Tiered Pricing and Cost Functions: Are Equity, Cost Recovery and Economic Efficiency Compatible Goals?

Suppliers of water and energy are frequently natural monopolies, with their pricing regulated by governmental agencies. Pricing schemes are evaluated by the efficiency of the resource allocation they lead to, the capacity of the utilities to capture their costs and the distributional effects of the policies, in particular, impacts on the poor. One pricing approach has been average cost pricing, which guarantees cost recovery and allows utilities to provide their product at relatively low prices. However, average cost pricing leads to economically inefficient consumption levels, when sources of water and energy are limited and increasing the supply is costly. An alternative approach is increasing block rates (hereafter, IBR or tiered pricing), where individuals pay a low rate for an initial consumption block and a higher rate as they increase use beyond that block. An example of IBR is shown in Figure 1 (on next page), which shows a rate structure for residential water use. With the rates in Figure 1, a household would be charged $0.46 and $0.71 per hundred gallons for consumption below and above 21,000 gallons per month, respectively.

Impact of Solvent Quality on the Density Profiles of Looped Triblock Copolymer Brushes by Neutron Reflectivity Measurements

Preferential adsorption of poly(2-vinylpyridine)-deuterated polystyrene-poly(2-vinylpyridine) (PVP-dPS-PVP) triblock copolymers from toluene onto silicon leads to the formation of dPS loops tethered by the PVP end blocks. Using neutron reflectometry, we have determined the segment density profiles of these looped polymer brushes in toluene, a good solvent for the dPS block, and in cyclohexane at 20 °C (poor solvent), 32 °C, (near-Θ solvent), and 50 °C (marginal solvent). While the swelling behavior qualitatively agrees with that observed for singly grafted brushes, there are interesting differences in the local structural details: In a good solvent, the segment density profiles are composed of an inner parabolic region and a long, extended tail. In cyclohexane, the profiles are described by exponential decays. We ascribe these features to a novel polydispersity effect that arises due to tethering the PS loops by both ends. The results also show that the less dense layers undergo more significant changes in swollen height as solvent quality is changed and that the looped brushes of different molecular weight, asymmetry, and tethering density adhere to scaling relationships derived for lightly cross-linked polymer gels.

High-Pressure Micellar Solutions of Polystyrene-block-polybutadiene and Polystyrene-block-polyisoprene in Propane Exhibit Cloud-Pressure Reduction and Distinct Micellization End Points

Micellar solutions of polystyrene-block-polybutadiene and polystyrene-block-polyisoprene in propane are found to exhibit significantly lower cloud pressures than the corresponding hypothetical nonmicellar solutions. Such a cloud-pressure reduction indicates the extent to which micelle formation enhances the apparent diblock solubility in near-critical and hence compressible propane. Concentration-dependent pressure-temperature points beyond which no micelles can be formed, referred to as the micellization end points, are found to depend on the block type, size, and ratio. The cloud-pressure reduction and the micellization end point measured for styrene-diene diblocks in propane should be characteristic of all amphiphilic diblock copolymer solutions that form micelles in compressible solvents.

Association and Structure of Thermosensitive Comblike Block Copolymers in Aqueous Solutions

The structures and association properties of thermosensitive block copolymers of poly(methoxyoligo( ethylene glycol) norbornenyl esters) in D2O were investigated by small angle neutron scattering (SANS). Each block is a comblike polymer with a polynorbornene (PNB) backbone and oligo ethylene glycol (OEG) side chains (one side chain per NB repeat unit). The chemical formula of the block copolymer is (OEG3NB) 79- (OEG6.6NB) 67, where subscripts represent the degree of polymerization (DP) of OEG and NB in each block. The polymer concentration was fixed at 2.0 wt % and the structural changes were investigated over a temperature range between 25 and 68°C. It was found that at room temperature polymers associate to form micelles with a spherical core formed by the block (OEG3NB) 79 and corona formed by the block (OEG6.6NB) 67 and that the shape of the polymer in the corona could be described by the form factor of rigid cylinders. At elevated temperatures, the aggregation number increased and the micelles became more compact. At temperatures around the cloud point temperature (CPT) T ) 60 °C a correlation peak started to appear and became pronounced at 68 °C due to the formation of a partially ordered structure with a correlation length ∼349 Å.