This paper analyzes the impact of Covid-19 and uncooperative trade policies on world food markets. It quantifies the initial shock due to the pandemic under the assumption that products that are more labor intensive in production are more affected through workers' morbidity and containment policies. It then estimates how escalating export restrictions to shield domestic food markets could magnify the initial shock. The analysis shows that, in the quarter following the outbreak of the pandemic, the global export supply of food could decrease between 6 and 20 percent and global prices increase between 2 and 6 percent on average. Escalating export restrictions would multiply the initial shock by a factor of 3, with world food prices rising by up to 18 percent on average. Import food dependent countries, which are in large majority developing and least developed countries, would be most affected.