If income is doubled and all prices are doubled, then the demand for luxury goods will more than double.

The statement seems to be based on the assumption that luxury goods are normal goods. Normal goods are those for which demand increases when income increases, all other things being equal. However, the statement also implies that luxury goods have an income elasticity of demand greater than 1, meaning they are luxury goods in the economic sense: demand for them increases more than proportionally as income increases.

Here are the steps to understand this:

1. Income doubles: When income doubles, people have more disposable income. This means they can afford to buy more goods and services than before.

2. All prices are doubled: When all prices double, the real purchasing power of income does not change. This is because while people have more money, everything costs more. So, they can still buy the same amount of goods and services as before.

3. Demand for luxury goods more than doubles: This is based on the assumption that luxury goods are normal goods with an income elasticity of demand greater than 1. This means that when income increases, demand for these goods increases more than proportionally. So, if income doubles, demand for luxury goods will more than double.

However, it's important to note that this is a simplified scenario. In reality, many other factors can affect demand for luxury goods, such as changes in tastes and preferences, the availability of substitutes, and expectations about future income and prices.