Self-serving altruistic behavior and its implications for consumption,trade,and foreign exchange rates

Abstract

Altruistic behavior is typically defined as an action(s) that could increase another’s welfare. This can result from motivations that are self-serving. For example, on a national level, it affects a countries’ consumption through an expansion of trade. When growth in one country’s consumption raises marginal utility of consumption in another country, altruism can be considered self-serving. In this paper, using this framework, economic reciprocity in countries’ preferences are introduced to highlight the importance of trade. Our results indicate an existence of self-serving altruism when both countries are reciprocally self-altruistic. The underlying results depend on countries’ preferences, cost structure and trades with implications for consumption and prices. Since each country’s utility function includes both domestic and foreign countries’ consumption, we use a multi-agent Cournot model. In this paper, the price paid by one country for the growth of consumption by another country is defined as an altruistic premium. Besides the demand side, where inverse demand prices are set using a Nash conjecture, we study the supply side with an analysis of trade and determine optimal global supply. When supply capacities are constrained in one country (or in both), imports and exports modify the basic supply side economy. Different cases that may lead to purchasing power parity (PPP) are shown emphasizing both prices and global marginal costs. PPP in the supply side and in the demand side are distinguished. This paper shows that parity exists for prices under PPP, as well as for production costs. Under this framework, a number of international trade issues, including the effects of foreign exchange rates and the effects of altruism on prices with specific examples are elaborated.

Keywords

Altruism utility of consumption trade foreign exchange rate

1. Introduction

Altruistic consumption is generated when one country’s utility increases due to another country’s consumption. Countries promote internal employment and expand foreign trade to maintain their competitive advantage. Self-serving altruism can result from lower production costs and therefore lower domestic prices. Therefore, in a utilitarian sense, a countries’ utility of consumption may also include the consumption of another country. Using this definition, it is also self-serving and altruistic when a country’s utility cross-partial derivatives with respect to consumption are positive. Self-serving altruistic preferences can, on the one hand, be justified and thrive, contributing to increased trade and international aid. On the other hand, self-serving altruism may contribute to internal challenges due to structural economic changes, e.g., migration, of jobs, capital and industry; sovereign states’ increased interdependence challenges traditional models of sovereign governance. Self-serving altruistic considerations underlie the evolution of globalization and its gating (through protectionist measures, restrictions and trade barriers).

Globalization has opened domestic economy with increased international trade and investments fueling consumption and providing more business opportunities alongside economic and industrial specialization. Thus, increasing exchanges between countries and raising consumption and global supply synchronously with the growth of complex global supply chains, it contributed further to greater interdependence between nations. At the same time, we observe that sovereign states have become more gated, with an increasing international inequality and consequent political repercussions. These circumstances raise the following questions. Can consumption of “plenty” in one country exist alongside an under-consuming nation, and can this state remain stable? In other words, can a rich country remain oblivious to the potential risks emanating from the plight of struggling neighbors as well as more distant ones?

A number of papers emphasizing philanthropic behavior have been added to the literature of altruistic consumption. These include Samuelson [36], Simon [37], Becker [6], Bergstrom [7], Bulow et al. [8], Kolm [25], Andreoni [1,2], Wintrobe [42], and many others. For example, Elster [12] studies the sources of altruistic motivations and emphasizes their political origins. He refers to a “warm glow” effect which describes the satisfaction derived from the act of giving, and also provides different examples explaining altruistic behavior caused by interest.1 The purpose of this paper is to pursue this train of thought and establish the relationship of trade between countries and its effect on foreign exchange in this context.

The importance of reciprocity in social relations and its connection to altruism, with evidence and motivations, was studied by Kolm [26]. He covered different types of reciprocity and their connection to different social relations: comparative-reciprocity’s relationship to fairness, liking-reciprocity’s relationship to altruism, and continuation-reciprocity’s relationship to joint interest. Moreover, he describes the relationship between exchanges and markets with reciprocity and opposes purely self-interested exchanges. Georg Simmel states that “social equilibrium and cohesion could not exist without the reciprocity of service and return service. All contacts among men rest on the scheme of giving and returning the equivalence” (see Frisby [16], p. 298). Reciprocity can be exemplified by the favorable treatment of others because they treat you favorably as well.

In addition, experimental evidence, particularly from experimental games, measures different types of altruism and indicates an existence of motivations by preferences, e.g., other-regarding preferences, as distinct from the material self-interested preferences. This is stressed in Fehr and Schmidt [13], p. 683, as “fundamental questions of social life cannot be understood on the basis of a self-interest model. The evidence indicates that other-regarding preferences are important for bilateral negotiations, for the enforcement of social norms, for understanding the functioning of markets and economic incentives.” Emphasizing the interaction between agents with different preferences, they also argue that behavior of a selfish agent can be changed by an agent whose preferences are other-regarding. Moreover, they highlighted the importance of an “ultimatum game” (where a fixed amount of money is divided between a proposer and responder) for contributing in people’s understanding that “the self-interest hypothesis is problematic” as the results of this game indicated that “many responders do not behave in a self-interest maximizing manner” (Fehr and Schmidt [13], pp. 621–622). Among the variety of games, pure altruism can be shown to result in dictator games (where allocations are dictated by the proposer) which are extensively explained in Forsythe et al. [14], Andreoni and Miller [3], and Fehr and Schmidt [13]. In particular, Andreoni and Miller [3] studied behavior of subjects under the general axiom of revealed preferences (or GARP) and observed a presence of consistent altruistic preferences. They concluded that “it is indeed possible to capture altruistic choices with quasi-concave utility functions for individuals-altruism is rational” (Andreoni and Miller [3], p. 750).

There are many empirical studies, e.g., Holmes [23] and Popp [33], which have attempted to test for the presence of altruism (pure/strong and self-serving/weak) in the environmental protection of future generations. Altruistic motivation is a well-established concept in the environmental preservation literature, where one entity’s welfare frequently depends upon the welfare of another. Naturally, one is interested in the costs to society and to business. Popp [33] showed the existence of weak altruism, which is somewhere between pure altruism and pure self-interest. In addition, altruism analysis can be applied to countries where one country benefits from another country’s policies to protect the environment. Besides the intergenerational impact, environmental externalities resulting from environmental degradation, e.g., greenhouse gas buildup, include the risks not only of the costs to the polluting country itself, but also to other countries, especially as a result of phenomena such as global climate change and SO₂ pollution of water, as identified in Frankel [15]. Thus, a risk management approach for the externalities caused by environmental damage can be adopted. Incorporating altruism into environmental issues is complicated for a variety of reasons. First, by definition, environmental effects are often global. Consequently however, distinguishing self-interest from altruism is not obvious. However, some environmental effects have pronounced local effects. In these cases, altruistic behavior may be more easily identified and thus it is a far more universal theme that affects both societies at large as well as their economic policies.

