The argument that luxury retailers should refocus their attention to lower-priced markets due to the high unemployment rate and consumer fears is not entirely logically convincing since it ignores certain crucial assumptions. First, the argument assumes that all socio-economic levels buy luxury items. Second, the argument never states where the the geography of the statistical analysis was sampled. Finally, there are other reasons that could possibly explain the decline of the luxury goods industry.
In order to assume that the high unemployment rate directly influences the decline in luxury retailer's profits, you have to show that their clientele is the population that is affected by the unemployment rise. If this percent of the population has a particularly low unemployment rate, then their expendable income will most likely not be affected. Thus, allowing them to spend the same amount of money on luxury and essential items. Therefore, these retailers do not need to refocus their attention to lower-priced markets.
Also, if the demographic of the economy being hit the most with job lay offs, was the only sample that was taken to determine the unemployment rate your statistics will be skewed. Never letting the reader know sample size and demographic will automatically make for a faulty argument leaving the reader uneasy about the conclusion.
Lastly, there are many reasons for a decline in luxury goods and it doesn't necessarily have to correlate with a high unemployment rate. For instance, the values of the consumer might have change and they find themselves spending more money on other goods. For example recently there has been a huge growth in "green friendly" items which could result in less money being spent on luxury items.
Thus, this argument is not completely sound. It could have been strengthened by including the socio-economic background of the luxury item consumer in comparison to that of the increased unemployment rate to convince the reader that these two groups are representatives of each other. It also needs to include the demographics of their statistical analysis, also allowing the reader to see the correlation between these two groups. Finally, this author of this argument needed to rule out other possibilities for the decline in the luxury goods industry. By touching briefly on these three simple items, the argument would have been exponentially more valid.