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Jane is searching for a summer job. She has surveyed the market and has determined that the offer distribution for summer jobs is uniform with a...

Jane is searching for a summer job. She has surveyed the market and has determined that the offer distribution for summer jobs is uniform with a lower bound of $5, 000 and an upper bound of $20,000. Hence, any offer in the range between $5,000 and $20,000 is equally likely, so Pr(offer = x) = 1/15000, for any x ∈ [5000, 20000]. Obtaining offers requires resources and effort, and Jane has determined that the cost of obtaining an offer is equivalent to a monetary payment of c = 500 dollars. Jane can draw as many offers as she pleases. Each one costs her 500 dollars. After each draw she decides to accept or reject the current offer. If she rejects the offer, she draws again. If she accepts, she is done searching. Define the reservation level, R, such that all offers below R are rejected and all offers at or above R are accepted.
1. Determine the average value of a draw from the offer distribution.
2. For a given reservation level, R, determine the expected search cost.
3. For a given reservation level, R, determine the expected value of a job conditional on it being accepted.
4. The value of search for a given reservation level strategy is the sum of expected search costs and the expected value of an acceptable job. Determine the value of searching as a function of the given reservation level, U(R). Draw U(R) in a figure with R on the horizontal axis and U(R) on the vertical axis. Include the 45◦ line in the graph.
5. Determine the optimal choice of R. 6. What is the average value of a job that Jane accepts? What is the average number of offers
that Jane will draw before an acceptable offer is made?
7. Suppose that the offer distribution changes so that the lower bound is 0 dollars and the upper bound is $25,000. The distribution remains uniform so all offers between 0 and 25000 are equally likely. What is the value of the average realization from the distribution? What is Jane’s new optimal choice of R? What is the average number of offers Jane will draw before accepting? Explain why R changes and the direction of change.

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