For example, a number of studies address the relationships between environment and trade, as well as the impacts of globalization and international cooperation. These include Dean [11], Copeland and Taylor [10], Barret [4], and Frankel [15]. In particular, Frankel [15] emphasizes the positive impact of both trade and openness on the environment through, for example, the purchasing power of environment conscious consumers. One obvious theoretical way to estimate altruistic costs would be to use Cournot competition, but with increased costs (due to environmental policy). To calculate the Nash equilibrium, the best response functions of firms would first be calculated and a new equilibrium computed. Moreover, an “altruistic premium” may then be defined as the difference between the equilibrium profits with/without environmental cost.

In a global economic environment fueled by global consumption growth, consumption saturation (and therefore stable or declining domestic markets) can lead to economic stagnation with foreign consumption needed to maintain and expand economic growth. As a result, the traditional presumption that consumption preferences are “selfish”, underlying traditional economic assumptions may be misleading. When self-serving altruism is combined with economic reciprocity (embedded in countries’ preferences), globalization can be a “win-win” economic development. Such situations have both consumption and price implications, depending on countries’ preferences, their cost structures and their trades.

Based on a Cournot model for two countries, both faced with demand and supply, this paper presents a utility function of both countries’ consumption, and defines an “altruism premium” by the price one country pays to expand consumption in another. Given both consumption demand and supply sides including trade between these countries we use a Nash conjecture to determine countries’ inverse demand functions. This implies that consumption in one country takes for granted consumption in another when deciding how much to consume as a function of the consumption price. On the supply side, optimal global supply results in prices that are linearly related and function of the countries preferences. We show different circumstances that may lead to purchasing power parity (PPP), in particular the case when prices are calculated net of their global marginal costs. When supply capacities are constrained in one country or in both, imports and exports alter the basic supply side economy. Different cases outlining the implications of such situations are considered.

In this framework, we elaborate a number of international trade issues such as the effects of the relative efficiency of countries’ production functions (technologies, resource constraints etc.) and the effects of foreign exchange rates (see also Tapiero [40]; Nyambuu and Tapiero [30]).

2. The demand sides, altruistic consumption preferences

Empirical work suggests that altruistic behavior is mostly prevalent in environmental conservation. Simon [37] and Solow [39] present definitions of sustainability that lead to altruistic behavior, e.g., show how a present generation should care for future generations. Solow [38], p. 181, suggests that one defines sustainability as “an obligation to conduct ourselves so that we leave to the future the option or the capacity to be as well off as we are.”

We can distinguish between two cases where beneficial actions’ returns accrue to future generations, accrue to a specific region or classification and do not benefit the originating party. Difficulties stem from the fact that economics does not capture human intention, only action. It is difficult, using economic categories to capture and distinguish between values, needs, self-interest, and, specifically, altruism. Economists are, of course, aware of this; hence the term “revealed preferences,” i.e., the theory that allows for things like value to be revealed by analyzing what consumers are willing to pay for them and what they will accept in exchange for their loss; see Goodstein [17] for further discussion. Two issues arise. First, human interests originate from diverse sources, some more easily traded than others (see Sagoff [35]). Second, most established methodologies, e.g., game theory, preference orderings, have difficulty with the issues concerning future generations, the exact place where Popp [33] seeks altruism. Popp’s approach suggests that we look at deviations from traditional optimal solutions and interpret these as altruistic.

Becker [6] refers to Adam Smith’s (1853) “The Wealth of Nations”, stating that altruism is important in a family while markets are selfish. Using this presumption Becker proposes an economic utility framework for one based on another (see also Becker [5,6], Collard [9], Hammond [19], Margolis [29] and Rabin [34]), emphasizing the notion of “prior” feelings and reciprocity. In the context of this paper, altruism essentially questions “Is increased utility of consumption in one country contributes to increased utility in the other?” Such a question, in an international setting however, implies and underlies a propensity to trade, each bettering itself by the exchange (reflected in the other’s inverse demand function). The pursuit of collaborative and “politically philanthropic or foreign aid pursuits” are additional means that point out to self-serving altruism in international affairs. For a review of related trade questions, we refer to Grossman and Rogoff [18], Obstfeld and Rogoff [31], Helpman and Krugman [20], and Krugman [27].

Typical altruistic consumption preferences imply that a growth of consumption in another country increases one’s own country utility. Explicitly, say that the utility of consumption in a country is $u_{i} (Q_{1}, Q_{2})$ with $Q_{1}$ and $Q_{2}$ denoting consumption in countries 1 and 2, respectively with $\frac{\partial u_{i}}{\partial Q_{i}} > 0$ , $\frac{\partial^{2} u_{i}}{\partial Q_{i}^{2}} < 0$ . If the derivative $\frac{\partial u_{i}}{\partial Q_{j}} > 0$ is strictly positive, we shall state that country i’s utility is altruistic, and it is not if $\frac{\partial u_{i}}{\partial Q_{j}} ⩽ 0$ . If $\frac{\partial u_{i}^{2}}{\partial Q_{i} \partial Q_{j}} > 0$ , then the altruism is self-serving as an increase of consumption in one country does increase the marginal utility of consumption in the other. In the first case, it implies that an increase in a domestic consumption increases its utility when consumption of the foreign country also increases. A rationality of this proposition (in addition to the common philanthropic interpretation) is based on the fact that an increased consumption induces additional needs and therefore contributes to economic growth in both countries. Inversely, in the second case, consumption growth in one country, which is not compensated by a growth in the other country, leads to greater disparities and therefore to potential adverse consequences as discussed above, such as discontent, potential upheaval, and rogue States. Note that the utility functions $u_{i} (Q_{i}, Q_{j})$ can also be implicit in another country’s utility function such as: $u_{i} (Q_{i}, u_{j} (Q_{j}))$ or $u_{i} (Q_{i}, Q_{j}, u_{j} (Q_{i}, Q_{j}))$ . In these cases, we obtain slightly more complex expressions of the utility function of consumption assumed above.

