To describe: The effects of the system on the number of size the carry-ons are brought to the plane and efficiency of overhead space allocation.

Explanation of Solution
Earlier the passengers were charged for check-in bags, they would select whether to check-in baggage or carry them in the aircraft depending on their willingness to trade time for the hassle of handling with carry-on baggage. That is, the passengers who valued time saving by not having to deal with baggage claim will be higher than the handling cost with carry-on baggage will prefer to carry on.
The fact that passengers are now being charged for check-in bags but not for the bags carried onto the aircraft will inefficiently placed overhead space. Passengers are carrying bigger bags to save the rates charged, and resulting in full the overhead luggage containers. Overhead spaces are used on the first come first serve bases, rather than being evenly distributed. Bags checked (without any fees) at the gates would prefer to carry on even without any charges to have to go through checks, which will be a loss to the company. Those who prefer to carry their baggage in order to evade the fee, but rather prefer to check their bags, also result in an inefficiency.
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