Socialism is impossible

1. Socialism abolishes Private Property in capital goods and natural resources
2. The socialist state is sole owner of the material factors of production so no trade/exchange can occur (One cannot trade with oneself)
3. Without trade there can be no market prices, i.e. they cannot derive which factors are expensive to cheap relative to their scarcity (No way of knowing if material A is wanted more than material B, etc etc)
4. Without price signals, the socialist state cannot calculate the cost of production of the goods it produces. (Cannot compare which materials that have alternative uses is best suited for producing the good)
5. Without the ability to calculate the cost of production, profits and losses cannot be determined (profits/losses indicate degrees of efficiency/inefficiency respectively), therefore they cannot know the most valuable uses of scare resources (economizing), meaning it is strictly impossible

Concisely, socialism is impossible because it cannot overcome the economic calculation problem.