Ramsey Pricing Research Articles

MAXIMIZING THE U.S. POSTAL SERVICE'S PROFITS FROM COMPETITIVE PRODUCTS

The Postal Regulatory Commission (PRC) regulates the pricing of the U.S. Postal Service's products, including products not protected by the Postal Service's statutory monopolies that the enterprise sells in competition with the products of private firms. The Postal Accountability and Enhancement Act (PAEA) of 2006 created new requirements for the PRC's pricing regulation of competitive products. I evaluate the economic implications of the PAEA's three primary requirements with respect to the Postal Service's pricing of competitive products: preventing cross subsidy of competitive products by monopoly products, ensuring that competitive products cover their “attributable” costs, and allocating to competitive products an appropriate share of the Postal Service's common costs (known as “institutional” costs in postal regulatory jargon). The first has a relatively straightforward economic interpretation: the PRC can use either the incremental cost test or the standalone cost test to detect cross subsidy, subject to some nuances when the Postal Service does not break even. To ensure that the Postal Service's competitive products meet the PAEA's attributable-cost requirement, the PRC can apply an incremental cost test using Shapley values. Given the evolution of the Postal Service's network to support competitive products, the PRC should use incremental costs that are neutral with respect to the order in which the Postal Service has introduced its product lines. Next, I explain that the appropriate share of institutional costs for the Postal Service to recover from competitive products depends on understanding in precise economic terms the alternative rationales for empowering the PRC to regulate the Postal Service's competitive products. I identify and analyze the implications of three possible rationales: (1) ensuring that the Postal Service fulfills its essential mandate to deliver monopoly (“market-dominant”) mail services, (2) ensuring that the Postal Service fulfills its fiduciary duty to taxpayers as a state-owned enterprise, and (3) preserving competitive parity in markets in which the Postal Service competes with private firms. I find that those goals indicate that the optimal allocation of institutional costs to competitive products would maximize the Postal Service's profit from its sale of competitive products—thereby enabling revenues from competitive products to cover as much of the Postal Service's overhead as possible. I review how a multiproduct firm maximizes profits using Ramsey prices. I then propose a simple shortcut by which the PRC could approximate those prices for its competitive products with limited information and at relatively low administrative cost. By gradually increasing the share of institutional costs that competitive products must bear, the PRC can identify the profit-maximizing price for competitive products and thus iterate toward the precise allocation of institutional costs that maximizes the profits that the Postal Service earns from its offerings of competitive products. Finally, I show how the Postal Service's Board of Governors could obviate the PRC's intervention by independently implementing profit-maximizing prices for competitive products and why, in the absence of other remedies, Congress should enact legislation to ensure that the Postal Service maximizes the profits that it earns from its competitive products.

Ramsey prices in the Italian electricity market

In this paper, we derive optimal zonal prices in the Italian day-ahead electricity market using estimation of a complete system of hourly demand in 2010–2011. In Italy, the hourly equilibrium price for all buyers is computed as a uniform average of supply zonal prices, resulting from market splitting due to line congestion. We model ex-ante individual bids expressed by heterogeneous consumers, which are distinguished by geographical zones. Using empirical estimations, we compute demand elasticity values and new zonal prices, according to a Ramsey optimal scheme. This is a new approach in the wholesale electricity market literature, as previous studies have discussed the relative merit of zonal prices, considering only the issue of line congestion. Our results show that the optimal pricing scheme can improve welfare in the day-ahead Italian electricity market, with respect to both the existing uniform price scheme and the proposal to charge the existing supply zonal prices to the demand side.

Studying a modified ramsey model with variable production flexibility

A one-dimensional nonlinear problem of optimal control on an infinite planning horizon is considered that is a modification of Ramsey‘s model for endogenous economic growth with the Cobb–Douglas production function. The model is innovative in its consideration of variable production flexibility, a parameter of the Cobb–Douglas function. As the first step in the study, the problem is considered for piecewise-smooth and piecewise-constant flexibility functions. Optimal solutions are constructed on the basis of a special integral representation of the functional and are unique for each type of flexibility function. The optimal solutions include singular modes. The final results can be used to estimate the effect of uncertainty in a Ramsey problem with constant parameters.

The End of the International Reference Pricing System?

