Chapter 5 The Firm And the Isoquant Map Chapter 5 The Firm And the Isoquant Map

ISOQUANT- ISOCOST ANALYSIS Isoquant A line indicating the level of inputs required to produce a given level of output Iso- meaning - ‘Equal’ – –As in ‘Iso’-bars -’Quant’ as in quantity Isoquant – a line of equal quantity Isoquant A line indicating the level of inputs required to produce a given level of output Iso- meaning - ‘Equal’ – –As in ‘Iso’-bars -’Quant’ as in quantity Isoquant – a line of equal quantity

Units of K Units of L Point on diagram a b c d e a Units of labour (L) Units of capital (K) An isoquant yielding output (TPP) of 5000 units

Units of K Units of L Point on diagram a b c d e a b Units of labour (L) Units of capital (K) An isoquant yielding output (TPP) of 5000 units

Units of K Units of L Point on diagram a b c d e a b c d e Units of labour (L) Units of capital (K) An isoquant yielding output (TPP) of 5000 units

ISOQUANT- ISOCOST ANALYSIS Isoquants – –their shape – –diminishing marginal rate of substitution – –Rate at which we can substitute capital for labour and still maintain output at the given level. Isoquants – –their shape – –diminishing marginal rate of substitution – –Rate at which we can substitute capital for labour and still maintain output at the given level. MRS =  K /  L Sometimes called Marginal rate of Technical Substitution MRTS =  K /  L

Units of capital (K) Units of labour (L) g h  K = 2  L = 1 isoquant MRS = 2 MRS =  K /  L Diminishing marginal rate of factor substitution

Units of capital (K) Units of labour (L) g h j k  K = 2  L = 1  K = 1  L = 1 Diminishing marginal rate of factor substitution isoquant MRS = 2 MRS = 1 MRS =  K /  L

ISOQUANT- ISOCOST ANALYSIS Isoquants – –their shape – –diminishing marginal rate of substitution – –an isoquant map Isoquants – –their shape – –diminishing marginal rate of substitution – –an isoquant map

An isoquant map Units of capital (K) Units of labour (L) Q 1 =5000

Q 2 =7000 Units of capital (K) Units of labour (L) An isoquant map Q1Q1

Units of capital (K) Units of labour (L) An isoquant map Q1Q1 Q2Q2 Q3Q3

Units of capital (K) Units of labour (L) An isoquant map Q1Q1 Q2Q2 Q3Q3 Q4Q4

Q1Q1 Q2Q2 Q3Q3 Q4Q4 Q5Q5 Units of capital (K) Units of labour (L) An isoquant map

ISOQUANT- ISOCOST ANALYSIS Isoquants E.g: Cobb-Douglas Production Function Q=K 1/2 L 1/2 Next topic: – –isoquants and returns to scale Isoquants E.g: Cobb-Douglas Production Function Q=K 1/2 L 1/2 Next topic: – –isoquants and returns to scale

Units of capital (K) Units of labour (L) Q 1 = 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?

Units of capital (K) Units of labour (L) Q 1 = 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?

Units of capital (K) Units of labour (L) Q 1 = What is the value of this new isoquant?

Units of capital (K) Units of labour (L) Q 1 = Suppose 20 K and 10 L gives 10,000 units then we say there are constant returns to scale

Units of capital (K) Units of labour (L) Q 1 = If Q(K,L) =5000 Then Q(2K,2L) = 2Q(K,L) =10,000 Q 2 =10,000 Constant Returns to Scale

Units of capital (K) Units of labour (L) Q 1 = If Q(K,L) =5000 Then IRS =>Q(2K,2L)=15,000 > 2Q(K,L) Q 2 =15,000 If Increasing returns to scale, IRS

Units of capital (K) Units of labour (L) Q 1 = So Increasing returns to scale, IRS=> Isoquants get closer together. Q 2 =15,000 Q 2 =10,000

Units of capital (K) Units of labour (L) Q 1 = If Q(K,L) =5000 Then DRS=> Q(2K,2L)=7,000 < 2Q(K,L) Q 2 =7,000 If Decreasing returns to scale, DRS

Units of capital (K) Units of labour (L) Q 1 = Q 2 =7,000 Q 2 =10,000 If Decreasing returns to scale=>Isoquants further apart

Units of capital (K) Units of labour (L) Q 1 = Q 2 =7,000 Q 2 =10,000 If Decreasing returns to scale=>Isoquants further apart

