Consider a manufacturing firm with a production process that relies on some technology that is inherently random. In particular, in each month, the productivity of the firm generates a baseline level of net revenue equal to 350 (in thousands of dollars). However, the actual net revenues generated vary due to the variation in output caused by the production technology. The variation can be represented as a risky lottery, P , with the resulting changes in net reven

Holt Mcdougal Larson Pre-algebra: Student Edition 2012
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ISBN:9780547587776
Author:HOLT MCDOUGAL
Publisher:HOLT MCDOUGAL
Chapter11: Data Analysis And Probability
Section11.8: Probabilities Of Disjoint And Overlapping Events
Problem 2C
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Consider a manufacturing firm with a production process that relies on some technology that is inherently random. In particular, in each month, the productivity of the firm generates a baseline level of net revenue equal to 350 (in thousands of dollars). However, the actual net revenues generated vary due to the variation in output caused by the production technology. The variation can be represented as a risky lottery, P , with the resulting changes in net revenue (in thousands of dollars) as the listed outcomes, given by

P= (.4, -50; .25, 10; .35, 50)

Now, suppose u(x)= x.2 is the utility function over net revenue (in thousands of dollars) for the firm's manager. (That is, u(350) gives the utility from 350 thousands of dollars.) The manager knows about a new technology that regulates the output so that there is no variation in productivity or net revenue. That is, if the firm buys this new technology, the resulting net revenue will be equal to 350 (thousands of dollars) with certainty (eliminating both the times when productivity is low and when it is high). However, the new technology will impose an additional cost of 2 (thousand dollars) per month. 

(c)  Finally, suppose u(x)= x.8 . Explain whether the manager is more or less risk averse than in part (b). Then calculate the risk premium for P with this new utility function and explain whether or not your answer (about whether to buy the technology) will change.
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