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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.
(b) Calculate the manager's risk premium for the prospect P and use it to explain whether or not he will buy the new technology.
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