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10.07 notes

Wed October 7, 2015

Fixed Costs and Market Structure: four themes

• reminder of fixed costs:

= F/Q → hyperbola, infinite at zero volume, zero at infinite

= see text for graph drawn more carefully than I can manage

• how affect number of firms?

= in industry after industry the early years see lots and lots of firms, then a weeding out

= Carroll, Glenn R., and Michael T. Hannan. 1995. Organizations in Industry: Strategy, Structure and Selection. Oxford University Press.

› See in particular Swaminathan, Anand, and Glenn R. Carroll. “Organizations in Industry: Strategy, Structure and Selection.” In op. cit., 223–43.

› A good overview is Jovanovic, Boyan. 2001. “Fitness and Age: Review of Carroll and Hannan’s Demography of Corporations and Industries.” Journal of Economic Literature 39 (March): 105–19.

= so is this economies of scale? yes, but that’s closer to a tautology than an explanation

• size distribution of firms

= many industries are comprised of a mix of large, medium and small firms

› same “power law” distribution found again and again: the proportion of large, medium and small firms follows a (negative) exponential pattern, cut size by 40% and the number of players of that size increases by the same proportion

› such power laws are widely observed, from the biology of food chains to the size of cities: the US can only support one “New York” and a couple “Los Angeles – Chicago” and … whereas China can perhaps support three such “megacities” and many more very large cities.

= how to explain?

› standard “core” good and differentiated goods?

› technology: variations let firms to produce at similar costs without being able to scale up/down?

› history matters: economies of scale are insufficiently strong that a stroke of good luck, especially early in an industry’s history, can leave a firm permanently larger. combine with the Carroll and Hannan demography story and in the initial years of many players, a few will be exceptionally lucky. but as numbers shrink and experience accumulates, there’s a regression towards the mean in growth rates

– so if it’s purely luck (with declining variance over time) then we should also see relative stability in who’s on top, but more volatility among the fringe firms in an industry

• numbers of firms

= our symmetric oligopoly profit formula lets us crank out an answer where F is fixed costs and (look at our standard demand curve formula) S size is 1/b. then we get:

› n = (a-c)√S/F – 1.

– if fixed costs are too high or size S too small we get zero firms

– if marginal costs are really low we get more firms

– it’s non-linear: if the market doubles, we get 1.4 → 40% more firms (if a market increases 50% then we get 20% more). all holding fixed costs constant. [so in the auto industry, with the rise of China and Brazil and India and so on … 50% growth! … have fixed costs risen? marginal costs? or is there now room for another global players and a proportional number of superluxury makers?]

• monopoly: what to do if the optimal number of firms n = 1?

= one answer: government Public Service Authorities that run water and sewage systems, and roads and … but roads are different, the optimal price is zero.

= analytically, these industries have very low marginal costs relative to fixed costs

› graphically, that means MC lies below AC

– setting MC = MR gives very high prices (such that some people choose not to have running water!)

– setting p = MC leaves p < AC so requires subsidies … not common in the US though we are seeing up-front money to lay fiber optic cables

– instead set p = AC at D. zero profit condition. in practice means being able to monitor the cost base

› for water treatment plants and water pipes is not so hard as they’re very standard with stable technology

› electricity is harder, as there’s been both technical change and volatility in the costs of fuel, and costs that vary with topography and density and access to ports and whether they have nuclear power or old, depreciated plants or … large power utilities also have complex management structures, especially if they are allowed to integrate into upstream / downstream / horizontal industries [which in turn muddies their cost base … so regulators try to prevent]

› hence these details mean a cost base-plus formula invites playing games, with ebb and flow as new opportunities arise and as the politics shift

• Next: dynamics of firm numbers

• Blog topics?! – list