. 36. ISOQUANT- ISOCOST ANALYSISISOQUANT- ISOCOST ANALYSIS • We now add the firms’ costs to the analysis ! • Suppose bank or venture Capitalist will only lend you £300,000 • How much capital and labour can you buy / hire? • ISOCOST- Line of indicating set of inputs with ‘equal’ Cost
37. 37. 0 5 10 15 20 25 30 0 5 10 15 20 25 30 35 40 An isocostAn isocost Units of labour (L) Unitsofcapital(K) Assumptions PK = £20 000 W = £10 000 TC = £300 000 a
38. 38. 0 5 10 15 20 25 30 0 5 10 15 20 25 30 35 40 Units of labour (L) Unitsofcapital(K) a b Assumptions PK = £20 000 W = £10 000 TC = £300 000 An isocostAn isocost
39. 39. 0 5 10 15 20 25 30 0 5 10 15 20 25 30 35 40 Units of labour (L) Unitsofcapital(K) a b c Assumptions PK = £20 000 W = £10 000 TC = £300 000 An isocostAn isocost
40. 40. 0 5 10 15 20 25 30 0 5 10 15 20 25 30 35 40 Units of labour (L) Unitsofcapital(K) TC = £300 000 a b c d Assumptions PK = £20 000 W = £10 000 TC = £300 000 An isocostAn isocost TC = WL + PKK
41. 41. 0 5 10 15 20 25 30 0 5 10 15 20 25 30 35 40 45 50 55 60 Units of labour (L) Unitsofcapital(K) Assumptions PK = £20 000 W = £5,000 TC = £300 000 Suppose Price of Labour (wages) fallsSuppose Price of Labour (wages) falls TC = £300 000 Slope of Line = -W/PK
42. 42. 0 5 10 15 20 25 30 0 5 10 15 20 25 30 35 40 45 50 55 60 Units of labour (L) Unitsofcapital(K) TC = £500 000 Assumptions PK = £20 000 W = £10 000 TC = £500 000 Suppose Bank increases Finance to £500,000Suppose Bank increases Finance to £500,000 TC = £300 000
43. 43. NOTE!NOTE! ISOQUANT and ISOCOST CURVES hopefullyISOQUANT and ISOCOST CURVES hopefully remind you a lot about INDIFFERENCEremind you a lot about INDIFFERENCE CURVES and BUDGET LINES...CURVES and BUDGET LINES...
44. 44. Efficient production:Efficient production: • Two types of problems: • 1. Least-cost-combination of factors for a given output level
45. 45. 0 5 10 15 20 25 30 35 0 10 20 30 40 50 Finding the least-cost method of productionFinding the least-cost method of production Units of labour (L) Unitsofcapital(K) Assumptions PK = £20 000 W = £10 000 TC = £200 000 TC = £300 000 TC = £400 000 TC = £500 000
46. 46. 0 5 10 15 20 25 30 35 0 10 20 30 40 50 Units of labour (L) Unitsofcapital(K) Finding the least-cost method of productionFinding the least-cost method of production Target Level = TPPTarget Level = TPP11
47. 47. 0 5 10 15 20 25 30 35 0 10 20 30 40 50 Units of labour (L) Unitsofcapital(K) Finding the least-cost method of productionFinding the least-cost method of production Target Level = TPPTarget Level = TPP11 TPP1
48. 48. 0 5 10 15 20 25 30 35 0 10 20 30 40 50 Units of labour (L) Unitsofcapital(K) Finding the least-cost method of productionFinding the least-cost method of production TC = £400 000 r TPP1
49. 49. 0 5 10 15 20 25 30 35 0 10 20 30 40 50 Units of labour (L) Unitsofcapital(K) Finding the least-cost method of productionFinding the least-cost method of production TC = £400 000 TC = £500 000 s r t TPP1
50. 50. ISOQUANT- ISOCOST ANALYSISISOQUANT- ISOCOST ANALYSIS • Least-cost-combination of factors for a given output level – Produce on lowest isocost line where the iosquant just touches it at a point of tangency – We’ll get back to this !
