Question

The demand and supply functions for seats on a special shuttle flight from Dubai to Jeddah, Saudi Arabia, have been estimated as follows:

Q_d =   90 - 2P + .05Y - 0.5W + 1.25P_c

Where: Q_d = quantity demanded; P = price; Y = Income; W = weather; P_c = price of competition;

Q_s =   - 20 - 5P_f + 3P      

Where: Qs = quantity supplied; P_f = price of fuel;

Assuming:                   Y = 100,       W = 70,         P_c = 16,      P_f = 6

1. Derive the demand equation. (1 Point)

2. Derive the supply equation. (1 Point)

3. Determine the equilibrium price and quantity. (1 Point)

4. What is the price elasticity of demand at the equilibrium price? (1 Point)

5. Calculate the income elasticity of demand EM. Is good X normal or inferior? (1 Point)

6. Show the effect of an increase in the price of the substitute from 16 to 20 AED on the equilibrium price and quantity. (1 Point)

Answer 1

(a) Q_d =   90 - 2P + .05Y - 0.5W + 1.25P_c

Put  Y = 100,       W = 70,         P_c = 16,

=> Qd = 90 - 2P + .05(100) - 0.5 (70) + 1.25 (16)

=> Qd = 90 - 2P + 5 - 35 + 20

=> Qd = 80 - 2P (Demand equation)

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(b) Q_s =   - 20 - 5P_f + 3P

Put    P_f = 6

=> Qs = -20 - 5(6) + 3P

=> Qs = -20 - 30 + 3P

=> Qs = -50 + 3P (Supply equation)

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(c) At equilibrium point; Qs = Qd = Q

=> -50 + 3P = 80 - 2P

=> 3P + 2P = 80 + 50

=> 5P = 130

=> P = 130 / 5

=> P = 26

Equilibrium pirce is 26.

And, Q = 80 - 2P

=> Q = 80 - 2(26)

=> Q = 28

Equilibrium quantity is 28

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(d) Price elasticity of demand = (ΔQd /Δ P) * (P / Qd)

Qd = 80 - 2P

=> ΔQd /Δ P = -2

And, at equilibrium point : P = 26 , Qd = 28

Price elasticity of demand = (ΔQd /Δ P) * (P / Qd)

Price elasticity of demand = (-2) (26 / 28)

=> Price elasticity of demand = -1.8571

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(e) Q_d =   90 - 2P + .05Y - 0.5W + 1.25P_c

ΔQd /Δ Y = .05

And, at Y = 100, Qd = 28

Income elasticity = (ΔQd /Δ Y) * (Y / Qd)

Income elasticity = (0.05) (100 / 28)

Income elasticity = 0.1785

Since, Income elasticity is positive. It means good is normal.

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(f) Now Pf increases from 16 to 20.

Q_d =   90 - 2P + .05Y - 0.5W + 1.25P_c

Put  Y = 100,       W = 70,         P_c = 20,

=> Qd = 90 - 2P + .05(100) - 0.5 (70) + 1.25 (20)

=> Qd = 90 - 2P + 5 - 35 + 25

=> Qd = 85 - 2P (New demand equation)

Qs = -50 + 3P

At equilibrium point; Qs = Qd = Q

=> -50 + 3P = 85 - 2P

=> 3P + 2P = 85 + 50

=> 5P = 135

=> P = 135 / 5

=> P = 27

New Equilibrium pirce is 27. Hence, equilibrium price increase from 26 to 27

And, Q = 85 - 2P

=> Q = 85 - 2(27)

=> Q = 31

New Equilibrium quantity is 31. Hence, the equilibrium quantity increases from 28 to 31