MICROECONOMICS
MICROECONOMICS
11th Edition
ISBN: 9781266686764
Author: Colander
Publisher: MCG
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Chapter 3, Problem 4QE
To determine

Solution to the central economic problems given by the centrally planned economy.

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2. Question The 'Democratic Family' consists of three members {mother m, father f, daughter d}, that have different preferences with respect to how much money X € [0,8] they think should be invested in the new family car. These preferences can be represented by the following utility functions: - Mother m: um(X) = 2X - X² Father f: uf(X) = 10X - X² - Daughter d: ud(X) = 4X - X² Calculate for each family member (f, m, d) the preferred amount of money to invest in the new car denoted by X; for i = {m, f,d}. Assume that (Xf, Xm, Xd) are the three alternatives on which the family must decide. Show that each family member has rational preferences over this domain. Preferences on the family level are determined by pairwise majority voting (all family members vote on two alternatives). Derive the family preference and check whether it is rational. Assume that the final family decision is made by conducting sequential pair- wise majority voting, where the loosing alternative is eliminated. Does…
3. Question You invented a new lateral-flow test for asymptomatic Covid-19 detection, where saliva is entered into a test-tube and then the result is shown directly on the device. However, to save on costly chemicals you designed the tests such that it always reports a negative test result. Assume that the incidence rate is 5 per 1000 and that your test is used for detection of asymptomatic cases (without symptoms). (a) Calculate the probability that 100 randomly determined volunteers receive a correct test result by using the AND-rule and the OR-rule. Can your test be qualified as a diagnostic test? (b) The health authorities are investigating the performance of your test. Government guidelines require a specificity (conditional probability to re- ceive a negative test result given that the test-taker is not infected with COVID19) of at least 97% and a sensitivity (conditional probability to receive a positive test result given that the test-taker is infected with COVID-19) of at…
3. Question You invented a new lateral-flow test for asymptomatic Covid-19 detection, where saliva is entered into a test-tube and then the result is shown directly on the device. However, to save on costly chemicals you designed the tests such that it always reports a negative test result. Assume that the incidence rate is 5 per 1000 and that your test is used for detection of asymptomatic cases (without symptoms). (a) Calculate the probability that 100 randomly determined volunteers receive a correct test result by using the AND-rule and the OR-rule. Can your test be qualified as a diagnostic test? (b) The health authorities are investigating the performance of your test. Government guidelines require a specificity (conditional probability to re- ceive a negative test result given that the test-taker is not infected with COVID19) of at least 97% and a sensitivity (conditional probability to receive a positive test result given that the test-taker is infected with COVID-19) of at…
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