Question

Two airlines compete in prices. The can differentiate the product so that their respective demand functions look like

Qa=4000-25Pa+12Pb

Qb=3000-20PPa

AVCa=MCa=160

AVCb=MCb=180

profit functions are

πa(Pa,Pb)=(Pa-160)(4000-25Pa+12Pb)

πb(Pa,Pb)=(Pb-180)(3000-20Pb-10Pa

Reaction functions are

Pa=160+(6/25)Pb

Pb=165+(1/4)Pa

(2 points) Use this information to draw each firms reaction function. (Hint: let pA be on the horizontal axis and pB in the vertical axis)

(3 points) Find the Nash equilibrium choice of prices.

Answer 1

a)

Pb	Pa=160+(6/25)*Pb
0.00	160.00
50.00	172.00
100.00	184.00
150.00	196.00
200.00	208.00
218.09	212.34
250.00	220.00

Pb=165+(1/4)*Pa	Pa
165.00	0.00
177.50	50.00
190.00	100.00
202.50	150.00
215.00	200.00
218.09	212.34
227.50	250.00

b)

We are given

Pb=165+(1/4)*Pa

Set Pa=160+(6/25)*Pb

Pb=165+(1/4)*[160+(6/25)*Pb]=165+40+(3/50)Pb

(47/50)Pb=205

Pb=(205*50/47)=$218.0851 or say $218.09

Pa=160+(6/25)*Pb=160+(6/25)*218.0581=$212.3409 or say $212.34