The weekly demand and supply functions for seats on flights between Syracuse and
ID: 1240260 • Letter: T
Question
The weekly demand and supply functions for seats on flights between Syracuse and Boston have been estimated as follows:Qd = 1600 - 2.5 Price + .040 Income - 4 Weather + 1.20 Pa ( where Pa is the price of alternative means of travel )
Qs = -50 + 4.25 Price
Assuming: Income( I ) = 6250, Weather (W) = 75, Pa = $250,
a. Write the equation for the demand curve.
b. Determine the equilibrium price and quantity.
c. How does an increase in the weather temperature (W) (from 75 to 115) affect the equilibrium price and quantity?
d. Keeping the weather temperature (W) at 75, determine the effect of an increase in the price of an alternative form of transportation, Pa, from $250 to $350 on the equilibrium price and quantity.
e. Now keeping the weather temperature at 75, Pa at 250, and income at $6250, use your demand function to write the total revenue ( TR ) equation.
f. Using the same demand function, also write the marginal revenue (MR) function.
g. Using the same demand function, determine at what price level the total revenue (sales) on these flights would be maximized.
Explanation / Answer
SOLUTION-
a. For demand curve, we only depict how the quantity demanded changes with the change in prices keeping other factors constant. So, the equation of demand curve can be written as -
Q d = 1600 - 2.5 Price
b. Q s = -50 + 4.25 price
Equating Qd and Qs for equilibrium values we get,
-50 + 4.25 price = 1600 - 2.5 Price
Price =$ 244.44
Quantity = 1600 - 2.5 * 244.44
= 1600 - 611.11
= 988.88 or approximately = 990 units
c. Increase in weather temperature by I unit reduces the quantity demanded by 4 units.
Increase of 20 units (115-75) will reduce the quantity demanded by 20 * 4 = 60 units
Since, this change will shift the demand curve, it will shift the demand curve leftwards.
The equilibrium price can be calculated by putting Q = 930 in supply equation
P =$ 230.6
d. It will increase the quantity demanded by 1.20 * 100 = 120 units.
It will shift the demand curve to right.
New equilibrium price = $272.9
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