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Comparative Economics: Two high-tech firms (1 and 2) are considering a joint venture. Each firm i can invest in a novel technology and can choose a level of investment xi ∈ [0, 5] at a cost of ci(xi) = xi2/4 (think of xi as how many hours to train employees or how much capital to spend for R&D labs). The revenue of each firm depends on both its investment and the other firm’s investment. In particular if firms i and j choose xi and xj , respectively, then the gross revenue to firm i is
⎧ ⎪⎨ 0
R(xi,xj)=⎪2 ⎩xi .xj
i f x i < 1
ifxi≥1 andxj<2 ifxi ≥1 andxj ≥2.
a. Write down mathematically and draw the profit function (gross rev- enue minus costs) of firm i as a function of xi for three cases: (i) xj < 2, (ii)xj =2,and(iii)xj =4.
b. What is the best-response function of firm i?
c. It turns out that there are two identical pairs of such firms; that is,
the description applies to both pairs. One pair is in Russia, where coordination is hard to achieve and businesspeople are very cautious, and the other pair is in Germany, where coordination is common andbusinesspeople expect their partners to go the extra mile. You learn that the Russian firms are earning significantly lower profits than the German firms, despite the fact that their technologies are identical. Can you use Nash equilibrium analysis to shed light on this dilemma? If so, be precise and use your previous analysis to do so.
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