Question

The weekly demand and supply functions for seats on flights between Syracuse and Boston have been estimated as follows:

Qd = 1800 - 3 Price + .045 Income - 4 Weather + 1.25 Pa   ( where Pa is the price of alternative means of travel )

Qs = -60 + 4 Price

Assuming: Income( I ) = 6500, Weather (W) = 75, Pa = $260,
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 means of transportation, Pa, from $260 to $360 on the equilibrium price and quantity.
e. Now again keeping the weather temperature at 75, Pa at 260, and income at $6,500, use your demand function to write the total revenue ( TR ) equation. (Hint: Remember that the revenue function must be written in terms of quantity,Q.)
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.

Answer 1

Od = 1800- 3P +0.45I - 4 w ť 1.25pa (a) Od = 1800-3P + 0.45(6500] -4 (752 +1.25(250) Od = 1800-3P+ 2825 - 300+ 325 Od = 47.50 - 32 Qs = -60 tup Os = od - 60 t up = 4750-3P up+3p = 4750460 - 7P = 4810 P = 687-14 Q = 4750 - 3(687.14) = 4750 - 2061.42 Q = 2688. 58 (c) Now w pes from 75 to 115 Od = 1800 - 3P + 0.45 (65002 – 4 (115) + 1.25(260) 1800- 3 P + 29 25 - 460 + 325 = ų 590 - 32 Os = -60+ up os = od -60t up = u590-3P - 4P+3P = ugot 60 7 P = - 4650 P = 664.28 Q : 4590-3(664.287 l 45 go- 1992.84 = 25 97:16

Thus, an in w from 75 to 115 leads to v in equilibrium price from 687. 14 to 664.28 and I in equilibrium quantity from 2688.58 to 2597.16 (d) pa i es from $260 to $360 Od = 1800 - 3P+0.45(65002 - 4(75) +1.25 (360) 1800 - 3P +- 2995 - 300 + 450 = 4875-3P Os = od 0 - 60 typ = 4875-38 up +3P = 4875+60 7p = 4935 - P = 705 0= 4875- 3(7052 4875 - 2115 2760 Ana in Pa from 260 to 360 reach to i in equilibrium price from 687.14 to 705 and alro p in equilibrium. quantity from 2688. 58 to 2760