How do food stamps impact the output or product mix of the economy as compared to a government purchase of a good or service such as public education?

Food stamps are impact the output and product mix in more than one way.

The first impact is that they are funded by taxes taken from productive market actors, and given to less or non productive individuals of low/no income. Taxes are a withdrawal from the circular flow of economic activity. That means less income to be used for exchange in the marketplace for goods and services. Excessive subsidies such as food stamps can cause inefficiencies that have an effect on the entire market. Remember that everything has to be paid for by somebody. Productive workers whose income is taken via taxes to fund the less productive, must now work harder to make up the losses to support themselves.

Another impact is the fact that food stamps are given to those who show no substantial official income on paper. However these individuals may have significant income from the informal market, which can be very extensive. For example, an individual may rate food stamps because he has no official income. However when he goes to purchase food with the stamps, he drives to the store in a Mercedes wearing a Hugo Boss suit, all with income acquired in the informal market, which is not claimed on government tax returns.

Government vouchers for education are no less of a drain than food stamps are. The difference is that the subsidies are given to attain education rather than food. Again, everything has to be paid for by somebody. If you send your kids to private school and pay tuition, you still have to pay for other kids to go to the public schools in your district. With vouchers, you are adding more kids to the list of tax consumers, thus increasing the burden on the more productive to pick up the tab.