Doesn't the same argument hold true when income tax is reduced?
Prices should go up because everyone has more money to spend?
First of all, everyone doesn't have more money to spend. Only income tax payers get to keep more of the money they earned. It's not free money that everybody gets. The amounts vary depending on your income and some will get nothing. But, generally speaking, any time the market has more expendable resources it increases demand and if supply remains the same, prices go up. With tax cuts, especially on the top marginal incomes, the results are more supply oriented, businesses are expanded which increases supply. This means lower prices.
A good exercise with proposals such as yours is to amplify them and examine potential results. Why not give everyone $50,000? Or better yet, let's give everybody, including the homeless bums, $500,000! Why wouldn't this be awesome? If your idea is good, this should be phenomenal.... but you can imagine it wouldn't work. Why? Whatever reasons it wouldn't work are true with your proposal as well, all that is different is the scale.
Now, you will notice your proposal isn't very popular. According to the poll, 65% agree with me, there should be no minimum universal income. It's because most mature people who are capable of thinking above a 5-year-old level, understand that nothing is free. There isn't a magic money tree that can solve all our problems.