Final answer:
The claim that if the consumer's income doubles, then his optimal purchases of all goods will double is false.
Step-by-step explanation:
The claim that if the consumer's income doubles, then his optimal purchases of all goods will double is false. While it is true that an increase in income generally leads to an increase in consumption, the extent to which consumption will double depends on the nature of the goods. Some goods may be considered normal goods, where a rise in income leads to a rise in quantity consumed, while others may be inferior goods, where a rise in income leads to a fall in quantity consumed. Therefore, it is not accurate to say that all goods will double in consumption when the consumer's income doubles.