This thesis examines the theoretical properties of different price cap schemes that have been applied in the UK and the USA. The objective is to assess the consequences for price structures and welfare of different ways of defining the regulated price index. Chapter 2 surveys the literature on regulation under asymmetric information that is related to price caps. Chapter 3 presents a general analysis of five main types of price cap when the regulated firm sets linear tariffs. The schemes are the Tariff Basket (TB) scheme, the Fixed Weights (F) scheme, the Average Revenue (AR) scheme, the Average Revenue (Lagged) scheme, and the Paasche Price Index (PPI) scheme. The TB and PPI schemes generate efficient price structures in the long run, whereas prices are inefficient under the other schemes. In Chapter 4 the consequences of allowing freedom to set different prices, relative to the case of uniform prices, are analyzed. The conditions for price freedom to be desirable are derived for the case where the price level is not regulated. When the price level is regulated it is shown that AR regulation can cause welfare to be below the level that obtains without any regulation. Chapter 5 contains an analysis of the five price caps examined in Chapter 3 for the case where the firm sets a two-part tariff. The AR and PPI schemes are dominated, and the conditions under which TB, F and ARL are optimal are established. Chapter 6 explores some issues in the regulation of nonlinear tariffs by AR and TB price caps. Chapter 7 considers some extensions of the analysis. It is shown that when quality is a choice variable, the regulator is concerned about income distribution and there is demand growth the TB scheme can be adapted and retains its desirable properties. Chapter 8 contains conclusions and suggestions for future work.