3. Two-country Cournot model

In a global economic world with a global supply capacity that outstrips demand, growth is essentially fueled by an increase in demand. Lacking the demand, such an economy may be declining. Inversely, when consumption is rationed due to supply capacity (for example, due to basic materials or production capacity), their effects on consumption distribution between countries are pronounced as well, leading to international disparities. In both cases, the demand sides of ample and rationed supply problems are defined by the following Cournot consumption model: $\begin{matrix} (1) & \begin{matrix} \underset{Q_{i}}{Max} {u_{i} (Q_{i}, Q_{j}) - π_{i} Q_{i}} \\ Subject to : Q_{1} + Q_{2} ⩽ \bar{q} : Ample Supply or \\ Q_{1} + Q_{2} ⩾ \bar{q} : Rationing \end{matrix} \end{matrix}$ where $(π_{1}, π_{2})$ denote the inverse demand functions of both countries and $\bar{q}$ shows the global production capacity. When supply is rationed and demand is greater than supply, $Q_{1} + Q_{2} > \bar{q}$ , and therefore $Q_{2} = \bar{q} - Q_{1}$ , while, for ample supply, the capacity inequality constraint is not effective.

The cost of global supply, including the cost of trade, is given by: $C (\bar{Q})$ with $\bar{Q} = Q_{1} + Q_{2}$ . For clarity, assume a global production function $C ({\bar{q}}_{1}, {\bar{q}}_{2} | q_{1}^{c}, q_{2}^{c})$ where $q_{1}^{c}$ , $q_{2}^{c}$ are the countries’ supply capacities and ${\bar{q}}_{1}$ , ${\bar{q}}_{2}$ are the countries’ production function for both respective domestic markets $(q_{1}, q_{2})$ and exports, $(q_{12}, q_{21})$ . In this case, ${\bar{q}}_{1} = q_{1} + q_{12} ⩽ q_{1}^{c}$ , ${\bar{q}}_{2} = q_{2} + q_{21} ⩽ q_{2}^{c}$ , ${\bar{q}}_{1} + {\bar{q}}_{2} = \bar{q}$ , $Q_{1} = q_{1} + q_{21}$ , $Q_{2} = q_{2} + q_{12}$ . To simplify our notation, we define a global production function by $C (\bar{Q}) = C (\bar{Q} : {\bar{q}}_{1}, {\bar{q}}_{2})$ with $\partial C (\bar{Q}) / \partial Q_{i}$ the global marginal cost of production for consumption in country i. When countries’ consumption and production are independent (namely, there is no trade and altruism), the supply side in each country is determined by the countries’ production functions or $C_{i} (Q_{i})$ , $i = 1, 2$ . Namely, the supply price is determined by the marginal cost of production, and the domestic supply price is set to: $π_{i} = \partial C_{i} (q_{i}) / \partial q_{i}$ while the demand price side is $\partial u_{i} (Q_{i}) / Q_{i} = π_{i}$ and therefore, $π_{i} = \partial C_{i} (q_{i}) / \partial q_{i} = \partial u_{i} (Q_{i}) / Q_{i}$ . With altruistic preferences, such relationships are more complex as one country may supply the other (and therefore engage in trade) and thereby alter both its costs of production and the domestic utility of consumption. Altruism may thus affect countries’ prices (and thus their foreign exchange rates in case of a PPP). Under the basic assumptions stated above, we have demand and supply sides prices given by the following Proposition 1:

Proposition 1.
Let the utility functions of consumption be $u_{i} (Q_{i}, Q_{j})$ , $i, j = 1, 2$ , $i \neq j$ , $\frac{\partial u_{i}}{\partial Q_{i}} > 0$ , $\frac{\partial^{2} u_{i}}{\partial Q_{i}^{2}} < 0$ as well as $\frac{\partial u_{i}}{\partial Q_{j}} > (or ⩽) 0$ , $\frac{\partial u_{j}}{\partial Q_{i}} > (or ⩽) 0$ and set: $U_{i} = \frac{\partial u_{i}}{\partial Q_{i}} + \frac{\partial u_{j}}{\partial Q_{i}}$ , $j \neq i$ . Then, Nash equilibrium inverse demand consumption prices and supply side global marginal costs in both countries are given by the following simultaneous system of equations: $\begin{array}{l} (2) & \begin{matrix} (π_{1} - \frac{\partial u_{1}}{\partial Q_{1}}) (π_{2} - \frac{\partial u_{2}}{\partial Q_{2}}) \\ = \frac{\partial u_{2}}{\partial Q_{1}} \frac{\partial u_{1}}{\partial Q_{2}} or \\ (M P_{1}) (M P_{2}) = M U_{12} M U_{21} \end{matrix} \\ (3) & \begin{matrix} \frac{π_{1} - \frac{\partial C (\bar{Q})}{\partial Q_{1}}}{π_{2} - \frac{\partial C (\bar{Q})}{\partial Q_{2}}} = \frac{U_{1} - \frac{\partial C (\bar{Q})}{\partial Q_{1}}}{U_{2} - \frac{\partial C (\bar{Q})}{\partial Q_{2}}} or \\ \frac{M P_{1}}{M P_{2}} = \frac{N e t U_{1}}{N e t U_{2}} \end{matrix} \end{array}$ where U stands for utility, Q represents consumption, π is price, $M P$ denotes marginal profit, $M U$ shows marginal utility, $N e t U$ denotes net utility.
Proof.
See the Appendix. □