ISOQUANT- ISOCOST ANALYSIS Isoquants – –their shape – –diminishing marginal rate of substitution – –isoquants and returns to scale – –isoquants and marginal returns Isoquants – –their shape – –diminishing marginal rate of substitution – –isoquants and returns to scale – –isoquants and marginal returns

ISOQUANT- ISOCOST ANALYSIS Isoquants – –isoquants and marginal returns: – –Marginal Returns means changing one variable and keeping the other constant. – –To see this, suppose we examine the CRS diagram again, this time with 3 isoquants, – –5000, 10,000, and 15,000 Isoquants – –isoquants and marginal returns: – –Marginal Returns means changing one variable and keeping the other constant. – –To see this, suppose we examine the CRS diagram again, this time with 3 isoquants, – –5000, 10,000, and 15,000

Units of capital (K) Units of labour (L) Q 1 = Q 2 =10,000 Q 3 =15000

ISOQUANT- 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 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

Units of capital (K) Units of labour (L) Q 1 = Q 1 =10,000 Q 3 =

Units of capital (K) Units of labour (L) Q 1 = Q 1 =10,000 Q 3 =15000 With K Constant, Q 1 to Q 2 requires 8 L 23 2

Units of capital (K) Units of labour (L) Q 1 = Q 1 =10,000 Q 3 =15000 With K Constant, Q 1 to Q 2 requires 8 L With K Constant, Q 2 to Q 3 requires 13 L 2 23

ISOQUANT- ISOCOST ANALYSIS So 5000 to 10,000 requires 8 extra L 10,000 to 15,000 requires 13 extra L So 5000 to 10,000 requires 8 extra L 10,000 to 15,000 requires 13 extra L

Units of capital (K) Units of labour (L) Q 1 = Q 1 =10,000 Q 3 = What principle is this?

ISOQUANT- ISOCOST ANALYSIS So 5000 to 10,000 requires 8 extra L 10,000 to 15,000 requires 13 extra L What principle is this? 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 can have CRS and diminishing marginal returns

ISOQUANT- ISOCOST ANALYSIS Isoquants – –their shape – –diminishing marginal rate of substitution – –isoquants and returns to scale – –isoquants and marginal returns Isocosts Isoquants – –their shape – –diminishing marginal rate of substitution – –isoquants and returns to scale – –isoquants and marginal returns Isocosts

ISOQUANT- ISOCOST ANALYSIS Isoquants – –their shape – –diminishing marginal rate of substitution – –isoquants and returns to scale – –isoquants and marginal returns Isoquants- focussing on issue of efficient way to produce – –E.g. Supply Tesco’s with Yogurt Isoquants – –their shape – –diminishing marginal rate of substitution – –isoquants and returns to scale – –isoquants and marginal returns Isoquants- focussing on issue of efficient way to produce – –E.g. Supply Tesco’s with Yogurt

ISOQUANT- ISOCOST ANALYSIS Other focus might be on Costs: Suppose bank or venture Capitalist will only lend you £300,000 What capital and labour will that buy you? ISOCOST- Line of indicating set of inputs that give ‘equal’ Cost Other focus might be on Costs: Suppose bank or venture Capitalist will only lend you £300,000 What capital and labour will that buy you? ISOCOST- Line of indicating set of inputs that give ‘equal’ Cost

An isocost Units of labour (L) Units of capital (K) Assumptions P K = £ W = £ TC = £ a

Units of labour (L) Units of capital (K) a b Assumptions P K = £ W = £ TC = £ An isocost

Units of labour (L) Units of capital (K) a b c Assumptions P K = £ W = £ TC = £ An isocost

Units of labour (L) Units of capital (K) TC = £ a b c d Assumptions P K = £ W = £ TC = £ An isocost TC = WL + P K K

ISOQUANT- ISOCOST ANALYSIS Isoquants – –their shape – –diminishing marginal rate of substitution – –isoquants and returns to scale – –isoquants and marginal returns Isocosts – –slope and position of the isocost – –shifts in the isocost Isoquants – –their shape – –diminishing marginal rate of substitution – –isoquants and returns to scale – –isoquants and marginal returns Isocosts – –slope and position of the isocost – –shifts in the isocost

Units of labour (L) Units of capital (K) Assumptions P K = £ W = £5,000 TC = £ Suppose Price of Labour (wages) fell TC = £ Slope of Line = -W/P K

Units of labour (L) Units of capital (K) TC = £ Assumptions P K = £ W = £ TC = £ Suppose Bank increases Finance to £500,000 TC = £

Efficient production: Effectively have two types of problem 1.Least-cost combination of factors for a given output E.g: The supplying Tesco’s problem Effectively have two types of problem 1.Least-cost combination of factors for a given output E.g: The supplying Tesco’s problem

