1. Stark Real Estate (S) competes with Rogers Properties (R) in the St. Louis market for commercial real estate. The demand for retail space is given by

P = 52 3Q

where Q = Q_S + Q_R is the total available retail space in thousands of square feet. S's cost function is C(Q_S) = 4Q_S, so that S's marginal costs are MC_S = 4.

R's cost function is C(Q_R) = 10Q_R, so that R's marginal costs are MC_R = 10.

Given the demand relationship above, S's marginal revenue function is

MR_S= 52 3Q_R 6Q_S

while R's marginal revenue function is

MR_R = 52 3Q_S 6Q_R.

What are the Cournot equilibrium quantities (Q_S and Q_R) and price in this market?

Sub in QR = 7-1/2Qs in S's revenue curve

Qs = 8-1/2(&-1/2Qs)

• 8-7/2+1/4Qs
• Qs-1/4Qs = 9/2
• 3/4Qs = 9/2
• Qs = 9/2*4/3
• Qs = 6

Sub in Qs = 8-1/2QR in Rs reaction curve.

• Qr = 7-1/2 (801/2QR)
• QR = 7-4+1/4QR
• QR-1/4QR = 3
• 3/4QR = 3
• QR=3*4/3
• QR =4

Since Qs = 6 & QR =4 & Q = Qs+QR

• Q = 10

Q = 10 in demand curve.

P = S2-3(10)

P = S2 -30

• P = 22