Ramsey Prize

Ramsey prices (after Frank Plumpton Ramsey ) are in economics a form of prices for the second best solution within the framework of the regulation of a natural monopoly . The aim is to achieve economic efficiency and the best possible allocation efficiency, which is achieved with the help of surcharges on marginal cost prices.

background

Natural monopolies arise primarily when very high fixed costs , but comparatively low variable costs arise for the production or the offer of a product or a service . Thus falling average costs prevail.

One example of this is the telecommunications sector . A single large provider can work far more cost-effectively than several small providers, at least in the fixed network area. The reason for this are sunk costs , for example for buried telephone lines, which can no longer be reversed or put to another use. It is similar with the German water supply. For example, in water management, there is market failure because of the many small natural monopolies in regional markets. Consumers are limited to the infrastructure and have no option to consider alternatives.

An unregulated monopoly has strong incentives to maximize its profit by setting a monopoly price ( Cournot's point ). This monopoly price is higher than the price that would result in perfect competition (price equals marginal costs ). This is associated with a loss of welfare . This is particularly the case with natural monopolies for drinking water and electricity.

Opportunities to achieve the (welfare-optimized) first-best solution (perfect competition) would be nationalization of the company (and thus dictating the price setting) or subsidies equal to the difference between average costs and marginal costs.

However, there are objections to regulating pricing with marginal cost prices. If natural monopolies charged their marginal cost, the monopoly could be charged losses. Instead of maintaining the price at the level of marginal costs, the company would close and exit the market, since its average costs are always above the marginal costs. Of course, the state can also run the company itself. However, private owners have a constant drive to minimize costs, provided that profits can be increased from this. In contrast, failure by government managers affects customers as well as taxpayers.

Of course, the state could intervene by subsidizing the difference between the average and marginal costs. For this, the cost functions of the company would have to be known, which they are usually not. In addition, taxes would have to be levied for this, which cause their own welfare losses. Furthermore, there are no longer any incentives on the part of the monopolist to reduce costs (waste), because every success-oriented company in competitive markets strives for cost reductions through process innovations, as this increases profits. However, it is known that the monopoly does not benefit from the successes of rationalization because it is then obliged to reduce prices.

An alternative is to have a second best ( second best ) to aim and to influence the pricing of natural monopoly by government regulation. The Ramsey Prize is one such solution.

definition

In the second-best optimization, social welfare is maximized on the condition that the company is able to break even . In the single-goods case, i.e. if the company only offers a homogeneous good, the second-best solution is to equate the price with the average costs. This means that fixed and variable costs are precisely covered.

However, if the company offers several different goods (for example: local and long-distance calls), then it operates price discrimination and serves different demand groups (for example: commercial and private customers), the result of the optimization is:

${\ displaystyle {\ frac {p_ {i} -GK} {p_ {i}}} = {\ frac {k} {\ eta _ {i}}}}$

The left part of the equation stands for the mark-up on the marginal costs, from which the price results. It stands for the price of the good and the marginal costs. The right part of the equation represents the price elasticity of the demand group . The factor is the same , which results from the optimization ( Lagrange parameter ). ${\ displaystyle p_ {i}}$ ${\ displaystyle i}$ ${\ displaystyle GK}$ ${\ displaystyle \ eta _ {i}}$ ${\ displaystyle i}$ ${\ displaystyle k}$ ${\ displaystyle {\ frac {1- \ lambda} {\ lambda}} = constant}$ ${\ displaystyle \ lambda}$

The result makes it clear that the Ramsey rule only determines the price structure. The constant must be set so that the profit restriction (cost recovery) is met.

