Multi-item EOQ model while demand is sales price and price break sensitive

In this paper, the authors study a multi-item deterministic EOQ (economic order quantity) model for a vendor when the demand rate of the essential commodities decreases quadratically with increasing sales price and increase exponentially with increasing level of price breaks. A price discount is offered to the customers when the revenue of the vendor crosses the level of price break. The main aim of the present article is to find out the optimal order quantities, optimal selling prices and optimal level of price break in order to maximize the average profit of the whole products. Numerical examples are also illustrated to test of our proposed model.     

RETAIL PRICE REGULATION AND THE OPTION TO DELAY

ABSTRACT ** :  This paper examines a two-period model of an investment decision in a network industry characterized by demand uncertainty, economies of scale and sunk costs. In the absence of regulation we identify the market conditions under which a monopolist decides to invest early as well as the underlying overall welfare output. In a regulated environment, we consider a monopolist who faces no downstream (final good) competition but is subject to retail price regulation. We identify the welfare-maximizing regulated prices when the unregulated market outcome is set as the benchmark. We show that if the regulator can commit to ex post regulation – that is, regulated prices that are contingent to future demand realization – then regulated prices that allow the firm to recover its total costs of production are welfare-maximizing. Thus, under ex post price regulation there is no need to compensate the regulated firm for the option to delay that it foregoes when investing today. We argue, however, that regulators cannot make this type of commitment and, therefore, price regulation is often ex ante – that is, regulated prices are not contingent to future demand. We show that the optimal ex ante regulation, and the extent to which regulated prices need to incorporate an option to delay, depend on the nature of demand uncertainty.     

The optimal pricing of computer software and other products with high switching costs

The paper studies the determinants of the optimum prices of computer programs and their upgrades. It is based on the notion that because of the human capital invested in the use of a computer program by its user, this product has high switching costs, and on the finding that pirates are responsible for generating over 80% of new software sales. A model to maximize the present value of the program to the program house is constructed to determine the optimal prices of initial programs and for those upgrading their programs. It is shown that an upward shift of the demand function of upgrades leads to an increase in the optimum price of upgrades and to a decline in that of initial copies. However, and upward shift of the demand function of initial copies increases their optimal price without affecting that of upgrades. The price of upgrades is higher, the smaller (greater) the absolute value of the derivative of the initial copy demand with respect to the upgrade price (its own price), the smaller the number of pirates purchasing their initial legitimate copies and, normally, the later they do it. The prices of these goods often move in opposite directions despite the fact that the goods can best be characterized as complements. Copy-protection is generally not optimal with standard programs having competing unprotected products, and it is normally optimal to use a drug pusher's strategy in pricing and in other respects: get the user hooked and cash in on the upgrades.     

Optimal Worksharing Discounts

Forty percent of first-class mail is workshared, meaning that mailers perform part of the postal service work, such as sorting, in exchange for a price discount. Here the optimal discount is shown to depend on whether mailers workshare all their mail. If they do, their marginal decisions will affect usage of the mail, and the normal Ramsey inverse-elasticity rule will apply. If they do not, and their marginal decision involves the amount of their worksharing, then worksharing supply elasticities play a role in the optimal discount. In the latter case, margins will be greater for workshared letters. Problems in balancing these solutions, and in estimating cost savings from worksharing, are also discussed.     

Monopoly Price Dispersion Under Demand Uncertainty

When a monopolist sets its price before its demand is known, then it may set more than one price and limit the availability of its output at lower prices. This article adds demand uncertainty and price rigidities to the standard model of monopoly pricing. When there are two states of demand and the ex post monopoly price is greater when demand is high then the monopolist's optimal ex ante pricing strategy is to set two prices and limit purchases at the lower price.     

碳交易及补贴机制下供应链差别定价研究

研究了碳交易机制、补贴机制以及碳交易及补贴机制下,一个二级供应链中普通产品和低碳产品竞争的差别定价策略,通过求解Stackelberg博弈模型得出单一的补贴政策并不能激励制造商进行节能减排,应与碳交易机制结合使用,其节能减排效果优于单一的碳交易机制。最后通过一个算例分析验证了碳交易及补贴机制的有效性。研究表明：碳交易价格升高到一定程度时,普通产品的零售价批发价均升高,低碳产品的价格均下降,普通产品的销量下降,低碳产品销量上升,碳排放总量下降;随着低碳补贴的增加,普通产品的零售价,低碳产品的批发价、零售价均降低,普通产品的销量下降,低碳产品的销量上升,其中低碳产品的价格和需求量对低碳补贴的反应更加敏感,使碳排放量降低的同时还提高了制造商和零售商的利润。     

Integrating dynamic pricing and inventory control for fresh‐agri product under consumer choice

In this article, we investigate a joint pricing and inventory problem for a retailer selling fresh‐agri products (FAPs) with two‐period shelf lifetime in a dynamic stochastic setting, where new and old FAPs are on sale simultaneously. At the beginning of each period, the retailer makes ordering decision for new FAP and sets regular and discount prices for new and old inventories, respectively. After demand realisation, the expired leftover is disposed and unexpired inventory is carried to the next period, for continuing selling. Unmet demand of all FAPs is backordered. The objective is to maximise the total expected discount profit over the whole planning horizon. We present a price dependent, stochastic dynamic programming model taking into account zero lead‐time, linear ordering costs, inventory holding and backlogging costs, as well as disposal cost. As the influence of the perishability, each customer selects his preferred choice based on the utility of product price and quality. By the way of constructing demand rate vector, the original formulation can be transferred to be jointly concave and tractable. Finally, we characterise the optimal policy and develop effective methods to solve the problem. We also conduct numerical studies to further characterise the optimal policy, and to evaluate the loss of efficiency under static policies when compared to the optimal dynamic policy.     

