烏克蘭農地面積改變對全球小麥市場 之衝擊分析：Nash-Cournot模型

Abstract

2022年2月，俄羅斯入侵烏克蘭，持續不斷的衝突已經顯著降低了烏克蘭的穀物生產和出口。烏克蘭是世界主要的穀物生產國和出口國之一，其生產和出口受到入侵的影響已經成為全球關注的焦點。與2021年相比，玉米和小麥的生產量分別下降了36%，出口量則分別下降了17%和28%。 本研究旨在分析如果烏克蘭的生產和出口下降，主要的小麥出口國的出口數量變化。通過使用Nash-Cournot競爭模型，本研究將模擬這些變化對全球小麥市場的影響。Nash-Cournot模型對於分析生產類似商品或服務的公司之間的競爭很有用，Nash-Cournot模型被制定為線性互補問題（Linear Complementarity Problem），並且通過應用拉格朗日乘數法推導出KKT最優性條件，並使用GAMS和PATH solver進行解析。通過了解每個出口國的決策將如何影響整體市場，本研究可以提供有價值的洞察，了解烏克蘭減產和出口減少的潛在影響。 模擬結果表明儘管尚未達到最大產能的國家可以幫助出口更多小麥，但它們增加的出口量不足以彌補烏克蘭因戰爭而損失的出口量，進而導致出口數量下降而引起小麥價格上漲。

The Russian invasion of Ukraine began in February 2022 and the ongoing conflict in Ukraine has caused a significant decrease in its grain production and exports. Ukraine is one of the world's major grain producers and exporters, the impact of the invasion on Ukraine's production and exports has become a global concern. Production quantities for both corn and wheat have declined by 36% compared to 2021, while its export quantities have declined by 17% and 28%, respectively. This research study aims to analyze the changes in export quantity among the main wheat exporters worldwide if Ukraine experiences a drop in production and exports. By using a Nash-Cournot competition model, this study will simulate the impact of these changes on the global wheat market. The Nash-Cournot model is useful for analyzing competition between firms that produce similar goods or services. The KKT optimality conditions are derived by applying the Lagrangian multiplier method and combining them to form a Linear Complementarity Problem (LCP). The model is solved using GAMS and the PATH solver. By understanding how each exporter's decision will affect the overall market, the study can provide valuable insights into the potential impact of Ukraine's decreased production and exports. While countries that have not yet reached their maximum capacity can help to export more wheat, their increased quantity is not sufficient to cover the loss from Ukraine’s quantity. Resulting a rise in wheat price due to the decline in export quantity.