How are prices determined in a socialist economy?
The government determines both level of output and acceptable prices for labor, goods, and services.
How are prices determined in a capitalist economy?
Supply and demand in the system determines prices in a capitalist economy. If consumers and producers can agree on a price for a sale, that is how much the price will be, even if some people think it is unfair.
Proponents of socialism claim that it will lead to a more equitable system of prosperity for the masses. Is that true?
Historically, no. The most prosperous societies have traditionally owed their success more to capitalist than socialist policies. Modern examples of Cuba and Venezuela, or China before embracing capitalism show little to no effect in lifting their poorest citizens from poverty.