PRICE DYNAMICS WITH CUSTOMER MARKETS

Using microdata from a U.S. retailer we document that customer turnover responds to pricing. We study the optimal price setting of a firm when its demand has an extensive margin that is elastic to price due to customers' opportunity to search for an alternative supplier. The price pass‐through of idiosyncratic productivity shocks is incomplete, with the most productive firms passing through more. Firm demand is more persistent than price. Higher demand is associated with lower markups due to higher search intensity, despite flexible prices. We find empirical support for these predictions in microdata from the retail industry.     

Bundling and Optimal Auctions of Multiple Products

We study the optimal ( i.e. revenue maximizing) auction of multiple products. We make three major points. First, we extend the relationship between price discrimination and optimal auctions from the single-product case to the multiple-product case. A monopolist setting prices for multiple products may offer discounts on purchases of bundles of products; similarly, the optimal auction of multiple products facilitates price discrimination by allocating products inefficiently to customers who are willing to purchase both products. Second, we demonstrate that optimal auctions are qualitatively distinct from monopoly sales of multiple products. Because of uncertainty about the values of other consumers, two products are bundled probabilistically in an optimal auction for a customer who is willing to buy both of them. A customer may then receive a discount on a lower-valued product without receiving a higher-valued product. Third, we show that in an optimal auction of two products the allocation of one product may vary with the amount of competition for the other product.     

The effects of price on household demand for food and calories in poor countries: are our databases giving reliable estimates?

Food price policy relies heavily on estimated price elasticities of food demand to help balance the nutritional and economic objectives in poor countries. Economists use either unit values (ratios of household expenditure to quantity purchased) or community prices (enumerated from vendors in local markets) as proxies for market prices when estimating price elasticities with household survey data. Biases are believed to result from using unit values, due to measurement error and quality effects, but evidence on this issue is lacking and even less is known about community prices. This article provides an empirical evidence from Vietnam, which suggests that economists should exercise caution when estimating price elasticities from household surveys. A 14-food demand system is estimated alternatively with unit values or community prices, and the elasticity of calories with respect to rice prices is calculated. This elasticity is more than twice as large (?0.54 versus ?0.22) when community prices are used rather than unit values. Hence, conclusions about the nutritional effects of rice price increases appear sensitive to data choices made by economists. More generally, this discrepancy suggests that the household survey databases commonly used by economists may not provide reliable estimates.     

Strategic Consumption Complementarities: Can Price Flexibility Eliminate Inefficiencies and Instability?

Generally, two facts occur with strategic complementarities and fixed prices: (i) the equilibria are multiple and (ii) if the complementarities are strong, the law of demand is violated and the equilibrium is unstable. In this paper, we analyse the effect of price flexibility on these features as well as on market welfare properties. Assuming an exchange economy with H agents consuming two goods with one strategic complement, we show that flexibility of prices may remove both the multiplicity of the equilibria and the instability of behavior when the externalities are strong. Moreover, we find conditions to correct instability when it is caused by perverse wealth effects. When preferences are quasilinear and identical, if the externality is beneficial, any equilibrium is Pareto optimal despite the externality. But if the externality is detrimental, corrections are required.     

Dynamic demand and noncompetitive pricing strategies

This paper studies optimal noncompetitive pricing strategies when the evolution of demand is the result of intertemporal considerations. Two different hypotheses of price expectations (myopia and perfect foresight) are treated. The major implication is that the slight modification from an instantaneous to a very fast consumer reaction may completely modify a monopolist's price strategy. More precisely, the price strategy should be volatile if the equilibrium demand is convex, independent whether the consumers act myopically or employ rational expectations. On the other hand, asynchronous dynamics (e.g., due to competitive fringe supply or different segments of demand) cannot explain even damped price oscillations. The equilibrium price strategy of the noncompetitive supplier exceeds the static rule if consumers employ myopic expectations; rational expectations may lead to prices above or below the static rule depending on the rate of discount.I am grateful for the helpful and elaborate comments from three anonymous referees.     