Finding the least-cost method of production Units of labour (L) Units of capital (K) Assumptions P K = £ W = £ TC = £ TC = £ TC = £ TC = £

Units of labour (L) Units of capital (K) Finding the least-cost method of production Target Level = TPP 1

Units of labour (L) Units of capital (K) Finding the least-cost method of production Target Level = TPP 1 TPP 1

Units of labour (L) Units of capital (K) Finding the least-cost method of production TC = £ r TPP 1

Units of labour (L) Units of capital (K) Finding the least-cost method of production TC = £ TC = £ s r t TPP 1

ISOQUANT- ISOCOST ANALYSIS Least-cost combination of factors for a given output – –Produce on lowest isocost line where the iosquant just touches it at a point of tangency Least-cost combination of factors for a given output – –Produce on lowest isocost line where the iosquant just touches it at a point of tangency

ISOQUANT- ISOCOST ANALYSIS Least-cost combination of factors for a given output – –point of tangency – –comparison with marginal productivity approach Marginal Productivity Approach Least-cost combination of factors for a given output – –point of tangency – –comparison with marginal productivity approach Marginal Productivity Approach

Efficient production: Effectively have two types of problem 1.Least-cost combination of factors for a given output 2.Highest output for a given cost of production.Here have Financial Constraint:.E.g.: Venture Capital Effectively have two types of problem 1.Least-cost combination of factors for a given output 2.Highest output for a given cost of production.Here have Financial Constraint:.E.g.: Venture Capital

Finding the maximum output for a given total cost Q1Q1 Q2Q2 Q3Q3 Q4Q4 Q5Q5 Units of capital (K) Units of labour (L) O

O Isocost Units of capital (K) Units of labour (L) TPP 1 TPP 2 TPP 3 TPP 4 TPP 5 Finding the maximum output for a given total cost

O r v Units of capital (K) Units of labour (L) TPP 1 TPP 2 TPP 3 TPP 4 TPP 5 Finding the maximum output for a given total cost

O s u Units of capital (K) Units of labour (L) TPP 1 TPP 2 TPP 3 TPP 4 TPP 5 r v Finding the maximum output for a given total cost

O t Units of capital (K) Units of labour (L) TPP 1 TPP 2 TPP 3 TPP 4 TPP 5 r v s u Finding the maximum output for a given total cost

O K1K1 L1L1 Units of capital (K) Units of labour (L) TPP 1 TPP 2 TPP 3 TPP 4 TPP 5 r v s u t Finding the maximum output for a given total cost

Efficient production: Effectively have two types of problem 1.Least-cost combination of factors for a given output 2.Highest output for a given cost of production Comparison with Marginal Product Approach Effectively have two types of problem 1.Least-cost combination of factors for a given output 2.Highest output for a given cost of production Comparison with Marginal Product Approach

Units of capital (K) Units of labour (L) isoquant MRS = dK / dL Recall Recall MRTS = dK / dL Loss of Output if reduce K =-MPP K dK Gain of Output if increase L =MPP L dL Along an Isoquant dQ=0 so -MPP K dK =MPP L dL

Units of capital (K) Units of labour (L) isoquant MRTS = dK / dL Recall Recall MRTS = dK / dL Along an Isoquant dQ=0 so -MPP K dK =MPP L dL

Units of capital (K) Units of labour (L) isoquant MRTS = dK / dL Recall Recall MRTS = dK / dL Along an Isoquant dQ=0 so -MPP K dK =MPP L dL

Units of labour (L) Units of capital (K) What about the slope of an isocost line? Reduction in cost if reduce K = - P K dK Rise in cost if increase L = P L dL Along an isocost line P K dK = P L dL

Units of labour (L) Units of capital (K) What about the slope of an isocost line? Along an isocost line P K dK = wdL

Units of capital (K) O Units of labour (L) In equilibrium slope of Isoquant = Slope of isocost 100

Units of capital (K) O Units of labour (L) In equilibrium slope of Isoquant = Slope of isocost 100

Intuition is that money spent on each factor should, at the margin, yield the same additional outputIntuition is that money spent on each factor should, at the margin, yield the same additional output Suppose notSuppose not

Then extra output per £1 spent on labour greater than extra output per £1 spent on CapitalThen extra output per £1 spent on labour greater than extra output per £1 spent on Capital So switch resources from Capital to LabourSo switch resources from Capital to Labour MPP L ?MPP L ? –Down MPP K ?MPP K ? –Up  (Principle of Diminishing Marginal Returns)

