Question

1. Suppose an airline announces that its earnings this year are lower than expected due to reduced ticket sales. The airline spokesperson gives no information on how the company plans to turn things around, he only mentioned that the current demand curve is given by p2 -q - 4p = 0 and the supply curve is given by 2q + 8p – 4p3 = 2p2 a. Find the equilibrium points of the airline (10 marks) b. Find the Choke price (3 marks) C. Current owners of the airline's stock and potential buyers of the stock would adjust their estimates of what the value of the corporation's stock should be. As a result, the supply curve for the stock would increase by k for each price, (note: k is the last 3 digit from your mobile number). The demand curve for the stock would totally change to be represent by this equation 3p+32 -9 + 50 = 0, find the following 16 (2 marks) New supplied curve i. ii. Slope of demand curve

Answer 1

Demand Curve : p^2 - 1/3 * q - 4p = 0

or q/3 = p^2 - 4p

or q = 3p^2 - 12p

Supply curve : 2q +8p -4p^3 = 2p^2

or 2q = 4p^3 + 2p^2 - 8p

or q = 2p^3 + p^2 - 4p

At equilibrium: 3p^2 - 12p = 2p^3 + p^2 - 4p

or 2p^3 - 2p^2 + 8p = 0

The only real solution (non-imaginary solution) is p = 0

so q = 0

So the equilibrium point is P = 0, q = 0

The choke price is the price at which q = 0

So the choke price is p = 0

The last 3 digits of my phone number is 007

So the new supply curve is

q = 2p^3 + p^2 - 4p + 7

Depending on the last 3 digits of the phone number, the general equation of the supply curve is

q = 2p^3 + p^2 - 4p + k where k is the last 3 digits of the phone number

The new demand curve is

-(3p + 32)/16 - q + 50 = 0

or (3p + 32) /16 = 50 - q

or 3p + 32 = 800 - 16q

or 3p = 768 - 16q

or p = 256 - 16/3 * q

So the slope of the demand curve is the coefficient of the quantity q.

So the slope is -16/3

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