Consider the following 'partnership problem.' To friends start a joint venture and split profits equally. The...

 

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Consider the following 'partnership problem.' To friends start a joint venture and split profits equally. The revenue is split equally and varies with how much effort they invest in their partnership. Effort is measured here by how many hours they devote to the partnership. To fix ideas, say that the total profit is 1800(h1+h) + 40hh when friend i spends h, hours working for the partnership. The opportunity cost for devoting hi hours to the partnership is 20h. Hence payoffs are: Su(h, h) = 1800 (h1+2)+40h1h2 20h - u2 (h1, h2): - 20h3. 1800(h1+h2)+40h1h2 2 (a) Compute the best responses and represent them on a graph. (b) Represent the Nash equilibrium on the graph in (a), and compute it precisely (using algebra). (c) Is the Nash equilibrium computed in (b) Pareto efficient? Consider the following 'partnership problem.' To friends start a joint venture and split profits equally. The revenue is split equally and varies with how much effort they invest in their partnership. Effort is measured here by how many hours they devote to the partnership. To fix ideas, say that the total profit is 1800(h1+h) + 40hh when friend i spends h, hours working for the partnership. The opportunity cost for devoting hi hours to the partnership is 20h. Hence payoffs are: Su(h, h) = 1800 (h1+2)+40h1h2 20h - u2 (h1, h2): - 20h3. 1800(h1+h2)+40h1h2 2 (a) Compute the best responses and represent them on a graph. (b) Represent the Nash equilibrium on the graph in (a), and compute it precisely (using algebra). (c) Is the Nash equilibrium computed in (b) Pareto efficient?