The undocumented migration of Mexican nationals to the U.S. is largely influenced by the availability of labor demand in unskilled sectors in the U.S., making it more efficient than the legal channels of migration available to unskilled Mexican nationals. Labor demand in unskilled industries is larger than the available unskilled labor in the U.S., but Mexican migrants, who constitute the majority share of foreign-born individuals in the U.S., are immigrating at the lowest rates in modern times, with net Mexican migration at approximately zero. This paper simulates a market-based immigration system for Mexican nationals, with a focus on the partial equilibrium effects in long run supply and demand for undocumented Mexican migrant labor in the U.S. agriculture sector. Reducing the additive tax on Mexican wages in the model effectively simulates an immigration policy shift. I estimate the net-of-tax long run labor supply and demand curves for U.S. agriculture, simulating an open-border policy with Mexico. Eliminating the additive tax on Mexican wages (which represents immigration policy reform) increases the quantity of labor used in U.S. agriculture, decreases U.S. agriculture wages for Mexican migrants, and raises Mexican agriculture wages. Since the labor supply curve for Mexican nationals is extremely elastic, the largest benefits of an immigration policy shift go to the U.S. producers, who can use higher labor inputs in production to lower the price of production. The results of the experiments are very similar, even with large differences in the visa pricing scheme chosen; this represents an exciting finding: the demand for access to the U.S. unskilled labor market for Mexican nationals is inelastic, which explains the fact that migrant smuggler costs have increased from approximately $50 in 1990 to upwards of $5,000 in the mid-2010s.