All 28 EU member states except Sweden and the UK apply international reference pricing (IRP), international price comparison, external reference pricing or cross-reference pricing. The attractiveness of using prices of other countries as a benchmark for decisions within a national price control is obvious. Alternative models for price and reimbursement decision making such as value-based pricing (VBP), i.e. cost-effectiveness analyses, are more complicated. However, IRP provides incentives for stakeholders to take action not in line with optimal (welfare-maximizing) pricing. IRP is costly for two reasons. First, manufacturers are incentivised to limit or delay access to new innovative treatments in countries with small markets and/or a low income, which can be costly in terms of loss of health. Second, all countries also experience a loss of welfare (health) because IRP reduces the opportunities for differential pricing (Ramsey pricing), i.e. using the fact that the ability and willingness to pay differs between countries. Thus, IRP results in less sales revenue to finance research and development of new innovative drugs. We can now observe that payers and manufacturers are engaged in different types of risk-sharing schemes, price-volume negotiations, payback arrangements, confidential discounts, coverage with evidence developments, etc., all with the purpose of returning to the old model of price discrimination and Ramsey pricing. Shortly, real prices for use in IRP systems will cease to exist and, thus, we expect to soon see the end of IRP, a new system for price discrimination and an increasing demand for VBP.

Zero Lower Bounds in New Keynesian Models and a Constrained Ramsey Problem

There exist difficulties in escaping from stagnation and/or deflation if the economy hits zero lower bounds on short-term nominal interest rates because the central bank cannot stimulate the economy further using rate cuts. How can it escape from them? Answering the question, we extend a closed-looped solution of a Ramsey problem (also known as a Stackelberg problem) by introducing zero lower bounds. Herein, we formulate a constrained Ramsey problem and derive a solution for it. In our extension, we found that the discounted Lyapunov equation is necessary to obtain the shadow price of the economy that hits the zero lower bounds. Herein we apply our method to new Keynesian models with zero lower bounds. Our simulation shows that committing to mild inflation engenders positive effects on the economy and that managing inflation expectations is necessary to escape from the bounds.

Two-stage auction and subscription pricing for awarding monopoly franchises

This paper examines an efficient market organization for awarding monopoly franchises to assure investment efficiency and revenue sufficiency under conditions of increasing returns. A two-stage auction design achieves ex ante and ex post efficiency by ensuring that the firm with the best technology will be selected, and after winning, the firm will operate at the least cost and price at the marginal cost. Priority-differentiated subscription service fosters self-revelation of demand functions and facilitates fixed cost recovery. With known demand functions, a linear subscription price schedule based on the beneficiary-pay principle achieves efficient fixed cost recovery. With unknown demand functions, a two-part subscription price menu based on nonlinear Ramsey pricing attains an incentive-compatible, second-best result.

Ramsey Equilibrium in a Model with Liberal Borrowing

This paper considers a multi-agent one-sector Ramsey equilibrium growth model with borrowing constraints. The extreme borrowing constraint used in the classical version of the model, surveyed in Becker (2006), and the limited form of borrowing constraint examined in Borissov and Dubey (2015) are relaxed to allow more liberal borrowing by the households. A perfect foresight equilibrium is shown to exist in this economy. We describe the steady state equilibria for the liberal borrowing regime and show that as the borrowing regime is progressively liberalized, the steady state wealth inequality increases. Unlike the case of a limited borrowing regime, an equilibrium path need not converge in the case of liberal borrowing regime. We show through an example that a two period cyclic equilibrium exists when agents are allowed to borrow against their two period future wage income. This result is similar to the possibility of non-convergent equilibrium capital stock sequences in the model with no borrowing.

Kernel Lower Bounds using Co-Nondeterminism: Finding Induced Hereditary Subgraphs

This work further explores the applications of co-nondeterminism for showing kernelization lower bounds. The only known example prior to this work excludes polynomial kernelizations for the so-called Ramsey problem of finding an independent set or a clique of at least k vertices in a given graph [Kratsch 2012]. We study the more general problem of finding induced subgraphs on k vertices fulfilling some hereditary property Π, called Π-Induced Subgraph. The problem is NP-hard for all nontrivial choices of Π by a classic result of Lewis and Yannakakis [1980]. The parameterized complexity of this problem was classified by Khot and Raman [2002] depending on the choice of Π. The interesting cases for kernelization are for Π containing all independent sets and all cliques, since the problem is trivially polynomial time solvable or W[1]-hard otherwise. Our results are twofold. Regarding Π-Induced Subgraph, we show that for a large choice of natural graph properties Π, including chordal, perfect, cluster, and cograph, there is no polynomial kernel with respect to k . This is established by two theorems, each one capturing different (but not necessarily exclusive) sets of properties: one using a co-nondeterministic variant of OR-cross-composition and one by a polynomial parameter transformation from Ramsey. Additionally, we show how to use improvement versions of NP-hard problems as source problems for lower bounds, without requiring their NP-hardness. For example, for Π-Induced Subgraph our compositions may assume existing solutions of size k--1. This follows from the more general fact that source problems for OR-(cross-)compositions need only be NP-hard under co-nondeterministic reductions. We believe this to be useful for further lower-bound proofs, for example, since improvement versions simplify the construction of a disjunction (OR) of instances required in compositions. This adds a second way of using co-nondeterminism for lower bounds.

