425-hw4-singh-vives - p i = f i ( q i ; q j ) . (c) Find...

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ECON 425 Assignment #4 Consider the following duopoly model of di/erentiated products where the goods can be either substitutes q 1 = 120 2 p 1 + 2 q 2 = 90 + 1 2 p 2 where q 1 and q 2 measures the degree that the two goods are related in demand. If & > 0 the goods are substitutes. If & < 0 the goods are compliments. 1. For the case where = 1
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Unformatted text preview: p i = f i ( q i ; q j ) . (c) Find the mixed Nash equilibrium pro&amp;ts when i. Firm one chooses price and &amp;rm two chooses quantity ii. Firm one chooses quantity and &amp;rm two chooses price. Note that since the demand functions are not symmetric, your answer to (ii) will not be the reverse of (i) 2. Re-do question [1] with &amp; = &amp; 1 . 3. Using the pro&amp;ts calculated in [1] and [2], construct the payo/ matrix for the strategic game where the two &amp;rms simultaneously choose between a price or quantity strategy. Determine for each case ( &amp; = 1 ; &amp; = &amp; 1 ) whether there is a dominant strategy 1...
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