In which direction, I will set the model?
Is price a function of wage or wage is a function of price?
In case, How I will check the reverse causality and fix which one is the response for another?
I think that it depends on the market. If you study labor wage in agriculture, it should have positive correlation with food price. If the sector is competitive and more economic value is produced, wage there should increase.
If you study wage of workers in city and food price there, there might be also positive correlation. The richer are workers, the more they are able to pay for food and price may grow if food supply is not enough competitive.
In the first case food price drives agricultural wage, while in the 2nd industrial wage drives food price in cities. Note that food price in cities is higher than in rural area, because of transport cost and distribution mark-up.
I would suggest using causalTree/causalForest and other analytic tools to study and estimate causal effects (not just correlations)
https://github.com/susanathey/causalTree
https://arxiv.org/abs/1504.01132
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