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Hi I am an Economics Major going to get my Master's degree.
A high minimum wage can increase the prices of goods but not due to inflation. Inflation only occurs when the money supply increases greater than Real GDP growth.
A higher minimum wage forces firms to higher less workers and sell less product (due to having less workers). Society is at a loss overall with a high minimum wage.
The best way to increase prices is to increase the output of each worker or increase the amount of jobs available to choose from.