LONG-RUN COSTS Derivation of long-run costs from an isoquant map – –derivation of long-run costs Derivation of long-run costs from an isoquant map – –derivation of long-run costs

Units of capital (K) O Units of labour (L) Deriving an LRAC curve from an isoquant map TC At an output of 100 LRAC = TC 1 / 100

Units of capital (K) O Units of labour (L) TC TC At an output of 200 LRAC = TC 2 / 200 Deriving an LRAC curve from an isoquant map

Units of capital (K) O Units of labour (L) TC 1 TC 2 TC 3 TC 4 TC 5 TC 6 TC Deriving an LRAC curve from an isoquant map

Units of capital (K) O Units of labour (L) TC 1 TC 2 TC 3 TC 4 TC 5 TC 6 TC Deriving an LRAC curve from an isoquant map Are the Isoquants getting closer or further apart here?

Units of capital (K) O Units of labour (L) TC 1 TC 2 TC 3 TC 4 TC 5 TC 6 TC Deriving an LRAC curve from an isoquant map Getting Closer up to 400, getting further apart after 400

Units of capital (K) O Units of labour (L) TC 1 TC 2 TC 3 TC 4 TC 5 TC 6 TC Deriving an LRAC curve from an isoquant map What does that mean?

Units of capital (K) O Units of labour (L) TC 1 TC 2 TC 3 TC 4 TC 5 TC 6 TC Note: increasing returns to scale up to 400 units; decreasing returns to scale above 400 units Deriving an LRAC curve from an isoquant map

LONG-RUN COSTS Derivation of long-run costs from an isoquant map – –derivation of long-run costs – –the expansion path Derivation of long-run costs from an isoquant map – –derivation of long-run costs – –the expansion path

Units of capital (K) O Units of labour (L) TC 1 TC 2 TC 3 TC 4 TC 5 TC 6 TC Expansion path Deriving an LRAC curve from an isoquant map

TC Total costs for firm in Long -Run MC =  TC /  Q=20/1=20  Q=1  TC=20

A typical long-run average cost curve Output O Costs LRAC

A typical long-run average cost curve Output O Costs LRAC Economies of scale Constant costs Diseconomies of scale

A typical long-run average cost curve Output O Costs LRAC MC

What about the Short-Run Derivation of short-run costs from an isoquant map – –Recall in SR Capital stock is fixed Derivation of short-run costs from an isoquant map – –Recall in SR Capital stock is fixed

Units of capital (K) O Units of labour (L) TC 1 TC 2 TC 3 TC 4 TC 5 TC 6 TC Deriving a SRAC curve from an isoquant map Suppose initially at Long-Run Equilibrium at K 0 L 0 L0L0 K0K0 What would happen if had to produce at a different level?

Units of capital (K) O Units of labour (L) TC 1 TC 2 TC 3 TC 4 TC 5 TC 6 TC Deriving a SRAC curve from an isoquant map Suppose initially at Long-Run Equilibrium at K 0 L 0 L0L0 K0K0 To make life simple lets just focus on two isoquants, 700 and 100

Units of capital (K) O Units of labour (L) TC 1 TC 2 TC 3 TC 4 TC 5 TC 6 TC Deriving a SRAC curve from an isoquant map Consider an output level such as Q=700 Hold SR capital constant at K 0 L0L0 K0K0

Units of capital (K) O Units of labour (L) TC 1 TC 2 TC 3 TC 4 TC 5 TC 6 TC Deriving a SRAC curve from an isoquant map Locate the cheapest production point in SR on K 0 line L0L0 K0K0 TC in SR is obviously higher than LR

Units of capital (K) O Units of labour (L) TC 1 TC 2 TC 3 TC 4 TC 5 TC 6 TC Deriving a SRAC curve from an isoquant map Similarly, consider an output level such as Q=100 L0L0 K0K0 Again TC in SR is obviously higher than LR

LRTC Total costs for firm in the Short and Long -Run SRTC

What 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? 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?

A typical short-run average cost curve Output O Costs LRAC SRAC

Note this will apply even if have CRS in Long-Run Output O Costs LRAC SRAC WHY?

Output O Costs LRAC SRAC Here, L and Q are too low given K. As Q rises, we are spreading fixed cost over more output & AC goes down

Output O Costs LRAC SRAC Here, L is now being employed with fixed K and Diminishing returns to LABOUR have set in. Hence AC are rising.

Output O Costs LRAC SRAC Note motivation for shape is different from Economies of scale story in Long Run