Optimal Two‐Part Pricing under Demand Uncertainty

This paper examines the pricing behavior of a risk‐averse monopolistic firm under demand uncertainty. The firm produces a single good at a constant marginal cost. To facilitate sales, the firm uses a two‐part pricing contract that includes a membership fee and a selling price per unit. The good is sold to a continuum of heterogeneous consumers who are subject to a common demand shock. We show that the global and marginal effects of risk aversion are to push the unit price closer to the constant marginal cost and to shrink the market coverage so as to limit the firm’s risk exposure to the demand uncertainty. The more risk‐averse firm as such charges a higher membership fee to consumers. We further show that an increase in the fixed cost of production induces the firm to lower (raise) the unit price, to raise (lower) the membership fee, and to shrink (enlarge) the market coverage under decreasing (increasing) absolute risk aversion. The firm’s optimal two‐part pricing contract, however, is unaffected by changes in the fixed cost under constant absolute risk aversion. Finally, we show that a mean‐preserving‐spread increase in the demand uncertainty induces the firm to lower the unit price, to raise the membership fee, and to shrink the market coverage under either decreasing or constant absolute risk aversion. The firm’s risk preferences as such play a pivotal role in determining the optimal two‐part pricing under demand uncertainty. Copyright © 2013 John Wiley & Sons, Ltd.     

The golden rule of urban transportation investment

The purpose of this paper is to find an optimal taxation rule for transportation investment in an ever growing urban economy. First we dynamize a standard circular-city model with identical residents by introducing population growth and transportation improvements over time. Assuming that utility functions are of a constant-elasticity form and transportation investment is financed by an income tax, we prove the existence, uniqueness and stability of a balanced growth equilibrium for each given tax rate. Then, an optimal tax rate is determined so as to maximize the balanced growth equilibrium level of utility for every resident in the city. It is also shown that our simple rule remains valid in the case of two income classes.     

Pricing a contract of linking home reversion plan and long-term care insurance via the principle of equivalent utility

Home reversion plans allow homeowners to tap into the value of their house and live in it until their death. The article considers a contract linking home reversion plan and long-term care insurance, which could better prepare seniors for their retirement and long-term care needs. Here, we assume the product exposes an insurer to two risks: the uncertainty of nursing care cost from disable, and the home value decreasing in real estate markets at the time of sale. Because the market is incomplete, we apply the principle of equivalent utility to price the contract under exponential utility.     

Mergers with Product Market Risk

This paper studies the causes and the consequences of horizontal mergers among risk-averse firms. The amount of diversification depends on the allocation of shares among the merging firms, with a direct risk-sharing effect and an indirect strategic effect. If firms compete in quantities, consolidation makes firms more aggressive. Mergers involving few firms are then profitable with a relatively low level of risk aversion. With strong enough risk aversion, mergers reduce prices and improve social welfare. If firms instead compete in prices, consumers do not benefit from mergers in markets with demand uncertainty, but can easily benefit with cost uncertainty.     

A comment on gasoline prices and urban structure

The effect of higher gasoline prices on urban concentration and aggregate work travel is investigated with a simple closed-city general equilibrium model used by Robson and Scheffman. Their approximate solution is shown to be invalid at reasonable parameter values; for the case of a Cobb-Douglas utility function, numerical solution indicates a long-run reduction in average trip length of 1.4% to 2.9% from an increase in transportation cost of 0.5 cents per mile. It is noted that this is still much larger than estimates obtained by other means.     

What effect does uncertainty have on the length of labor contracts?

The literature on duration of explicit labor contracts has suggested that increased uncertainty should be associated with shorter labor contracts. More recently, it has been argued that the effect of uncertainty on contract duration depends on the type of uncertainty involved. Specifically, if the uncertainty pertains to aggregate real shocks, then contract durations should increase as workers seek to insure themselves against the repercussions of such shocks. Using a sample of 1876 labor contracts signed during the period 1977–1988, this paper provides an empirical test of the foregoing hypothesis (known as the efficient risk sharing hypothesis). The paper presents results from estimation of a generalized-probit, simultaneous equation model, in which the dependent variables are contract length, indexation of the contract through a cost-of-living allowance, and the rate of wage change specified in the contract. The empirical findings confirm the efficient risk sharing hypothesis.     

