The advent of "smart meters" will make possible Real Time Pricing of electricity: customers will face and react to wholesale spot prices, thus consumption of electric power will be aligned with its opportunity cost. This article determines the marginal value of a fraction of demand (or a consumer) switching to Real Time Pricing. First, it derives this marginal value for a simple yet realistic specification of demand. Second, using data from the French power market, it estimates that, for the vast majority of residential customers whose peak demand is lower than 6 kV A, the net surplus from switching to Real Time Pricing is lower than 1 euro/year for low demand elasticity, 4 euros/year for high demand elasticity. This finding casts a doubt on the economic value of rolling out smart meters to all residential customers, for both policy makers and power suppliers.