An Economics Approach to Fixing the Fare of the Parking Lot Service in Bogotá Using Price Cap Regulation

This article presents an application of the Ramsey Pricing approach to establish the price cap or pricing ceiling per minute for the parking lot service in Bogotá (Colombia), using the microeconomic framework for price fixing from a costs analysis (total fixed costs, total variables costs, average total cost, and marginal cost) of the provision of parking lot service in Bogotá. These results were evidenced by means of a dynamic panel data model for estimating total cost functions through generalized method of moments estimators. Also, from the econometric outcome and using the Ramsey Pricing approach and mathematical optimization (comparative statics), I obtained the maximum fare per minute that should pay the consumers of the parking lot service in Bogotá. I conclude that the current maximum fee per minute, paid by parking users, does not cover the fixed costs incurred by firms that provide legally this service in Bogotá.

Supply-based dynamic Ramsey pricing: Avoiding water shortages

In many countries, current water-pricing policies are dictated by the sole objective of financial breaking even. This results in large withdrawals, which are not sustainable in the long run, hence not optimal. In this paper, we derive the optimal dynamic pricing policy, which targets efficient distribution while breaking even through a rebate scheme. Using data from Turkey, we estimate the demand for water by user groups. We carry out simulations to compare the effects of the current and optimal pricing policies on the frequency and severity of shortages. We find that, under the policy of break-even prices, the supplier runs into a shortage every 8 years. In contrast, if the prices were to set optimally, shortages would be practically nonexistent over the next century.

A characterization of Ramsey equilibrium in a model with limited borrowing

This paper considers a one-sector economic growth model with several infinitely-lived heterogeneous households, who differ both in the discount factors as well as preferences over consumption. Unlike the extreme form of borrowing constraint observed in the classical Ramsey model, recently surveyed in Becker (2006), we allow limited borrowing by the households and prove the existence of a perfect foresight equilibrium. We also show that irrespective of production technology employed by the firms, the capital stock sequence converges to the steady state stock and from some time onward all impatient households are in the maximum borrowing state, whereas the most patient household owns entire capital stock and the debts of all other households.

A Characterization of Ramsey Equilibrium in a Model with Limited Borrowing

This paper considers a one-sector economic growth model with several infinitely - lived heterogeneous households, who differ both in the discount factors as well as preferences over consumption. Unlike the extreme form of borrowing constraint observed in the classical Ramsey model, recently surveyed in Becker (2006), we allow limited borrowing by the households and prove the existence of a perfect foresight equilibrium. We also show that irrespective of production technology employed by the firms, the capital stock sequence converges to the steady state stock and from some time onward all impatient households are in the maximum borrowing state, whereas the most patient household owns entire capital stock and the debts of all other households.

Optimal fiscal policy in the neoclassical growth model revisited

This paper studies optimal taxation in a version of the neoclassical growth model in which investment becomes productive within the period, thereby making the supply of capital elastic in the short run. Because taxing capital is distortionary in the short run, the government׳s ability/desire to raise revenues through capital income taxation in the initial period or when the economy is hit with a bad shock is greatly curtailed. Our timing assumption also leads to a tractable Ramsey problem without state-contingent debt, which can give rise to debt-financed budget deficits during recessions.

On the Grid Ramsey Problem and Related Questions: Fig. 1.

The Hales–Jewett theorem is one of the pillars of Ramsey theory, from which many other results follow. A celebrated theorem of Shelah says that Hales–Jewett numbers are primitive recursive. A key tool used in his proof, now known as the cube lemma, has become famous in its own right. In its simplest form, this lemma says that if we color the edges of the Cartesian product Kn × Knin r colors, then, for nsufficiently large, there is a rectangle with both pairs of opposite edges receiving the same color. Shelah’s proof shows that n=r � r+1 2 � + 1 suffices. More than 20 years ago, Graham, Rothschild, and Spencer asked whether this bound can be improved to a polynomial in r. We show that this is not possible by providing a superpolynomial lower bound in r. We also discuss a number of related problems.

Optimal consumption of the stochastic Ramsey problem for non-Lipschitz diffusion

The stochastic Ramsey problem is considered in a growth model with the production function of a Cobb-Douglas form. The existence of a unique classical solution is proved for the Hamilton-Jacobi-Bellman equation associated with the optimization problem. A synthesis of the optimal consumption policy in terms of its solution is proposed.MSC:49L20, 49L25, 91B62.

