Steve Win has purchased land ( an old landfill-from rags to riches) from the cit

Question

Steve Win has purchased land ( an old landfill-from rags to riches) from the city of atlantic city in the marina section of the city. there are stories of a new casino building boom in atlantic city (mgeem is also talking about entering and gump is opening his fourth casino). some talk is circultating that win subdivide his new land purchase and perhaps three casino will e built on the site. suppose that win subdivides his land into two parcels. he builds on one site ans sells the other to another gambling entrepreneur. win estimates that the demand for gambling in the marina area of atlantic city ( After accounting for the presence of two existing casinos in he marina and adjusting for the rest of the casino in atlantic city) to be P= 750 - 5Q. Win of course does not sell the other parcel until his casino is built, thus he has a first mover advantage. win tital cost of producing gampling is TCw=20+40Qw+15.5Qw^2, wins rival is TCr=10+50Qr+20Qr^2. (Qw+Qr=Q). Would atlantic city have done better to sell the land as two seperate parcels rather than as a single parcel to win (given that win was going to subdivide, win and his rival could not collude and win did not have the ability to produce as a monopolist)? you may assume that win and his rival could have been cournot duopolist. if atlantic city could do better, show why and and by how much?   

Can Someone help me ?

Explanation / Answer

At monopoly the optimal solution owuld be the point where MR=MC of Win

MR = dTR/dQ = d(P*Q)/dQ = d(750-5Qw)Qw/dQw = 750-10Qw

and MC=dTC/dQ = d(20_40Qw+15.5w2)/dQw = 40+31Qw

Equating MR and MC

750-10Qw = 40+31Qw

Qw=17.317

and P = 750-5Qw = 750-5(17.317) = $663.42

Now If Win and Rival produce simultanoeusly under cournot competition then their response function will be as -

Qw=17.317-0.1220Qr

and

Qr=14-0.1Qw

From the aboev two response function we get

Qw = 15.80 and

Qr=12.42

and P = $608.90

If Win can act as first mover then Qw = 16 and Qr=12.4 at price of P=$608

And as you can see that the first mover advantage is not much for WIn hence atlantic city have done better to sell the land as two seperate parcels rather than as a single parcel to win.

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