51. 51. Efficient production:Efficient production: • Effectively have two types of problem • 1. Least-cost combination of factors for a given output • 2. Highest output for given production costs • Here have Financial Constraint: E.g.: Venture Capital
52. 52. Finding the maximum output for given total costsFinding the maximum output for given total costs Q1 Q2 Q3 Q4 Q5 Unitsofcapital(K) Units of labour (L) O
53. 53. O Isocost Unitsofcapital(K) Units of labour (L) TPP1 TPP2 TPP3 TPP4 TPP5 Finding the maximum output for given total costsFinding the maximum output for given total costs
54. 54. O r v Unitsofcapital(K) Units of labour (L) TPP1 TPP2 TPP3 TPP4 TPP5 Finding the maximum output for given total costsFinding the maximum output for given total costs
55. 55. O s u Unitsofcapital(K) Units of labour (L) TPP1 TPP2 TPP3 TPP4 TPP5 r v Finding the maximum output for given total costsFinding the maximum output for given total costs
56. 56. O t Unitsofcapital(K) Units of labour (L) TPP1 TPP2 TPP3 TPP4 TPP5 r v s u Finding the maximum output for given total costsFinding the maximum output for given total costs
57. 57. O K1 L1 Unitsofcapital(K) Units of labour (L) TPP1 TPP2 TPP3 TPP4 TPP5 r v s u t Finding the maximum output for given total costsFinding the maximum output for given total costs
58. 58. Efficient production:Efficient production: • 1. Least-cost combination of factors for a given output • 2. Highest output for a given cost of production • Comparison with Marginal Product Approach
59. 59. 0 2 4 6 8 10 12 14 0 2 4 6 8 10 12 14 16 18 20 22 Unitsofcapital(K) Units of labour (L) isoquant MRS = dK / dL RecallRecall MRTS = dK / dL Loss of Output if reduce K =-MPPKdK Gain of Output if increase L =MPPLdL Along an Isoquant dQ=0 so -MPPKdK =MPPLdL
60. 60. 0 2 4 6 8 10 12 14 0 2 4 6 8 10 12 14 16 18 20 22 Unitsofcapital(K) Units of labour (L) isoquant MRTS = dK / dL RecallRecall MRTS = dK / dL Along an Isoquant dQ=0 so -MPPKdK =MPPLdL K L MPP MPP dL dK −=
61. 61. 0 2 4 6 8 10 12 14 0 2 4 6 8 10 12 14 16 18 20 22 Unitsofcapital(K) Units of labour (L) isoquant MRTS = dK / dL RecallRecall MRTS = dK / dL Along an Isoquant dQ=0 so -MPPKdK =MPPLdL K L MPP MPP dL dK MRTS −==
62. 62. 0 5 10 15 20 25 30 0 5 10 15 20 25 30 35 40 Units of labour (L) Unitsofcapital(K) What about the slope of an isocost line?What about the slope of an isocost line? Reduction in cost if reduce K = - PKdK Rise in cost if increase L = PLdL Along an isocost line -PKdK = PLdL
63. 63. 0 5 10 15 20 25 30 0 5 10 15 20 25 30 35 40 Units of labour (L) Unitsofcapital(K) What about the slope of an isocost line?What about the slope of an isocost line? Along an isocost line -PKdK = PL dL K L P P dL dK −=
64. 64. Unitsofcapital(K) O Units of labour (L) In equilibrium slope of Isoquant = Slope of isocostIn equilibrium slope of Isoquant = Slope of isocost 100 K L K L P P MPP MPP dL dK MRTS −=−==
65. 65. Unitsofcapital(K) O Units of labour (L) In equilibrium slope of Isoquant = Slope of isocostIn equilibrium slope of Isoquant = Slope of isocost 100 K L K L P P MPP MPP = K K L L P MPP P MPP =⇒
66. 66. • Intuition is that money spent on each factorIntuition is that money spent on each factor should, at the margin, yield the sameshould, at the margin, yield the same additional outputadditional output • Suppose notSuppose not K K L L P MPP P MPP =⇒ K K L L P MPP P MPP >⇒
67. 67. • Then extra output per £1 spent on labour greaterThen extra output per £1 spent on labour greater than extra output per £1 spent on Capitalthan extra output per £1 spent on Capital • So switch resources from Capital to LabourSo switch resources from Capital to Labour • MPPMPPLL?? – DownDown • MPPMPPKK?? – UpUp  (Principle of Diminishing Marginal Returns)(Principle of Diminishing Marginal Returns) K K L L P MPP P MPP =⇒ K K L L P MPP P MPP Suppose >
68. 68. LONG-RUN COSTSLONG-RUN COSTS • Derivation of long-run costs from an isoquant map – derivation of long-run costs
69. 69. Unitsofcapital(K) O Units of labour (L) Deriving anDeriving an LRACLRAC curve from an isoquant mapcurve from an isoquant map TC 1 100 At an output of 100 LRAC = TC1 / 100
70. 70. Unitsofcapital(K) O Units of labour (L) TC 1 100 TC 2 200 At an output of 200 LRAC = TC2 / 200 Deriving anDeriving an LRACLRAC curve from an isoquant mapcurve from an isoquant map
71. 71. Unitsofcapital(K) O Units of labour (L) TC 1 TC 2 TC 3 TC 4 TC 5 TC 6 TC 7 100 200 300 400 500 600 700 Deriving anDeriving an LRACLRAC curve from an isoquant mapcurve from an isoquant map
72. 72. Unitsofcapital(K) O Units of labour (L) TC 1 TC 2 TC 3 TC 4 TC 5 TC 6 TC 7 100 300 400 500 600 700 Deriving anDeriving an LRACLRAC curve from an isoquant mapcurve from an isoquant map Are the Isoquants getting closer or further apart here?
