Lecture 6 - Production & Cost in the Long Run What is long run Production???? What is an isoquant????

Production & Cost in the Long Run What are the characteristics of an isoquant??? Represents different combinations of K & L for producing different outputs What is Marginal Rate of Technical Substitution????

Production & Cost in the Long Run What is the relationship between MRTS & MP???? MRTS = - ΔK = MPL = w ΔL MPK r MPL = w MPK r

Production & Cost in the Long Run MPL = MPK w r Principle to produce a given level of output at the lowest cost when 2 input K & L are variable and respectively prices of the inputs w & r

Output maximization for a given level of cost Principle In the case of 2 variable inputs K & L the manager of the firm maximises output for a given number of cost by using L & K such that MRTS = w/r. Refer to graph Fig 9.5 Page 204

Optimization and Cost What is the expansion path????? Refer o fig 9.6

Optimization and Cost What is constant returns to scale??? What is increasing returns to scale??? What is decreasing returns to scale???

Long Run Costs What is LR cost or LAC???? What is LR marginal cost or LMC????

Economies of Scale The advantages of large scale production that result in lower unit (average) costs (cost per unit) AC = TC / Q Economies of scale – spreads total costs over a greater range of output

Economies of Scale Internal – advantages that arise as a result of the growth of the firm Technical Commercial Financial Managerial Risk Bearing

Economies of Scale External economies of scale – the advantages firms can gain as a result of the growth of the industry – normally associated with a particular area Supply of skilled labour Reputation Local knowledge and skills Infrastructure Training facilities

Economies of Scale Capital Land Labour Output TC AC Scale A 5 3 4 100 Scale B 10 6 8 300 Assume each unit of capital = £5, Land = £8 and Labour = £2 Calculate TC and then AC for the two different ‘scales’ (‘sizes’) of production facility What happens and why?

Economies of Scale Capital Land Labour Output TC AC Scale A 5 3 4 100 57 0.57 Scale B 10 6 8 300 164 0.54 Doubling the scale of production (a rise of 100%) has led to an increase in output of 200% - therefore cost of production PER UNIT has fallen Don’t get confused between Total Cost and Average Cost Overall ‘costs’ will rise but unit costs can fall Why?

Economies of Scale Internal: Technical Specialisation – large organisations can employ specialised labour Indivisibility of plant – machines can’t be broken down to do smaller jobs! Principle of multiples – firms using more than one machine of different capacities - more efficient Increased dimensions – bigger containers can reduce average cost

Economies of Scale Indivisibility of Plant: Not viable to produce products like oil, chemicals on small scale – need large amounts of capital Agriculture – machinery appropriate for large scale work – combines, etc.

Economies of Scale Principle of Multiples: Some production processes need more than one machine Different capacities May need more than one machine to be fully efficient

Economies of Scale Principle of Multiples: e.g. Machine A Machine B Machine C Machine D Capacity = 10 per hour Capacity = 20 per hour Capacity = 15 per hour Capacity = 30 per hour Cost = £100 per machine Cost = £50 per machine Cost = £150 per machine Cost = £200 per machine Company A = 1 of each machine, output per hour = 10 Total Cost = £500 AC = £50 per unit Company B = 6 x A, 3 x B, 4 x C, 2 x D – output per hour = 60 Total Cost = £1750 AC = £29.16 per unit The aim here is to show a simple example of how a production process involving a combination of machines operating at different capacities can have an effect on unit costs. The example could be a bottling plant with each machine doing a different task – filling the bottles, labelling, putting the tops on and packaging. Company A being small can only afford 1 of each machine, it is constrained by the capacity of the slowest machine – machine A, the rest of the machines are not being used to their full capacity and so are wasted for some of the time. They still however represent a cost to the firm but there is no return coming in. The larger company can afford to buy multiples of each machine to ensure that they are all working to full capacity, the point to stress is that the total cost rises – obviously because there are more machines – by 2.5 times compared to company A but the output rises by 5 times the output level of company A hence AC falls. The point can be made that company A is at a significant cost disadvantage and hence this could affect its pricing structure and put it at a distinct competitive disadvantage.

Economies of Scale Increased Dimensions: e.g. Transport container = Volume of 20m3 Total Cost: Construction, driver, fuel, maintenance, insurance, road tax = £600 per journey AC = £30m3 2m 2m 5m Total Cost = £1800 per journey AC = £11.25m3 The explanation that accompanies this slide is fairly straight forward – The first container has a carrying capacity of 20 cubic metres. The cost of carrying the product involves the actual construction of the container/lorry etc, the cost of the maintenance, driver etc. This is assumed to be £600 per journey and as such gives an average cost of £30 per cubic metre. Doubling the dimensions of the container increases the carrying capacity by 8 times. However, the cost of the construction, maintenance etc is not likely to rise by 8 times. The example shows cost having risen 2 times. As a result the cost per unit is now £11.25 per cubic metre! Again the point about the relative competitive advantage is worth highlighting. 4m 4m 10m Transport Container 2 = Volume 160m3

Economies of Scale Commercial Large firms can negotiate favourable prices as a result of buying in bulk Large firms may have advantages in keeping prices higher because of their market power

Economies of Scale Financial Large firms able to negotiate cheaper finance deals Large firms able to be more flexible about finance – share options, rights issues, etc. Large firms able to utilise skills of merchant banks to arrange finance

Economies of Scale Managerial Use of specialists – accountants, marketing, lawyers, production, human resources, etc.

Economies of Scale Risk Bearing Diversification Markets across regions/countries Product ranges R&D

Economies of Scale Minimum Efficient Scale – the point at which the increase in the scale of production yields no significant unit cost benefits Minimum Efficient Plant Size – the point where increasing the scale of production of an individual plant within the industry yields no significant unit cost benefits

Economies of Scale Unit Cost Scale A 82p Scale B 54p LRAC MES Output

Diseconomies of Scale The disadvantages of large scale production that can lead to increasing average costs Problems of management Maintaining effective communication Co-ordinating activities – often across the globe! De-motivation and alienation of staff Divorce of ownership and control

Long run costs What are economies of scope???

Summary In the long run inputs are variable. Isoquants show all possible combinations of labor and capital capable of producing a given level of output. Isoquants are downward sloping reflecting if larger amounts of labor are used less capital is required to produce same output.

Summary MRTS is the absolute value of the slope of an isoquant and measures the rate at which the 2 inputs can be substituted for one another while maintaining a constant level of output MRTS = - ΔK = MPL ΔL MPK

Summary Isocost curves the various combinations of inputs that maybe purchased for a given dollar output. The slope of the isocost is (-w/r) A manager minimizes the total cost of producing a given level of output by choosing an input combination at point of tangency between isocost and isocurve.

Summary Optimization condition slopes of isocosts and isoquants MPL = MPK w r The expansion path shows equilibrium input combination for every level of output.

Summary All points on the expansion path are both cost minimising and output maxising combinations of K & L LMC lies LAC over range for which LAC is decreasing and vice versa. When LAC is decreasing there is economies of scale

Summary When LAC is increasing there is diseconomies of scale LAC gives the lowest possible unit cost of producing various outputs because in the LR all outputs are variable or adjusted optimally.