企业私有化程度提高则社会环境会变差？

从企业私有化角度出发,构建二元经济理论模型和实证模型分析私有化对环境污染的影响。理论研究发现,由于城市部门资本密集程度高于农村部门,而且如果农村劳动者从环境改善中获得的边际效用小于城市劳动者从环境改善中获得的边际效用,那么提高私有化导致单位产出污染排放减少时会引起：（1）劳动和资本要素会向城市流动,城市工业部门产出增加;农业部门由于劳动和资本流出而导致产出减少,即城市扩张而农村收缩;(2)城市地区的失业总人数会增加;(3)私有化导致单位产出污染排放减少的效应大于工业产出增加导致污染排放增加的效应,最终导致社会环境改善,但如果私有化导致单位产出污染排放增加,则会得出相反的结论。实证结果表明：企业私有化水平提高有利于降低单位产出固体废物、废水、二氧化硫和烟尘等污染物的排放,资本投入也有利于降低单位产出污染物的排放。     

Household behavior under income uncertainty in a monocentric urban area

For a household living outside of but commuting to and from the CBD of an urban area and experiencing income uncertainty, housing consumption and location (distance from the CBD) are inversely related to the probability of unemployment and directly related to the level of unemployment compensation under fairly unrestrictive assumptions. Under more restrictive assumptions, it is found that these variables are inversely related to housing price and transportation costs. Finally, income compensation causes housing consumption and location to be directly related to the probability of unemployment and the level of unemployment compensation.     

不完全信息投标报价模型

考虑现实竞标过程中投标方彼此成本信息不对称及未来市场的不确定性。利用模糊数刻画竞标方彼此成本信息不对称,并用线性风险损失刻画竞标方面临的失标风险及赢者诅咒风险,构造信息不完全背景下竞标方报价模型。通过数据模拟分析通胀风险因子对竞标方报价及期望效用的影响,得到以下结论:通胀风险因子的存在会致使竞标方报价高于传统报价,且竞标方报价与通胀风险因子呈正比;竞标方的期望效用则由于通胀风险因子相应降低,与通胀风险因子呈负相关。     

Optimal Two‐part Pricing under Cost Uncertainty

This paper examines the optimal two‐part pricing under cost uncertainty. We consider a risk‐averse monopolistic firm that is subject to a cost shock to its constant marginal cost of production. The firm uses two‐part pricing to sell its output to a continuum of heterogeneous consumers. We show that the global and marginal effects of risk aversion on the firm's optimal two‐part pricing are to raise the unit price and lower the fixed payment. We further show that an increase in the fixed cost of production induces the firm to raise (lower) the unit price and lower (raise) the fixed payment under decreasing (increasing) absolute risk aversion. The firm's optimal two‐part pricing is unaffected by changes in the fixed cost under constant absolute risk aversion. Finally, we show that a mean‐preserving spread increase in cost uncertainty induces the firm to raise the unit price and lower the fixed payment under either decreasing or constant absolute risk aversion. Copyright © 2011 John Wiley & Sons, Ltd.     

Are generalized call-spreads efficient?

In order to explain coexistence of a deductible for low values of the loss and an upper limit for high values of the loss in insurance contracts, we consider the exchange of risk between two rank dependent expected utility maximizers. It is shown that if the insurer (insured) takes more into account the lowest outcomes – hence maximal losses – than the insured (insurer), then the optimal contract has an upper limit (includes a deductible for high values of the loss). If furthermore, the insured (insurer) neglects the highest outcomes while the insurer (insured) does not, the optimal contract includes a deductible (full insurance) for low values of the loss.     

Incorporating a “no claim bonus” in insurance agency contract

A bonus received by an agent from an insurer when the insured does not make a claim is called a “no claim bonus” (NCB). An NCB rewards the agent's risk‐management (RM) effort that reduces the probability that the insured suffers a loss. This paper designs an incentive compatible contract that induces the agent to choose an RM effort. If the agent's RM effort cost is lower than a threshold, feasible ranges of NCB and premium values exist such that the insurer can offer an incentive compatible agency contract with an NCB that is acceptable to the agent.     

Multi‐unit pricing

A price takes the form of a cost for either one unit (single‐unit pricing) or multiple units (multi‐unit pricing). I consider a monopolist selling units of a good to a population of homogeneous consumers to explain why one is preferred to the other. A mental cost arises if the division problem a multi‐unit price causes is done. If marginal utility remains high multiple units are desired. Multi‐unit pricing is preferred since it creates a cost if fewer units are purchased. If utility exhibits strong diminishing returns single‐unit pricing is used to avoid the calculation. Copyright © 2008 John Wiley & Sons, Ltd.     

