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 b 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

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

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 = 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

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 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

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

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

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

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

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 Gain of Output if increase L Along an Isoquant dQ=0 so

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

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

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

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

Units of capital (K) O Units of labour (L) TC 1 TC 4 TC Deriving a SRAC curve from an isoquant map Suppose initially at Long-Run Equilibrium at K 0 L 0 L0L0 K0K0

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

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