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There are at least two different ways to answer this question.
One thing we can say is that the presence of a minimum wage in a market economy shows that that economy is not a pure market economy. In a pure market economy, individuals make the decisions that answer the basic economic questions. If a company pays too little to make it worth it to work for them, workers will not work there. This will establish a natural minimum wage. If the government imposes a minimum wage, the economy is no longer a pure market economy because the government has decided how products will be made (by saying they will not be made by people making less than minimum wage). In this view, then, a minimum wage demonstrates that the economy is not a pure market economy.
If we believe in classical economic theory, a minimum wage in a market economy shows us that the government should not interfere in economic affairs. A minimum wage is a form of a price floor because it does not allow the price of labor to drop below a certain wage. According to economic theory, a price floor causes a surplus to develop. When the minimum wage is set higher than equilibrium, more hours are supplied (the number of hours people want to work) than are demanded (the number of hours employers want to buy). This causes a surplus because employers are not willing to buy all the hours of labor that workers are willing to sell. In this view, a minimum wage demonstrates that government should stay away from interfering in the economy.
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