From equation (2), we see that if one of the parties is not altruistic, then $(M P_{1}) (M P_{2}) = 0$ and therefore, $(M P_{1}) = 0$ , or $(M P_{2}) = 0$ or both are null. From equation (3), we derive the following relationship between the marginal profits and net utilities where the product of marginal profit in country 1 and net utility of country 2 equals the product of marginal profit in country 2 and net utility of country 1: $\begin{matrix} (4) & M P_{1} N e t U_{2} = M P_{2} N e t U_{1} \end{matrix}$ Say countries’ utilities of consumption are independent, or $\frac{\partial u_{2}}{\partial Q_{1}} = \frac{\partial u_{1}}{\partial Q_{2}} = 0$ . This yields $π_{1}^{} = \frac{\partial u_{1}}{\partial Q_{1}}$ and $π_{2}^{} = \frac{\partial u_{2}}{\partial Q_{2}}$ . In Tapiero [41], two different prices are distinguished with an emphasis on “willing to pay” ( $π_{i}^{}$ ) and “actual pay” ( $π_{i}$ ) for consumption. Inserting these into equation (2), we have: $(π_{1} - π_{1}^{}) (π_{2} - π_{1}^{}) = \frac{\partial u_{2}}{\partial Q_{1}} \frac{\partial u_{1}}{\partial Q_{2}}$ which implies that for reciprocal utilities and non-reciprocal utilities: $\begin{matrix} (5) & \{\begin{matrix} 0 < (π_{1} - π_{1}^{}) (π_{2} - π_{1}^{}) \\ if \frac{\partial u_{2}}{\partial Q_{1}} \frac{\partial u_{1}}{\partial Q_{2}} > 0 : Reciprocal utilities \\ 0 > (π_{1} - π_{1}^{}) (π_{2} - π_{1}^{}) \\ if \frac{\partial u_{2}}{\partial Q_{1}} \frac{\partial u_{1}}{\partial Q_{2}} < 0 : Non-reciprocal utilities \end{matrix} \end{matrix}$ This implies that reciprocity leads in both countries to higher or to lower prices. When prices are lower, altruism is self-serving. When the utilities are not reciprocal, prices in one country will be lower than the competition (one country) price while it will be higher for the other country: $\begin{matrix} (6) & \begin{matrix} (π_{1} - \frac{\partial u_{1}}{\partial Q_{1}}) = \frac{\frac{\partial u_{2}}{\partial Q_{1}} \frac{\partial u_{1}}{\partial Q_{2}}}{(π_{2} - \frac{\partial u_{2}}{\partial Q_{2}})} > 0, \\ \frac{\partial u_{2}}{\partial Q_{1}} < 0, \frac{\partial u_{1}}{\partial Q_{2}} > 0, π_{2} < \frac{\partial u_{2}}{\partial Q_{2}} \end{matrix} \end{matrix}$ While the premium price for the first country is positive, it is negative for the other (resulting in an altruistic transfer from one to the another): $\begin{matrix} (7) & \begin{matrix} Δ π_{1} = (π_{1} - \frac{\partial u_{1}}{\partial Q_{1}} - \frac{\frac{\partial u_{2}}{\partial Q_{1}} \frac{\partial u_{1}}{\partial Q_{2}}}{(π_{2} - \frac{\partial u_{2}}{\partial Q_{2}})}) > 0 and \\ Δ π_{2} = (π_{2} - \frac{\partial u_{2}}{\partial Q_{2}} - \frac{\frac{\partial u_{2}}{\partial Q_{1}} \frac{\partial u_{1}}{\partial Q_{2}}}{(π_{1} - \frac{\partial u_{1}}{\partial Q_{1}})}) < 0 \end{matrix} \end{matrix}$ As a result, altruism can be self-serving if two countries are reciprocally altruistic. If both countries have reciprocal utilities but are not altruistic, i.e. $\frac{\partial u_{2}}{\partial Q_{1}} < 0$ , $\frac{\partial u_{1}}{\partial Q_{2}} < 0$ , then prices can be higher than $π_{i}^{}$ for country i as seen below due to increased marginal costs of supply.

The consumption supply cost effects are defined by equation (3). Setting $c_{i} = \frac{\partial C (\bar{Q})}{\partial Q_{i}}$ as marginal cost of supply in a country (including the import and exports costs of supply), then a solution of equations (2) and (3) yields a linear price relationship as indicated by equation (8). This relationship indicates a price net of global supply costs PPP. In other words, when factor inputs are accounted for, the product specific PPP is maintained since: $\begin{matrix} (8) & \begin{matrix} π_{1} - c_{1} = \frac{U_{1} - c_{1}}{U_{2} - c_{2}} (π_{2} - c_{2}) or \\ \frac{π_{1} - c_{1}}{π_{2} - c_{2}} = \frac{U_{1} - c_{1}}{U_{2} - c_{2}} \end{matrix} \end{matrix}$ Say that $ξ = \frac{π_{1}}{π_{2}}$ and let $ρ = \frac{π_{1} - c_{1}}{π_{2} - c_{2}}$ then $ξ = ρ + (c_{1} - ρ c_{2}) / π_{2}$ and $ξ = ρ$ if $c_{1} - ρ c_{2} = 0$ , in which case, $ρ = c_{1} / c_{2}$ which indicates both a price and production costs parity. In other words, if PPP holds in input factors, it also holds in finished products. A FX rate (price) is thus determined by the prices of say a given product and the supply (and production) costs of its input factors. For example, say that in country 2 marginal costs are much lower than in country 1, and let $ρ^{'}$ be the “product specific exchange rate”, then, $ρ^{'} < ρ$ . A solution of (2) and (3) yields a quadratic equation: $\begin{matrix} (9) & \{\begin{matrix} ρ π_{2}^{2} - π_{2} θ - μ = 0, \\ θ = ((\frac{\partial u_{1}}{\partial Q_{1}} - c_{1}) + ρ (c_{2} + \frac{\partial u_{2}}{\partial Q_{2}})) and \\ μ = \frac{\partial u_{2}}{\partial Q_{1}} \frac{\partial u_{1}}{\partial Q_{2}} + (c_{1} - ρ c_{2} - \frac{\partial u_{1}}{\partial Q_{1}}) \frac{\partial u_{2}}{\partial Q_{2}} \end{matrix} \end{matrix}$ Thus, prices are defined by: $\begin{matrix} (10) & π_{2}^{o} = (\frac{θ}{2 ρ}) (1 + \sqrt{1 + \frac{4 μ ρ}{θ^{2}}}) \end{matrix}$ Assuming that $4 \frac{ρ μ}{θ^{2}} < 1$ we have $\sqrt{1 + 4 \frac{ρ μ}{θ^{2}}} = 1 + 4 \frac{ρ μ}{θ^{2}}$ and therefore $π_{2}^{o} = \frac{θ}{ρ} + \frac{2 μ}{θ}$ . In this case, we have a FX rate: $\begin{array}{l} ξ & = \frac{π_{1}^{o}}{π_{2}^{o}} = ρ + \frac{c_{1} - ρ c_{2}}{π_{2}^{o}} \approx ρ + \frac{c_{1} - ρ c_{2}}{\frac{θ}{ρ} + \frac{2 μ}{θ}} \\ (11) & \approx ρ (1 + \frac{θ (c_{1} - ρ c_{2})}{θ^{2} + 2 ρ μ}) \end{array}$ In other words, assuming a PPP, the FX rate price is a function of multiple factors that contribute to supplies marginal costs and countries’ prices as seen above. In the following figures, using the solutions in equation (10), we illustrate the changes in the FX rate in response to different values of ρ, θ, and marginal cost, c. Figure 1 shows the relationship between the FX rate, ξ, ρ and $c_{2}$ . We observe a narrow range of controllability (while ρ remains in the interval of $0 ⩽ ρ ⩽ 1$ ) where FX rate (ξ) is well-behaved. The range for $c_{2}$ , on the other hand, is the more expansive interval $(5, 10)$ . Outside of these ranges, ξ is explosive. Then, from $0 ⩽ ρ ⩽ 1$ , we derive $0 ⩽ π_{1} - c_{1} ⩽ π_{2} - c_{2}$ . This means $π_{1} ⩾ c_{1}$ and $π_{2} ⩾ c_{2}$ as well as $ξ - (1 / ξ) ⩽ (c_{1} - c_{2}) / π_{2}$ .

