Micro Effects on Government

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ECON30600 Microeconomics III Semester 2 Tutorial 1: Information Questions adapted from Information Economics: Birchler and Butler are labelled with IE and the number of the problem in that text. IE Problem 3.3 Sunshine or rain? The probability of rain is 3/4 and of sunshine 1/4. A weather service has the following forecast probabilities: if it is to be sunny, the service announces “fair” with probability 3/4 and “bad” with probability 1/4; if it will rain, the service announces “fair” and “bad” with probability 1/2 each. What is the probability of a sunny day after a forecast “fair”? IE Problem 3.4 Debtor solvency. A bank would like to know the probability with which a debtor fails. From the debtor's profit and loss statement the bank can derive an estimate of these probabilities. We denote the probability of solvency Pr(S) by p > 1/2 and the probability of default Pr(F) by 1– p. In addition, the bank can conduct a special audit leading to a forecast f or s. The forecast reflects the true state with precision Pr(s|S) = Pr(f|F) = q. (a) What is the overall probability that the auditor will forecast a failure? (b) What is the probability that a bank is solvent, but the auditor forecasts a failure? (A better wording is "What is the probability that the auditor forecasts failure when the bank is solvent?") (c) What is the probability that after an auditor's forecasts of a failure, the bank turns out to be solvent? IE Problem 3.5 Medical testing. Tests for HIV have a very high accuracy. An infected (non-infected) individual has a 99.9 per cent chance of getting a positive (negative) test result. Some people have proposed that everyone should be tested for HIV. Others worry that too many healthy individuals would get a positive result. In Switzerland, 20,000 of the 7 million resident population are HIV positive. (The infection rate is higher compared

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