73. 73. Unitsofcapital(K) O Units of labour (L) TC 1 TC 2 TC 3 TC 4 TC 5 TC 6 TC 7 100 300 400 500 600 700 Deriving anDeriving an LRACLRAC curve from an isoquant mapcurve from an isoquant map Getting Closer up to 400, getting further apart after 400
74. 74. Unitsofcapital(K) O Units of labour (L) TC 1 TC 2 TC 3 TC 4 TC 5 TC 6 TC 7 100 300 400 500 600 700 Deriving anDeriving an LRACLRAC curve from an isoquant mapcurve from an isoquant map What does that mean?
75. 75. Unitsofcapital(K) O Units of labour (L) TC 1 TC 2 TC 3 TC 4 TC 5 TC 6 TC 7 100 200 300 400 500 600 700 Note: increasing returns to scale up to 400 units; decreasing returns to scale above 400 units Deriving anDeriving an LRACLRAC curve from an isoquant mapcurve from an isoquant map
76. 76. LONG-RUN COSTSLONG-RUN COSTS • Derivation of long-run costs from an isoquant map – derivation of long-run costs – the expansion path
77. 77. Unitsofcapital(K) O Units of labour (L) TC 1 TC 2 TC 3 TC 4 TC 5 TC 6 TC 7 100 200 300 400 500 600 700 Expansion path Deriving anDeriving an LRACLRAC curve from an isoquant mapcurve from an isoquant map
78. 78. 0 20 40 60 80 100 0 1 2 3 4 5 6 7 8 TC Total costs for firm in Long -RunTotal costs for firm in Long -Run MC = ∆TC / ∆Q=20/1=20 ∆Q=1 ∆TC=20
79. 79. A typical long-run average cost curveA typical long-run average cost curve OutputO Costs LRAC
80. 80. A typical long-run average cost curveA typical long-run average cost curve OutputO Costs LRACEconomies of scale Constant costs Diseconomies of scale
81. 81. A typical long-run average cost curveA typical long-run average cost curve OutputO Costs LRAC MC MC
82. 82. What about the Short-RunWhat about the Short-Run • Derivation of short-run costs from an isoquant map – Recall in SR Capital stock is fixed
83. 83. Unitsofcapital(K) O Units of labour (L) TC 1 TC 2 TC 3 TC 4 TC 5 TC 6 TC 7 100 200 300 400 500 600 700 Deriving a SDeriving a SRACRAC curve from an isoquant mapcurve from an isoquant map Suppose initially at Long-Run Equilibrium at K0L0 L0 K0 What would happen if had to produce at a different level?
84. 84. Unitsofcapital(K) O Units of labour (L) TC 1 TC 2 TC 3 TC 4 TC 5 TC 6 TC 7 100 400 700 Deriving a SDeriving a SRACRAC curve from an isoquant mapcurve from an isoquant map Suppose initially at Long-Run Equilibrium at K0L0 L0 K0 To make life simple lets just focus on two isoquants, 700 and 100
85. 85. Unitsofcapital(K) O Units of labour (L) TC 1 TC 2 TC 3 TC 4 TC 5 TC 6 TC 7 100 400 700 Deriving a SDeriving a SRACRAC curve from an isoquant mapcurve from an isoquant map Consider an output level such as Q=700 Hold SR capital constant at K0 L0 K0
86. 86. Unitsofcapital(K) O Units of labour (L) TC 1 TC 2 TC 3 TC 4 TC 5 TC 6 TC 7 100 400 700 Deriving a SDeriving a SRACRAC curve from an isoquant mapcurve from an isoquant map Locate the cheapest production point in SR on K0 line L0 K0 TC in SR is obviously higher than LR
87. 87. Unitsofcapital(K) O Units of labour (L) TC 1 TC 2 TC 3 TC 4 TC 5 TC 6 TC 7 100 400 700 Deriving a SDeriving a SRACRAC curve from an isoquant mapcurve from an isoquant map Similarly, consider an output level such as Q=100 L0 K0 Again TC in SR is obviously higher than LR
88. 88. 0 20 40 60 80 100 0 1 2 3 4 5 6 7 8 LRTC Total costs for firm in the Short and Long -RunTotal costs for firm in the Short and Long -Run SRTC
89. 89. What about the Short-RunWhat about the Short-Run • Derivation of short-run costs from an isoquant map – Recall in SR Capital stock is fixed • In SR TC is always higher than LR • ….and Average costs?
90. 90. A typical short-run average cost curveA typical short-run average cost curve OutputO Costs LRACSRAC