Fig. 1.
FX rate (ξ) and its relationship with ρ and $c_{2}$ . Note: z axis shows ξ, x axis shows ρ, and y axis shows $c_{2}$ . These variables range between $0 < ξ < 5$ , $- 2 < ρ < 5$ , and $- 2 < c_{2} < 10$ .

Furthermore, Fig. 2 illustrates the relationship between the FX rate (ξ), ρ and θ from different angles; this gives us a better view of the shape and the relationships between ξ and ρ and θ, and their classic saddle point, wherein ξ achieves a local maximum with respect to θ while achieving a local minimum with respect to ρ. In this figure, the saddle point is at around $(2, 2, 5)$ , and a local minimum is found at θ (by freezing ρ) while local maximum occurs at ρ (by freezing θ).

Fig. 2.
FX rate (ξ) and its relationship with ρ and θ. Note: z axis shows ξ, x axis is ρ, and y axis is θ. These variables range between $0 < ξ < 5$ , $- 3 < ρ < 5$ , $0 < θ < 10$ .

The effects of altruism on prices can then be examined by assessing their sensitivity to the utility altruism parameters. Their evaluation is necessarily complex as it is a function of both the utility and the consumption supply effects expressed by the marginal costs of production. Examples are considered in Section 4.
4. Marginal costs and trade

Say that each country has production capacities given by $q_{1}^{c}$ , $q_{2}^{c}$ and let the countries’ production (both domestic and exports) be $(q_{1}, q_{12})$ , $(q_{2}, q_{21})$ where $(q_{1} + q_{12} ⩽ q_{1}^{c})$ , $(q_{2} + q_{21} ⩽ q_{2}^{c})$ . Assume that the demand for consumption and its supplies are equal in all cases, or ( $q_{1} + q_{21} = Q_{1}$ ; $q_{2} + q_{12} = Q_{2}$ ). Assume no production to inventory and therefore global supply equals the global demand for consumption subject to the capacity constraints, or: $\begin{matrix} (12) & \begin{matrix} Q_{1} = q_{1} + q_{21}, Q_{2} = q_{2} + q_{12} and \\ {\bar{q}}_{1} = q_{1} + q_{12} ⩽ q_{1}^{c}, {\bar{q}}_{2} = q_{2} + q_{21} ⩽ q_{2}^{c} \end{matrix} \end{matrix}$ The average global marginal costs of countries 1 and 2 are then: $\begin{matrix} (13) & \{\begin{matrix} c_{1} = \frac{\partial C (\bar{Q})}{\partial Q_{1}} = \frac{\frac{\partial C_{1} ({\bar{q}}_{1})}{\partial {\bar{q}}_{1}} q_{1} + \frac{\partial C_{2} ({\bar{q}}_{2})}{\partial {\bar{q}}_{2}} q_{21} (1 + δ_{21})}{q_{1} + q_{21}}, \\ c_{2} = \frac{\partial C (\bar{Q})}{\partial Q_{2}} = \frac{\frac{\partial C_{2} ({\bar{q}}_{2})}{\partial {\bar{q}}_{2}} q_{2} + \frac{\partial C_{1} ({\bar{q}}_{1})}{\partial {\bar{q}}_{1}} q_{12} (1 + δ_{12})}{q_{2} + q_{12}} \end{matrix} \end{matrix}$ where $\frac{\partial C_{1} ({\bar{q}}_{1})}{\partial {\bar{q}}_{1}}$ is the marginal cost of production in country 1 (including the quantity produced for the domestic market and the quantity to be exported to the foreign market). Assuming economies of scale, the marginal cost of production has a negative second derivative $\frac{\partial^{2} C_{1} ({\bar{q}}_{1})}{\partial {\bar{q}}_{1}^{2}} < 0$ . Similarly, $\frac{\partial C_{2} ({\bar{q}}_{2})}{\partial {\bar{q}}_{2}}$ is the marginal cost of production of the product in country 2 while $(1 + δ_{21})$ is an added cost due to export from country 2 to country 1. These costs can include incentives from country 1 as well as levies imposed by country 1 if it chooses to reduce imports. When consumption is rationed, e.g., by excess demand, then $Q_{1} + Q_{2} = q_{1}^{c} + q_{2}^{c}$ while the equality constraints above hold at equality, or ${\bar{q}}_{1} = q_{1}^{c}$ , ${\bar{q}}_{2} = q_{2}^{c}$ . As a result, four cases arise:

(1)
${\bar{q}}_{1} < q_{1}^{c}$ , ${\bar{q}}_{2} < q_{2}^{c}$ : Ample supply
(2)
${\bar{q}}_{1} = q_{1}^{c}$ , ${\bar{q}}_{2} < q_{2}^{c}$ : Country 1 domestic production rationing
(3)
${\bar{q}}_{1} < q_{1}^{c}$ , ${\bar{q}}_{2} = q_{2}^{c}$ : Country 2 domestic production rationing
(4)
${\bar{q}}_{1} = q_{1}^{c}$ , ${\bar{q}}_{2} = q_{2}^{c}$ : Both countries domestic production rationing
The product input factors specific PPP between the two countries thus requires that $c_{1} / c_{2} = ρ$ , or: $\begin{array}{l} \frac{c_{1}}{c_{2}} = & ξ = ρ \\ = & ((q_{2} + q_{12}) (\frac{\partial C_{1} ({\bar{q}}_{1})}{\partial {\bar{q}}_{1}} q_{1} \\ + \frac{\partial C_{2} ({\bar{q}}_{2})}{\partial {\bar{q}}_{2}} q_{21} (1 + δ_{21}))) \\ / ((q_{1} + q_{21}) (\frac{\partial C_{2} ({\bar{q}}_{2})}{\partial {\bar{q}}_{2}} q_{2} \\ (14) & + \frac{\partial C_{1} ({\bar{q}}_{1})}{\partial {\bar{q}}_{1}} q_{12} (1 + δ_{12}))) \end{array}$ Given the broad diversity of countries’ production technologies, their production capacities and their intervention in international exchanges, such parity can hold practically.

