PRINCIPLES OF ECONOMICS
14th Edition
ISBN: 2810015433483
Author: OpenStax
Publisher: OpenStax
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Chapter 2, Problem 25P
If the
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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…
Chapter 2 Solutions
PRINCIPLES OF ECONOMICS
Ch. 2 - Suppose Alphonsos town raised the price of bus...Ch. 2 - Return to the example in Figure 2.4. Suppose there...Ch. 2 - Could a nation be producing in a way that is...Ch. 2 - What are the similarities between a consumers...Ch. 2 - Individuals may not act in the rational,...Ch. 2 - Would an op-ed piece in a newspaper urging the...Ch. 2 - Would a research study on the effects of soft...Ch. 2 - Explain why scarcity leads to tradeoffs.Ch. 2 - Explain why individuals make Choices that are...Ch. 2 - What is comparative advantage?
Ch. 2 - What does a production possibilities frontier...Ch. 2 - Why is a production possibilities frontier...Ch. 2 - Explain why societies cannot make a choice above...Ch. 2 - What are diminishing marginal returns?Ch. 2 - What is productive efficiency? Allocative...Ch. 2 - What is the difference between a positive and a...Ch. 2 - Is the economic model of decision-making intended...Ch. 2 - What are four responses to the claim that people...Ch. 2 - Suppose Alphonsos town raises the price of bus...Ch. 2 - During the Second World War, Germanys factories...Ch. 2 - It is clear that productive inefficiency is a...Ch. 2 - What assumptions about the economy must he true...Ch. 2 - Do economists have any particular expertise at...Ch. 2 - If the price of a magazine is 4 each, what is the...Ch. 2 - If the price of a pie is 12, what is the maximum...Ch. 2 - Draw Maries budget constraint with pies on the...Ch. 2 - What is Maries opportunity cost of purchasing a...
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