Assumptions. The Cournot Model. Assumptions. Assumptions. Assumptions. Assumptions. P An important assumption, the heart of the Cournot model. D.

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1 Assumptions Two firms A, nd B Mngeril Economics-Chrles W. Upton Assumptions Assumptions Two firms A, nd B The industry demnd function is P Two firms A, nd B The industry demnd function is Firm A produces ; firm B produces B P Q Q Assumptions Assumptions Two firms A, nd B The industry demnd function is Firm A produces ; firm B produces B Firm A tkes its demnd function s - B P b Q Two firms A, nd B The industry demnd function is Firm A produces ; firm B produces B Firm A tkes its demnd function s - B P An importnt ssumption, the hert of the Cournot model. b Q

2 Solving problem Solving problem MR MC Solving problem Symmetry p* Just s Firm A is choosing to mximize profits, so too is Firm B choosing B to mximize profits. MR MC * Symmetry Just s Firm A is choosing to mximize profits, so too is Firm B choosing B to mximize profits. If B chnges its output, A will rect by chnging its output. A Rection We do the mthemticl pproch first nd then the grphicl pproch.

3 A Rection The industry demnd function Q = 00 p. A Rection The industry demnd function Q = 00 p. The inverse demnd function is P = 50 (/)Q A Rection The industry demnd function Q = 00 p. The inverse demnd function is P = 50 (/)Q demnd function is then P = 50 (/)( + B ) A Rection demnd function is then P = 50 (/)( + B ) The firm s profits re p = P 5 A Rection demnd function is then P = 50 (/)( + B ) The firm s profits re π = [50 (/)( + B )] 5 A Rection p = [50 (/)( + B )] 5 3

4 A Rection A Rection π = [50 (/)( + B )] 5 π = 50 (/) (/) B 5 π = [50 (/)( + B )] 5 π = 50 (/) (/) B 5 π = (/) (/) B A Rection A Rection π = b π = dπ d = b b A Rection Symmetry dπ d = = b b = 0 = (/) B There is similr rection function for B B = (/) 4

5 Solving for Solving for = (/) B B = (/) = (/)[ (/) ] =.5 + (/4) = (/)[ (/) ] Solving for Solving for = (/)[ (/) ] =.5 + (/4) (3/4) =.5 = (/)[ (/) ] =.5 + (/4) (3/4) =.5 = (4/3).5 Solving for A Grphicl Approch = (/)[ (/) ] =.5 + (/4) (3/4) =.5 = (4/3).5 = 30 B = 30 = (/) B We wnt to use the rection function to come to grphicl solution, 5

6 A Grphicl Approch A Grphicl Approch = (/) B When B produces nothing A should rect by producing the monopoly output (). = (/) B When B produces nothing A should rect by producing the monopoly output (). When B produces the output of the competitive industry (), A should rect by producing nothing. A Grphicl Approch = (/) B When B produces nothing A should rect by producing the monopoly output (). When B produces the output of the competitive industry (), A should rect by producing nothing. Similr rules pply for rections. Grphing the Rection Grphing the Rection If B produces nothing, A cts like monopoly If B produces the competitive output, A produces nothing. Grphing the Rection Rection 0 6

7 Grphing the Rection If A produces the competitive output, B produces nothing. If A produces nothing, B cts like monopoly. Rection Grphing the Rection Rection Rection Grphing the Rection If A nd B re off their rection functions, they rect nd chnge output. Here B expnds, A contrcts. Grphing the Rection Grphing the Rection If A is here, B wnts to be here Grphing the Rection If B is here, A wnts to be here 7

8 Euilibrium The Bsic Steps Rection Rection Plot the rection functions If B produces nothing, A behves like monopoly If B produces competitive output, A produces nothing Solve for their intersection End 003 Chrles W. Upton 8