For example, say that consumption is rationed, $Q_{1} + Q_{2} = q_{1}^{c} + q_{2}^{c}$ . Assume the case (2) with country 2 having both an excess capacity to its domestic demand and lower production cost than say country 1, or: $\begin{matrix} (15) & \{\begin{matrix} {\bar{q}}_{2} = q_{2} + Min (Q_{1} - q_{1}^{c}, q_{2}^{c} - q_{2}) ⩽ q_{2}^{c}, \\ {\bar{q}}_{1} = q_{1} = q_{1}^{c} \\ Q_{2} = q_{2}, \\ Q_{1} = q_{1}^{c} + Min (Q_{1} - q_{1}^{c}, q_{2}^{c} - q_{2}) \end{matrix} \end{matrix}$ Marginal costs are then defined by: $\begin{array}{l} \frac{\partial C (\bar{Q})}{\partial Q_{1}} = & (\frac{\partial C_{1} (q_{1}^{c})}{\partial {\bar{q}}_{1}} q_{1}^{c} \\ + \frac{\partial C_{2} ({\bar{q}}_{2})}{\partial {\bar{q}}_{2}} Min (Q_{1} - q_{1}^{c}, q_{2}^{c} - q_{2}) \\ (16) & \times (1 + δ_{21})) \\ / (q_{1} + Min (Q_{1} - q_{1}^{c}, q_{2}^{c} - q_{2})), \\ \frac{\partial C (\bar{Q})}{\partial Q_{2}} = & \frac{\partial C_{2} ({\bar{q}}_{2})}{\partial {\bar{q}}_{2}} \end{array}$ Thus, consumption in excess of domestic supply capacity is augmented by imports from country 2 which contributes to lower marginal costs in country 2 (and thus to reduced prices). These in turn contribute to more consumption in country 1 and therefore to a lower marginal utility in country 1 (resulting also in lower prices due to economies of scale). Note also that the FX rate can mitigate some of these effects temporarily by contributing artificially to an increase in price in country 1 (by an increase in its marginal import cost) which limits consumption. The FX rate has however a temporary effect as a reduction in exports from country 2 to country 1 will contribute to an expansion of country 2’s consumption and thereby to greater efficiency in its marginal supply costs. Another example will highlight supply side effects.
5. Examples with different utility functions

Example 1 (Quadratic Utilities).

