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In period t, firm X chooses x t to maximize (1 By t1 2 )x t 0.5x t 2 and firm Y chooses y t
In period t, firm X chooses xt to maximize (1 Byt12)xt 0.5xt2 and firm Y chooses yt to maximize (1 xt1)yt 0.5yt2.
(a) Describe the dynamic evolution of firm decisions by a dynamical system on (x, y) 2.
(b) Find all steady states of this system.
(c) Which steady states are locally stable? How does your answer depend on parameter B?
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