Factors that affect change in demand:
Change in income of travellers: Higher the income, higher the demand for it
Change in prices of other airlines in the market: Since other airlines are substitutes to United Airlines, change in ticket prices of other competitive airlines will affect demand for united airlines tickets
Change in consumer tastes and preferences: Demand for United Airlines tickets depends on consumer tastes and preferences.
Expectations of future price change: An expectation about change in guture prices affects consumer demand today. If consumers expect prices to fall in future, their demand today will fall.
However, change in price of United Airlines tickets will affect quantity demanded of it and thus lead to movement along demand curve and not shift it. There exists a negative relationship between the two.
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