$u_{i} (\cdot) = a_{i} Q_{i} - \frac{1}{2} λ_{i} Q_{i}^{2} + b_{i} Q_{j}$ and $\begin{matrix} (17) & \begin{matrix} π_{i}^{*} = \frac{\partial u_{i}}{\partial Q_{i}} = a_{i} - λ_{i} Q_{i}, \frac{\partial u_{1}}{\partial Q_{2}} = b_{1}, \\ \frac{\partial u_{2}}{\partial Q_{1}} = b_{2}, \end{matrix} \end{matrix}$ Assume global marginal costs for supply: $\partial C (\bar{Q}) / \partial Q_{i} = c_{i}$ , then: $\begin{matrix} (18) & \begin{matrix} (π_{1} - π_{1}^{*}) (π_{2} - π_{2}^{*}) = b_{1} b_{2} and \\ \frac{π_{1} - c_{1}}{π_{2} - c_{2}} = \frac{π_{1}^{*} + b_{2} - c_{1}}{π_{2}^{*} + b_{1} - c_{2}} \end{matrix} \end{matrix}$ For $0 < α = \frac{(π_{1}^{*} + b_{2} - c_{1})}{(π_{2}^{*} + b_{1} - c_{2})} = \frac{π_{1} - c_{1}}{π_{2} - c_{2}}$ then: $c_{1} + α (π_{2} - c_{2}) = π_{1}$ and therefore, $\begin{matrix} (19) & \{\begin{matrix} α π_{2}^{2} - π_{2} (α (π_{2}^{*} + c_{2}) + π_{1}^{*} - c_{1}) \\ + α π_{2}^{*} c_{2} + π_{2}^{*} (π_{1}^{*} - c_{1}) - b_{1} b_{2} = 0 or \\ π_{2} = \frac{1}{2 α} (α (π_{2}^{*} + c_{2}) + π_{1}^{*} - c_{1}) \\ + \frac{1}{α} (\frac{1}{4} {((α (π_{2}^{*} + c_{2}) + π_{1}^{*} - c_{1}))}^{2} \\ + α (b_{1} b_{2} - α π_{2}^{*} c_{2} - π_{2}^{*} {(π_{1}^{*} - c_{1})))}^{\frac{1}{2}} \end{matrix} \end{matrix}$ And therefore, the marginal effects of $b_{1}$ and $b_{2}$ on the price $π_{2}$ are: $\begin{matrix} (20) & \begin{matrix} \frac{d π_{2}}{d b_{2}} = \frac{1}{α} (\frac{b_{1}}{2 π_{2} - (α (π_{2}^{*} + c_{2}) + (π_{1}^{*} - c_{1}))}), \\ \frac{d π_{2}}{d b_{1}} = \frac{1}{α} (\frac{b_{2}}{2 π_{2} - (α (π_{2}^{*} + c_{2}) + (π_{1}^{*} - c_{1}))}) \end{matrix} \end{matrix}$ with $\frac{d π_{2}}{d b_{2}} / \frac{d π_{2}}{d b_{1}} = b_{1} / b_{2}$ . Similarly, let $s = {(2 π_{2} - (α (π_{2}^{*} + c_{2}) + (π_{1}^{*} - c_{1})))}^{- 1}$ , thus: $\begin{matrix} (21) & \{\begin{matrix} \frac{d π_{1}}{d b_{1}} = α b_{2} (\frac{1}{α} s - \frac{(π_{2} - c_{2})}{b_{2} (π_{2}^{*} + b_{1} - c_{2})}), \\ \frac{α (π_{2} - c_{2})}{(π_{2}^{*} + b_{1} - c_{2})} > s \\ \frac{d π_{1}}{d b_{2}} = α b_{1} (\frac{1}{α} s + \frac{(π_{2} - c_{2})}{(π_{1}^{*} + b_{2} - c_{1})}) \end{matrix} \end{matrix}$ Thus, the price in country 1 has the marginal effects: $\begin{array}{l} (22) & \begin{matrix} \frac{d π_{1}}{d b_{1}} \\ = \frac{b_{2} (π_{1}^{*} + b_{2} - c_{1})}{(π_{2}^{*} + b_{1} - c_{2})} \\ \times (\frac{1}{α (2 π_{2} - \frac{π_{1} - c_{1}}{π_{2} - c_{2}} (π_{2}^{*} + c_{2}) + (π_{1}^{*} - c_{1}))} \\ - \frac{(π_{2} - c_{2})}{b_{2} (π_{2}^{*} + b_{1} - c_{2})}) \end{matrix} \\ (23) & \begin{matrix} \frac{d π_{1}}{d b_{2}} \\ = \frac{b_{1} (π_{1}^{*} + b_{2} - c_{1})}{(π_{2}^{*} + b_{1} - c_{2})} \\ \times (\frac{1}{α (2 π_{2} - \frac{π_{1} - c_{1}}{π_{2} - c_{2}} (π_{2}^{*} + c_{2}) + (π_{1}^{*} - c_{1}))} \\ - \frac{(π_{2} - c_{2})}{(π_{1}^{*} + b_{2} - c_{1})}) \end{matrix} \end{array}$ which can be written concisely by setting: $\begin{matrix} (24) & \begin{matrix} r = {(2 π_{2} - \frac{π_{1} - c_{1}}{π_{2} - c_{2}} (π_{2}^{*} + c_{2}) + (π_{1}^{*} - c_{1}))}^{- 1}, \\ α = \frac{(π_{1}^{*} + b_{2} - c_{1})}{(π_{2}^{*} + b_{1} - c_{2})}, t = \frac{(π_{2} - c_{2})}{(π_{2}^{*} + b_{1} - c_{2})} \end{matrix} \end{matrix}$ And therefore, $\begin{matrix} (25) & \begin{matrix} \frac{d π_{1}}{d b_{1}} = b_{2} α (r - \frac{t}{b_{2}}), \\ \frac{d π_{1}}{d b_{2}} = b_{1} α (r + t), \\ \frac{d π_{2}}{d b_{2}} = b_{1} α, \frac{d π_{2}}{d b_{1}} = b_{2} α \end{matrix} \end{matrix}$ If $(b_{1}, b_{2}, α, t) > 0$ then, $\frac{d π_{2}}{d b_{2}} > 0$ , $\frac{d π_{2}}{d b_{1}} > 0$ and $\frac{d π_{1}}{d b_{2}} > 0$ , $\frac{d π_{1}}{d b_{1}} < 0$ if $r b_{2} < t$ . In other words, the first country can be self-serving altruistic if $r b_{2} < t$ (since greater altruism would contribute to a price reduction in its country). Namely, if: $\begin{array}{l} b_{2} < & \frac{(π_{2} - c_{2})}{(π_{2}^{*} + b_{1} - c_{2})} {2 π_{2} - \frac{π_{1} - c_{1}}{π_{2} - c_{2}} \\ \times (π_{2}^{*} + c_{2}) + (π_{1}^{*} - c_{1})} \\ (26) & > & 0 \end{array}$ In other words, if $b_{2}$ is small (or negative) then prices in country 1 decrease if country 1 is more altruistic. $\begin{matrix} (27) & \begin{matrix} Note that \frac{d π_{1}}{d b_{1}} < 0 if \frac{d π_{2}}{d b_{1}} < \frac{(π_{2} - c_{2})}{(π_{2}^{*} + b_{1} - c_{2})} \\ and \frac{d π_{2}}{d b_{1}} < 0 if \frac{d π_{1}}{d b_{2}} < \frac{b_{2} (π_{2} - c_{2})}{(π_{2}^{*} + b_{1} - c_{2})} < 0 . \end{matrix} \end{matrix}$ Assume at present that $(π_{2}^{*} + b_{1} - c_{2}) c_{1} = c_{2} (π_{1}^{*} + b_{2} - c_{1})$ or $c_{1} / c_{2} = (π_{1}^{*} + b_{2} - c_{1}) / (π_{2}^{*} + b_{1} - c_{2})$ then there is a product specific PPP exchange rate ρ that accounts for the countries’ altruistic consumption and is given by: $\begin{matrix} (28) & ρ = \frac{π_{1}}{π_{2}} = \frac{c_{1}}{c_{2}} = \frac{π_{1}^{*} + b_{2} - c_{1}}{π_{2}^{*} + b_{1} - c_{2}} \end{matrix}$ As we can see, it also equals a global marginal supply cost parity. In other words, considering equation (9), then: $\begin{array}{l} ρ = & \frac{π_{1}^{*} + b_{2} - c_{1}}{π_{2}^{*} + b_{1} - c_{2}} = \frac{c_{1}}{c_{2}} \\ = & (\frac{\partial C_{1} (q_{1}^{c})}{\partial {\bar{q}}_{1}} q_{1}^{c} + \frac{\partial C_{2} ({\bar{q}}_{2})}{\partial {\bar{q}}_{2}} \\ \times Min (Q_{1} - q_{1}^{c}, q_{2}^{c} - q_{2}) (1 + δ_{21})) \\ / ((q_{1} + Min (Q_{1} - q_{1}^{c}, q_{2}^{c} - q_{2})) \\ (29) & \times \frac{\partial C_{2} ({\bar{q}}_{2})}{\partial {\bar{q}}_{2}}) \end{array}$ This latter equation highlights the interdependency of the marginal production costs, production capacities as well as the quantities produced and consumed in each country.

Example 2 (Other Type of Utility Functions).