The relative addition to the marginal costs is therefore inversely proportional to the price elasticity. Accordingly, those who are worst able to evade (forego or substitute ) pay the highest prices. This process is also known as cross-subsidization - relatively higher prices are charged for the less price-elastic good ( <1) than for the more price-elastic good ( > 1), which contributes to a lesser extent to covering the company's fixed costs. ${\ displaystyle \ eta _ {i}}$ ${\ displaystyle \ eta _ {i}}$

Derivation

It is the aggregate consumer surplus of the demand functions

${\ displaystyle KR: \ sum _ {i} \ int _ {p_ {i}} ^ {\ infty} x_ {i} ({\ tilde {p}} _ {i}) d {\ tilde {p}} _ {i}}$

under the secondary condition that the company works cost-effectively to optimize:

${\ displaystyle st \ sum _ {i} p_ {i} x_ {i} (p_ {i}) - C \ left (\ sum _ {i} x_ {i} (p_ {i}) \ right) = 0 }$

Establishing the Lagrange function:

${\ displaystyle {\ mathcal {L}} = \ sum _ {i} \ int _ {p_ {i}} ^ {\ infty} x_ {i} ({\ tilde {p}} _ {i}) d { \ tilde {p}} _ {i} + \ lambda \ left [\ sum _ {i} p_ {i} x_ {i} (p_ {i}) - C \ left (\ sum _ {i} x_ {i } (p_ {i}) \ right) \ right]}$

Maximizing welfare under the secondary condition of economic viability:

${\ displaystyle {\ frac {\ partial {\ mathcal {L}}} {\ partial p_ {i}}} = - x_ {i} (p_ {i}) + \ lambda \ left [x_ {i} (p_ {i}) + p_ {i} x '_ {i} (p_ {i}) - C'x' \ right] = 0}$

${\ displaystyle \ Leftrightarrow {\ frac {{\ frac {dx_ {i}} {dp_ {i}}} (p_ {i} -GK)} {x_ {i}}} = {\ frac {1- \ lambda } {\ lambda}}}$

Ramsey rule:

${\ displaystyle \ Leftrightarrow {\ frac {p_ {i} -GK} {p_ {i}}} = {\ frac {k} {{\ frac {dx_ {i}} {dp_ {i}}} * {\ frac {p_ {i}} {x_ {i}}}}} = {\ frac {k} {\ eta _ {x_ {i}, p_ {i}}}}}$

literature

Mankiw, NG / Taylor, PM (2012): Fundamentals of Economics, 5th edition, Stuttgart: Schäffer-Poeschel

Pindyck, RS / Rubinfeld, DL (2013): Mikroökonomie, 8th edition, Pearson

Train, KE (1991): Optimal Regulation, The MIT Press, Cambridge, Massachusetts, London, England

Individual evidence

↑ N. Gregory Mankiw, Mark P. Taylor: Grundzüge der Volkswirtschaftslehre . 5th edition. Schäffer-Poeschel, Stuttgart 2012, ISBN 978-3-7910-3098-2 , pp. 380 f .
↑ ^a ^b N. Gregory Mankiw, Mark P. Taylor: Grundzüge der Volkswirtschaftslehre . 5th edition. Schäffer-Poeschel, Stuttgart 2012, ISBN 978-3-7910-3098-2 , pp. 404 f .
↑ Robert S. Pindyck, Daniel L. Rubinfeld: Microeconomics . 8th edition. Pearson, Munich 2013, ISBN 978-3-86894-167-8 , pp. 542 ff .
↑ Kenneth E. Train: Optimal Regulation: the economic theory of natural monopoly . 1991, ISBN 0-262-20084-8 , pp. 115 ff .

[1] N. Gregory Mankiw, Mark P. Taylor: Grundzüge der Volkswirtschaftslehre . 5th edition. Schäffer-Poeschel, Stuttgart 2012, ISBN 978-3-7910-3098-2 , pp. 380 f .

[:0-2] N. Gregory Mankiw, Mark P. Taylor: Grundzüge der Volkswirtschaftslehre . 5th edition. Schäffer-Poeschel, Stuttgart 2012, ISBN 978-3-7910-3098-2 , pp. 404 f .

[3] Robert S. Pindyck, Daniel L. Rubinfeld: Microeconomics . 8th edition. Pearson, Munich 2013, ISBN 978-3-86894-167-8 , pp. 542 ff .

[4] Kenneth E. Train: Optimal Regulation: the economic theory of natural monopoly . 1991, ISBN 0-262-20084-8 , pp. 115 ff .