Regional Electricity Pricing With Ramsey Approach: Tehran Case Study

In developing countries electricity power is not only used for energy’s demand responding, but also an essential element of developing. Furthermore the government pricing has comprehensive effect on economy of developing countries due to huge ratio of their governments. So in these countries the electricity pricing could affect welfare and development simultaneously. Therefore we use welfare maximizing as one of the most prevalent method for optimal price detection. As Ramsey rule (which is derived from welfare maximizing) is used in increasing return to scale situations it would be proper for natural monopoly position (that exist in electricity market). Elasticity and marginal cost is required to use Ramsey rule therefore we use Philippine rule and panel data approach to determine elasticity. We also use average cost and rate of return degree to detect marginal cost. Using these two numbers will eventually result in Ramsey prices. Finally we will drive that electricity prices should increase while steps differences should decrease.

Charges of uncongested German airports: Do they follow Ramsey pricing scheme?

Ramsey pricing is considered to be a quasi-optimum pricing scheme designed for a multiproduct natural monopolist. Ramsey prices are optimal for airports with cost recovery problems, but are inefficient for busy airports. If so then it is interesting to check if current charges are close to the optimal one, and if not then why and by how much do they differ?A menu of landing fees for five German airports using a Ramsey pricing setup is calculated. The paper concentrates on fees for different distances and three types of aircrafts. A new approach of estimating marginal cost for different aircrafts is used. The calculated fees are compared with the actual fees charged by these airports. We compare the actual fees with the calculated Ramsey prices and explain the difference on the basis of different factors. We find a clear monotone dependence: Ramsey prices increase with distance and MTOW faster than the real fees, especially in the short-distance markets, but the difference between theoretical optimum and practice needs to be better understood. Based on the current calculation we suggest some policy implications both concerning our current results and the possible improvements of the regulation of uncongested airports.

Learning the Ramsey Outcome in a Kydland & Prescott Economy

We study learning in the Kydland and Prescott environment. Our policy maker evaluates its potential strategies regarding the announced and the actual inflation rate using its mental model. This model is forward looking and adaptive at the same time. There are two types of agents: Believers who set their inflation forecast equal to the announced inflation, and nonbelievers who form static optimal forecast coupled with a forecast error correction mechanism. Our results show that the economy can reach near Ramsey outcomes most of the time. In the absence of believers, the economies almost always converge to the Ramsey outcome. In their experiments with human subjects, Arifovic and Sargent (2003) showed that experimental economies reach and stay close to the Ramsey outcome most of the time, giving support to the 'just do it' policy recommendation. In light of the experimental findings, our model is of particular interest as it is the only agent-based or adaptive learning model that consistently selects the Ramsey outcome.

Analysis of prices paid by low-income countries - how price sensitive is government demand for medicines?

BackgroundAccess to medicines is an important health policy issue. This paper considers demand structures in a selection of low-income countries from the perspective of public authorities as the evidence base is limited. Analysis of the demand for medicines in low-income countries is critical for effective pharmaceutical policy where regulation is less developed, health systems are cash constrained and medicines are not typically subsidised by a public health insurance systemMethodsThis study analyses the demand for medicines in low-income countries from the perspective of the prices paid by public authorities. The analysis draws on a unique dataset from World Health Organization (WHO) and Health Action International (HAI) using 2003 data on procurement prices of medicines across 16 low-income countries covering 48 branded drugs and 18 therapeutic categories. Variation in prices, the mark-ups over marginal costs and estimation of price elasticities allows assessment of whether these elasticities are correlated with a country’s national income.ResultsUsing the Ramsey pricing rule, the study’s findings suggest that substantial cross-country variation in prices and mark-ups exist, with price elasticities ranging from -1 to -2, which are weakly correlated with national income.ConclusionsGovernment demand for medicines thus appears to be price elastic, raising important policy implications aimed at improving access to medicines for patients in low-income countries.

Economical valuing of Water in Irrigation and Drainage Lattice in Khuzestan Province (1979-2013)

Since early times water has always been considered as the most important factor in development and applying the new, has played the vital part in obtaining the goal of food supply for the world's growing population. The shortage of sweet water in recent years has become a global problem and particularly in Iran due to water shortage the efficient consumption of agricultural water has achieved significant importance. Therefore water pricing policy has been applied in order to improve agricultural irrigation and determine certain approaches to improve irrigation efficiency. This study has adopted the Ramsey pricing method and time serial data throughout (1979 – 2013) years to present the model. ARDL model was used to estimate demand and supply functions. Cobb Douglas function was taken into consideration in order to present water supply function. Pricing capacity and final production costs were calculated according to demand function and production function and Ramsey water price for agriculture section was determined by these two variables by the help of MATLAB software. According to the results of this study, the estimated prices on the base of Ramsey pricing policy are higher than current prices. In fact the comparison between actual price (86 Riyal per qm in 2013) and Ramsey price (96 Riyal) shows that the amount of money paid by the farmers is less than the economic (Ramsey) value of water. This absence of conformity between the numbers indicates great loss for water and sewage companies and on the other hand low elasticity of water demand (-0.06) has resulted in more water consumption.