Ramsey rule

The Ramsey rule (after Frank Plumpton Ramsey ) is a result of the theory of optimal taxation. The Ramsey rule is often erroneously referred to as the inverse elasticity rule. However, the inverse elasticity rule is only a special case of the Ramsey rule, which excludes cross price effects.

Assume that a certain tax revenue is to be achieved and a flat tax ( head tax ) is not available, but only indirect taxes on the goods . Taxation should now take place in such a way that the entire welfare - the sum of producer surplus and consumer surplus - is maximized. This is particularly important for public infrastructure facilities with non-allocable fixed costs and constant marginal costs . Different product lines are offered here (such as freight transport and passenger transport for transport companies). ${\displaystyle i=1,\ldots ,n}$

Assuming that the demand functions are independent of one another, the Ramsey rule specifies which tax rates are to be levied on the individual goods. The tax rates are inversely proportional to the price elasticity of demand. This means that the tax rate has to be lower, the more sensitive the demand is to price increases.

The rule for optimally cost-covering fees is therefore as follows:

${\displaystyle {\frac {(p_{i}-M_{i})/p_{i}}{(p_{j}-M_{j})/p_{j}}}={\frac {\varepsilon _{j}}{\varepsilon _{i}}}}$

( = Price of the -th good; = marginal costs in the market of the -th good; = price elasticity of the demand for the -th good.) ${\displaystyle p_{i}}$ ${\displaystyle i}$ ${\displaystyle M_{i}}$ ${\displaystyle i}$ ${\displaystyle \varepsilon _{i}}$ ${\displaystyle i}$

If the demand functions are linear, then the demand for all goods decreases by the same percentage.

Unlike the golden rule savings rate of Phelps , the Ramsey rule takes into account time preferences . Another alternative, demand-dependent price differentiation is peak load pricing .

A continuation of the Ramsey rule is the Corlett-Hague rule .