ECO370Y5 Study Guide - Midterm Guide: Determinative, Substitute Good, Incentive Compatibility

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Two firms, a and b, compete as a duopoly on price in a market where xa and xb are imperfect (differentiated) substitutes. The demand curves and marginal costs for firms a and b are given as follows: A = tra tca = (pa- ca)xa . A = tra tca = (pa- ca)(1 pa + pb) 2 + papb ca + paca - capb)/dpa = 0 pa = (1/2)(1 + pb + ca) pb = (1/2)(1 + pa + cb) 2pa = 1 + pb + ca d a/dpa = d((pa- ca)(1 pa + pb))/dpa = 0 d a/dpa = d(pa pa d a/dpa = 1 2pa + pb 0 + ca - 0 = 0. 2pa = 1 + ((1/2)(1 + pa + cb)) + ca. Firm a: ca = cb = c pa = pb = (1 + c)/(2 - . Xa = 1 (1 - )(1 + c)/(2 - .

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