$u_{1} = α_{1} {(Q_{1})}^{β_{1}} {(Q_{2})}^{γ_{1}}$ , $u_{2} = α_{2} {(Q_{2})}^{β_{2}} {(Q_{1})}^{γ_{2}}$ with $\frac{\partial u_{i}}{\partial Q_{i}} = β_{i} \frac{u_{i}}{Q_{i}}$ , $\frac{\partial u_{i}}{\partial Q_{j}} = γ_{i} \frac{u_{i}}{Q_{j}}$ thus, equation (2) and (3) are reduced to: $\begin{array}{l} (30) & \begin{matrix} (π_{1} - β_{1} \frac{u_{1}}{Q_{1}}) (π_{2} - β_{2} \frac{u_{2}}{Q_{2}}) \\ = γ_{1} γ_{2} \frac{u_{1} u_{2}}{Q_{1} Q_{2}} \end{matrix} \\ (31) & \frac{π_{1} - c_{1}}{π_{2} - c_{2}} = \frac{Q_{2} (β_{1} u_{1} + γ_{2} u_{2} - c_{1} Q_{1})}{Q_{1} (β_{2} u_{2} + γ_{1} u_{1} - c_{2} Q_{2})} \end{array}$ Further, letting: $\begin{matrix} (32) & \{\begin{matrix} θ = (\frac{β_{1} u_{1}}{Q_{1}} - c_{1}) \\ + \frac{(β_{1} u_{1} + γ_{2} u_{2} - c_{1} Q_{1}) (c_{2} Q_{2} + β_{2} u_{2})}{Q_{1} (β_{2} u_{2} + γ_{1} u_{1} - c_{2} Q_{2})} \\ μ = \frac{1}{Q_{1} Q_{2}} (γ_{1} γ_{2} u_{1} u_{2} \\ + (c_{1} Q_{1} - ρ c_{2} Q_{1} - β_{1} u_{1}) β_{2} u_{2}) \\ μ = \frac{Q_{2} (β_{1} u_{1} + γ_{2} u_{2} - c_{1} Q_{1})}{Q_{1} (β_{2} u_{2} + γ_{1} u_{1} - c_{2} Q_{2})} \end{matrix} \end{matrix}$ In addition, consider the case in equation (16), or $\begin{matrix} (33) & \{\begin{matrix} c_{1} = \frac{\partial C (\bar{Q})}{\partial Q_{1}} \\ = \frac{\frac{\partial C_{1} (q_{1}^{c})}{\partial {\bar{q}}_{1}} q_{1}^{c} + \frac{\partial C_{2} ({\bar{q}}_{2})}{\partial {\bar{q}}_{2}} Min (Q_{1} - q_{1}^{c}, q_{2}^{c} - q_{2}) (1 + δ_{21})}{q_{1} + Min (Q_{1} - q_{1}^{c}, q_{2}^{c} - q_{2})}, \\ c_{2} = \frac{\partial C (\bar{Q})}{\partial Q_{2}} = \frac{\partial C_{2} ({\bar{q}}_{2})}{\partial {\bar{q}}_{2}} \end{matrix} \end{matrix}$ We have then the following price functions: $\begin{matrix} (34) & \{\begin{matrix} π_{2}^{o} (Q_{1}, Q_{2}) = \frac{θ}{2 α} + \frac{1}{α} \sqrt{{(\frac{θ}{2})}^{2} + ρ μ} \\ π_{1}^{o} (Q_{1}, Q_{2}) \\ = ρ (π_{2}^{o} (Q_{1}, Q_{2}) - c_{2}) + c_{1} \end{matrix} \end{matrix}$ Assuming a PPP, we have then: $\begin{array}{l} ξ & = \frac{π_{1}^{o} (Q_{1}, Q_{2})}{π_{2}^{o} (Q_{1}, Q_{2})} \\ (35) & = ρ + \frac{c_{1} - ρ c_{2}}{\frac{1}{α} \sqrt{{(\frac{θ}{2})}^{2} + ρ μ} + \frac{θ}{2 α}} \end{array}$ This is a nonlinear function of both countries’ utilities of consumption and their global marginal costs of production. As stated earlier, if $c_{1} / c_{2} = ρ$ a strong PPP is obtained with $ξ = ρ$ . Then the relationship between the FX rate and consumptions in countries 1 and 2 ( $Q_{1}$ and $Q_{2}$ ), using the utility functions and parameter values $α_{1} = 1$ , $β_{1} = 0.7$ , $γ_{1} = 0.1$ ; $α_{2} = 1.2$ , $β_{2} = 0.6$ , $γ_{2} = 0.02$ , with constant marginal costs of $c_{1} = 0.2$ , $c_{2} = 0.1$ is shown in Fig. 3. In this figure, we observe a change in the convexity with an inflection point. In this case, the second derivative is equal to zero.

Fig. 3.

FX rate relationship with consumption in country 1 ( $Q_{1}$ ), and consumption in country 2 ( $Q_{2}$ ). Note: z axis shows ξ, x axis shows $Q_{1}$ , and y axis shows $Q_{2}$ . These variables range between $0 < ξ < 1.5$ , $1 < Q_{1} < 30$ , $1 < Q_{2} < 15$ .

6. Conclusion

Preference functions are foundation of economic models which may express multi-faceted consumer behaviors. Consumers’ utility, with consumption by one accounting for the consumption “of the other” has been shown to express a broad set of intent and preferences including self-serving interests. Trade and exchange, for example, which have “selfish” motivation may also have altruistic as well as self-serving altruistic motives. Trade that results in the growth of global consumption and welfare is a particular example where an expanding trade and lower prices contribute to mutual consumption, and therefore to a potential for greater economies of scale (and thereby to lower prices and economic efficiency). In such cases, trade can be self-serving as well as altruistic by contributing and accounting for another country’s consumption as one’s own. In order to assess these effects, this paper used a Cournot model based on countries’ utility functions which are functions of both their and “others”’ consumption. Such an approach has allowed the definition of simultaneous and dependent inverse demand (price) functions for both countries. In addition, supply side global costs and countries’ marginal costs of supply (including local production costs, capacity constraints and trade costs) were considered. Inverse demand and capacitated supply marginal costs have thus defined the countries’ respective prices as a function of their altruistic utilities.

Although the utilities considered were strictly a function of consumption in both countries, we can also consider countries’ utilities to be a function of each other such as a linear combinations of their utilities, or $u_{1} = α v_{1} (x, y) + (1 - α) v_{2} (x, y)$ and $u_{2} = β v_{2} (x, y) + (1 - β) v_{1} (x, y)$ . Such formulations are merely specific cases of the general results we have obtained in this paper. Our results including the examples treated are indicative of the following: (1)

Altruistic consumption can be self-serving. In this case, globalization may be gateless.

(2)

Assuming PPP in the inverse demand function, we note that FX rate is a specific nonlinear function of the countries’ marginal utilities, their marginal cost of production and trade. Countries’ prices are however related to each other by a linear relationship however.

(3)

PPP in supply side factors and PPP in inverse demand side functions (prices) were distinguished.

(4)

If there is a PPP in supply side price (marginal costs) factors then there is a strong PPP which holds for both inverse demand prices and supply costs prices.

Altruistic consumption dependence arises for different reasons. Common interests and exchanges as well as altruism (whether self-motivated or not) contribute to preferences that can reflect a preference for greater equality between trading countries. Inherent inequalities due to production technologies, access to factor inputs in production processes as well as other factors arise that may lead to one country consuming at the expense of the other. Self-preservation of countries with ample consumption and production opportunities may in fact recognize that altruistic preferences are not only a “humanitarian” expression, but a concern to be nurtured for self-sustainability.

Additional issues such as supply constraints in one or in both countries were indicated although not treated in great detail. Such problems are particularly important however as they can be used to model supply and demand for rare earth. Other issues such as collaboration between countries were not considered. These and other problems arising from the complex environment within which global economies operate provide a fertile ground for future research.

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