Stochastic costly state verification and dynamic contracts

I consider a dynamic costly state verification environment in which a risk-averse agent enters into a contract with a risk-neutral principal. The agent has random income which is unknown to the principal but can be verified at a cost. The principal can commit to executing random verifications.I extend the standard recursive methods to study the problem and show that it is optimal to set verification probabilities strictly less than 1. If the agent׳s absolute risk aversion declines sufficiently slowly, the principal will use verification regardless of its cost. If the agent's income is verified then he would get consumption and continuation utility strictly higher than if his income were not verified.     

The effects of transportation system improvements on urban performances with heterogeneous residents

Through developing a spatial equilibrium model for a linear monocentric city with a bi-modal traffic corridor (i.e., highway and public transit), this paper examines the effects of transportation improvements (including the decreases of the fixed travel cost, the travel time and monetary cost per unit distance) on urban spatial structure and the utilities of the two resident classes, namely car-available-residents (CARs) and car-unavailable-residents (CURs). As a result, it is demonstrated that the city size increases with the improvements of vehicle-highway system and the degree of CARs’ travel mode choice rationality, but the improvement of public transit may produce a shrinkage rather than an expansion in city size. From the aspect of utility, both CARs and CURs benefit from the improvement of vehicle-highway system; however, the improvement of public transit might have an adverse effect on the utility of CARs. These findings would provide valuable reference for the future transportation and urban planning.     

The effects of uncertainty on investment and the expected long-run capital stock

This paper examines the effects of output price uncertainty on the optimal investment behavior of a risk-neutral competitive firm with a constant returns to scale production function. In the presence of convex costs of adjustment, investment is an increasing function of q, the shadow price of capital. Given the current price of output, we find that increased uncertainty will raise the current rate of investment. Increased uncertainty will also increase the expected long-run capital stock if the price of output is serially uncorrelated. However, if the price of output is serially correlated, then the direction of the effect of increased uncertainty on the expected long-run capital stock depends on the curvature of the marginal adjustment cost function. In this case, we obtain results which are directly opposite of the results in the literature and we locate the flaw in the existing analysis.     

Municipal costs and urban area

There are plausible reasons for believing that municipal service system costs will increase with urban “sprawl.” The costs of several municipal systems were thus analyzed, namely: water; sewage; roads and highways (capital outlays only); police, fire, and park systems; electricity distribution; gas distribution; and telephone service. The statistical relation between urban area and urban costs was weaker than a priori beliefs might suggest. Capital outlays for public municipal systems increase only about 1.6% for every 10% increment in land area. Public municipal operating costs, and the capital and operating costs of private utility systems are practically unaffected by urban area.     

The effect of reimbursement of worker's transport costs: The case of urban areas in Japan

In some economies, workers are compensated for their commuting costs to the workplace. The spatial structure of an urban area is analyzed comparing a transport cost compensated system to one where expenses are borne by workers. Profit maximizing behavior by firms results in lower wages being paid in the city where transport costs are compensated. It is shown that worker renters achieve a higher level of utility in the area where transport costs are not compensated. Numerical examples are constructed using a range of parameter values which yields measures of the increase in spatial size of the city where transport costs are compensated. The loss in welfare is also evaluated.     

Profit,productivity, and profit-sharing

This study is an investigation of the effect of profit-sharing on labor productivity. When monitoring labor performance is costly for management, a regular wage/salary contract is insufficient to induce profit-maximizing behavior from the worker. The authors demonstrate that when this profit-maximizing behavior can be induced only through profit-sharing, a linear profit-sharing program will increase productivity and the welfare of both management and labor. The benefit from profit-sharing is increasing up to the point where the utility of additional income is offset by the negative utility of extraordinary effort (working harder or providing higher quality work). The income effect, i.e., the change in negative utility of extraordinary effort given a change in income, can potentially either increase or decrease the point at which the income-effort tradeoff-reaches zero.     

论第三方物流合同违约责任的归责原则

20世纪末,第三方物流迅速发展,由传统第三方物流逐渐向现代整合性第三方物流过渡,相应的,第三方物流合同也逐渐从传统的运输、仓储合同向类型结合型的第三方物流合同转化。这种类型结合型的第三方物流合同系无名合同,其裁判依据包括双方之间订立的第三方物流合同本身(包括补充协议、体系解释、交易习惯)和民事法律规范。从双方之间订立的第三方物流合同角度而言,其违约责任多采用的是严格责任归责原则。从民事法律规范的角度来说,基于个案中能否确认货损发生的区间,第三方物流合同适用不同的违约责任的归责原则,或适用《合同法》总则的严格责任原则,或适用损失确认区间适用法律的违约责任的归责原则。