Hi Deepa,
I only took a quick look but here are my first thoughts.
Yes, price elasticities are negative. That means that changes in quantity are negatively correlated to price and vice versa. Price increase -> Lower volume. Price decrease -> Higher volume. So, in fact, a "normal" correlation between the two as you would expect with most goods. It is negative mathematically because Demand Curves are generally downwards-sloping if you put them in a Q / P chart.
Now, part A of the case clearly states that the capacity (or supply) is 990. So, they try to increase quantity from 900 to 990, basically bringing demand (currently 900) up to the supply (990). Since they want to INCREASE quantity, they need to DECREASE the price (again, this is what negative elasticity means - a negative correlation). In the other presented case, they are trying to lower the quantity, so they have to increase the price.
In Summary: negative price elasticities are the "norm", what you expect - i.e. regular goods, higher price lower vol, lower price higer vol. Luxury items have positive elasticities where a decrease in price would lead to lower quantity (no one would buy Gucci bags if you get them for just a few Dollars). Some other items are closer to or almost 0 (e.g. essential goods such as water, some foods, fuel). No matter the price, people will still buy that stuff.
Hope that helps,
Denis
(editiert)
That makes sense, thank you!