Exchange rates and multicommodity international trade: insights from spatial price equilibrium modeling with policy instruments via variational inequalities

Food security and multicommodity agricultural international trade: Quantifying optimal consumer subsidies for nutritional needs

“…Furthermore, the supply price, unit transportation cost, and the demand price are very reasonable (cf. Nagurney et al., 2023) and correspond to similar values achieved in practice prior to the war.…”

“…The highest commodity shipments are obtained in Example 2 across all the country trade flows. The prices are reasonable—recall that they are for a ton of grain (see, also, Nagurney et al., 2023).…”

“…(2001) and Nagurney et al. (2023). Spatial price equilibrium models have also been applied to the important agricultural commodity of soybeans by Barraza De La Cruz et al.…”

“…The spatial price equilibrium framework, in a variational inequality context (cf. Florian and Los, 1982; Dafermos and Nagurney, 1984), has yielded rich modeling advances and applications, especially to agricultural products (see, e.g.,Nagurney and Aronson, 1989; Nagurney, Li, and Nagurney, 2014; Nagurney et al., 2022; Nagurney and Besik, 2022; Nagurney et al., 2023). Definition A multicommodity shipment and Lagrange multiplier pattern $$(Q^*,\lambda ^*)\in {\cal K}^1$$ is an international trade equilibrium with food security nutritional minimum standards if it satisfies the following conditions: for each commodity h ; $$h=1,\ldots ,H$$, and for each pair of country supply and demand markets $$(i,j)$$; $$i=1,\ldots ,n$$; $$j=1,\ldots ,n$$: …”

“…The research in this paper builds on the work on spatial price equilibrium modeling (see Samuelson, 1952; Takayama and Judge, 1964, 1971) but utilizes the theory of variational inequalities (cf. Florian and Los, 1982; Dafermos and Nagurney, 1984; Nagurney and Aronson, 1989; Nagurney, 1999), with specific note on policies (Nagurney, Thore, and Pan, 1996; Nagurney, Nicholson, and Bishop, 1996; Nagurney et al., 2014, 2019, 2022, 2023). Spatial price equilibrium models have had wide applications to agricultural commodities and, therefore, this foundational framework is a reasonable one in which to also incorporate minimum nutritional standards for consumers in different countries.…”