Rubinstein2005-page104 - k experts (input) to prepare the...

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October 21, 2005 12:18 master Sheet number 102 Page number 86 86 Lecture Seven viewers as possible within 4 units of time. The wage paid to each worker is w (even when he is idle). In one unit of time, a worker can talk to one respondent or be involved in the transfer of information to or from exactly one colleague. At the end of the 4 units of time, the collected information must be in the hands of one colleague (who will announce the results). What is the Frm’s product? Calculate the cost function and examine its convexity. Problem 5. ( Moderately difFcult ) Consider a Frm producing one commodity using L inputs, which maximizes production subject to the constraint of nonnegative proFts. Show some interesting properties of such a Frm’s behavior. Problem 6. ( Standard ) An event that could have happened with probability 0 . 5 either did or did not occur. A Frm has to provide a report of the form “the event occurred” or “the event did not occur.” The quality of the report, q (the Frm’s product), is the probability that the report is correct. The Frm employs
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Unformatted text preview: k experts (input) to prepare the report. Each of them receives an independent signal whether the event occurred or not, which is correct with probability 1 > p > . 5. Calculate the production function q = f ( k ) for (at least) k = 1, 2, 3, . . . . We say that a discrete production function is concave if the sequence of marginal product is nonincreasing. Is the Frms production func-tion concave? Assume that the Frm needs information in order to make a decision whether to invest amount m that will yield revenue m if the event occurs, and 0 otherwise; the decision maker chooses k in order to maximize expected proFts. Assume that the wage of each worker is w . Explain why it is true that if f is concave, the Frm chooses k so that the k th worker is the last one for whom marginal revenue exceeds the cost of a single worker. Is this conclusion true in our case?...
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