Estimating a socially optimal water price for irrigation versus an environmentally optimal water price through the use of Geographical Information Systems and Social Accounting Matrices

This article develops a method for establishing water prices and their effects in order to provide policy makers an environmentally and socially optimal range of regional prices for irrigation water. Two prices are determined. The “environmentally optimal price” of water is defined as the one that internalizes the environmental costs generated by agricultural consumption. The “social optimally price” of water is defined as the one that maximizes levies on water for agriculture without affecting the regional economy. The environmentally optimal price is calculated with an economic model built over a Geographical Information System (GIS) that allows the economic quantification and valuation of the environmental cost of water in different basins. The optimal price is calculated with a demand curve for irrigation water introduced into a Social Accounting Matrix (SAM) to observe if the regional economy can accept higher prices without affecting the regional GDP. Potential water prices are established, ranging from prices that minimize the negative impact in the regional economy to those that totally internalize the environmental cost of water.     

Worksharing and factor prices

The aspect of worksharing on which this paper concentrates concerns an increase in the firm's workforce offset by a reduction in average working hours. Emphasis is given to the effect of relative factor prices on worksharing within a model structure which includes the capital stock and worker productivity as endogenous inputs. Factor prices include all the main categories of wage and non-wage labour payments as well as the user cost of capital. Special attention is given to the role of non-wages, both quasi-fixed and variable. An analysis of the effects of marginal employment subsidies on worksharing is also considered with reference to the French ‘solidarity contracts’.     

Worksharing and Access Discounts in the Postal Sector with Asymmetric Information*

This paper analyzes the optimal worksharing and access amounts granted to mailers and entrants in a liberalized postal sector when there is asymmetric information about the Post Office’s (PO) costs. I show that when the regulator is unable to ascertain which part of the total cost of sorting has to be attributed to each sorting facility, the optimal “access discount” given to entrants is set in a pro-competitive way. This facilitates the entry of firms that are less efficient than the PO. However, the optimal “worksharing discount” may prevent the entry of mailers that are more efficient than the PO.     

Durable-Goods Monopoly with Varying Demand

This paper solves for the profit-maximizing strategy of a durable-goods monopolist when incoming demand varies over time. We first characterize the consumers' optimal purchasing decision by a cut-off rule. We then show that, under a monotonicity condition, the profit-maximizing cut-offs can be derived through a myopic algorithm, which has an intuitive marginal revenue interpretation. Consumers' ability to delay creates an asymmetry in the optimal price path, which exhibits fast increases and slow decreases. This asymmetry creates an upward bias in the level of prices, pushing them above the price charged by a firm facing the average level of demand. The optimal policy outperforms renting and can be implemented by a time-consistent best-price provision.     

On generic vs. brand promotion of farm products in foreign markets

Farm groups and their governments spend millions of dollars each year advertising agricultural products in international markets. Intuitively, country-of-origin or ‘brand’ advertising should be more profitable than generic advertising in that it enhances product differentiation and reduces free riding. However, unlike generic advertising, brand advertising decreases the demand for competing imports and lowers their prices when supplies are upward sloping. In addition to inviting retaliation, the decline in the prices of competing products erodes the price of the advertised product through second-round or ‘market feedback’ effects. In this study, we develop a generalized model for assessing the relative effectiveness of generic and brand promotion in the international market when products are differentiated by source origin and supplies are uncontrolled. Applying the model to US beef promotion in Japan, we find that when brand and generic advertising are equally efficient in the sense that they cause equivalent horizontal shifts in the group and product-specific demand curves, generic advertising is indeed more profitable for most of the relevant parameter space. Distributional analysis suggests that, with equal export supply elasticities, the gross benefits of generic advertising are distributed across exporters in proportion to the expenditure elasticities for the products in question.     

Price Dynamics in Repeat-Purchase Markets*

A retail market in which customers repeat purchase is modelled. When customer movement between firms is sluggish, price overshooting characterizes firms' optimal response to demand or cost shocks. Thus retail prices would be predicted to be more variable than wholesale prices, a prediction at variance with empirical evidence. Uncertainty in demand and customer imperfect information are introduced into the model to attempt to reconcile this inconsistency between theory and evidence. The introduction of demand uncertainty actually increases the magnitude of price overshooting. By contrast, the introduction of imperfect customer information reduces the variability in retail prices.     

Optimal punishments in linear duopoly supergames with product differentiation

We analyze optimal penal codes in both Bertrand and Cournot supergames with product differentiation. We prove that the relationship between optimal punishments and the security level (individually rational discounted profit stream) depends critically on the degree of supermodularity in the stage game, using a linear duopoly supergame with product differentiation. The security level in the punishment phase is reached only under extreme supermodularity, i.e., when products are perfect substitutes and firms are price setters. Finally, we show that Abreu's rule cannot be implemented under Cournot behavior and strong demand complementarity between products.     

Fixed price plus rationing: an experiment

This paper theoretically and experimentally explores a fixed price mechanism in which, if aggregate demand exceeds supply, bidders are proportionally rationed. If demand is uncertain, in equilibrium bidders overstate their true demand in order to alleviate the effects of being rationed. This effect is the more intense the lower the price, and bids reach their upper limit for sufficiently low prices. In the experiment we observe a significant proportion of equilibrium play. However, subjects tend to overbid the equilibrium strategy when prices are high and underbid when prices are low. We explain the experimental evidence by a simple model in which the probability of a deviation is decreasing in the expected loss associated with it.

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