If all prices are doubled and money income is left the same, the budget set does not change because relative prices do not change.

Budget Set

The collection of all possible bundles of goods and services that a consumer can afford with their income at given prices.

Prices Doubled

A situation where the cost of goods, services, or commodities increases to twice their original amount.

Relative Prices

The price of one good or service compared to another, usually considered in terms of opportunity cost.