Luxury goods refers to the goods which are having positive income elasticity of demand. Positive income elasticity of demand is defined as the direct relationship between the demand of the goods and the income of the consumers.
If there is an increase in the income level of consumers then as a result there is an increase in the demand for luxury goods by a greater proportion. That's why the income elasticity of demand is relatively larger.
Elastic demand is where a change in price causes a significant change in demand, therefore 20 hats to 15 hats can be considered significant and we can conclude that it's elastic demand.
Ending merchandise = beginning Merchandise + net purchases- cost of goods sold Cost of goods sold= beginning merchandise + purchases during the period- ending merchandise