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Chapter 7: Problem 29

A survey of the opinions of 10 leading economists in a certain country showed that, because oil prices were expected to drop in that country over the next 12 months, 7 had lowered their estimate of the consumer inflation rate. 8 had raised their estimate of the gross national product (GNP) growth rate. 2 had lowered their estimate of the consumer inflation rate but had not raised their estimate of the GNP growth rate. How many economists had both lowered their estimate of the consumer inflation rate and raised their estimate of the GNP growth rate for that period?

Short Answer

Expert verified
In this problem, we are asked to find how many economists both lowered their estimate of the consumer inflation rate and raised their estimate of the GNP growth rate. Defining A as the set of economists who lowered the consumer inflation rate and B as the set of economists who raised the GNP growth rate, we have |A|=7, |B|=8, and |A鈭〣'|=2. From this, we can calculate the intersection of A and B as |A鈭〣|=|A|-2=7-2=5. Thus, 5 economists both lowered their estimate of the consumer inflation rate and raised their estimate of the GNP growth rate for that period.

Step by step solution

01

Define the sets

Let's define the sets as follows: - Let A be the set of economists who lowered their estimate of the consumer inflation rate. - Let B be the set of economists who raised their estimate of the GNP growth rate.
02

Fill in the given information

Using A and B, we can represent the given information as follows: - |A| = 7 (7 economists lowered their estimate of the consumer inflation rate) - |B| = 8 (8 economists raised their estimate of the GNP growth rate) - |A 鈭� B'| = 2 (2 economists lowered their estimate of the consumer inflation rate but did not raise their estimate of the GNP growth rate)
03

Calculate the intersection of A and B

We want to find out how many economists belong to both sets A and B, meaning we want to find |A 鈭� B|. Since, |A 鈭� B'| = 2, we can represent this as: \[|A \cap B'| = |A| - |A \cap B| \Rightarrow 2 = 7 - |A \cap B| \]
04

Compute |A 鈭� B|

Now, we solve for |A 鈭� B| using the equation we derived in step 3. \[|A \cap B| = |A| - 2 = 7 - 2 = 5\] So, 5 economists both lowered their estimate of the consumer inflation rate and raised their estimate of the GNP growth rate for that period.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Economist Surveys
Economist surveys are vital tools used to gather insights from economists about future economic trends and conditions. These surveys typically involve a selection of economists who are asked about their expectations for various economic indicators. In our example, economists were surveyed on their views regarding oil prices, the consumer inflation rate, and the gross national product (GNP) growth rate. This helps policymakers, businesses, and other stakeholders to anticipate economic conditions and make informed decisions.
  • Surveys provide a collective snapshot of expert opinions.
  • The focus is on predicting performance metrics like inflation and GNP.
  • Results from these surveys can influence economic policy and strategy.
Consumer Inflation Rate
The consumer inflation rate measures how fast the general level of prices for goods and services is rising, and, subsequently, how purchasing power is falling. It is typically expressed as an annual percentage increase. In practice, a lower estimate of the consumer inflation rate suggests that economists expect slower increases in the costs of living. This might occur due to factors like expected drops in oil prices, as mentioned in our exercise.
  • Major factor: determines cost of living changes.
  • Affects consumer purchasing capacity and monetary policy.
  • Low inflation may indicate economic stagnation or improved supply of goods.
Gross National Product (GNP)
Gross National Product (GNP) refers to the total value of all finished goods and services produced by a country's citizens in a given time period, including overseas activities. Economists use GNP to gauge a country's economic performance. An increase in GNP, as raised in estimates by many economists, indicates a potential uptick in economic output, employment, and national wealth. This expectation might arise from predicted stability or growth factors, such as reductions in oil prices, which can reduce operational costs and stimulate economic activity.
  • Reflects total economic output originating from a nation's citizens.
  • Higher GNP growth rates signal economic expansion and prosperity.
  • Affected by changes in domestic and international economic conditions.
Problem Solving in Mathematics
Problem-solving skills are crucial in mathematics, as they enable students and professionals to tackle and solve complex issues using logical reasoning and mathematical concepts. In the given exercise, set theory concepts are applied to find how many economists both lowered their estimate of inflation and raised their estimate of GNP growth rate. This involves understanding intersections of sets and using logical deductions.
  • Set Theory: Utilizes intersections and complements to solve problems.
  • Logical Reasoning: Essential for deducing information from given data.
  • Practical Application: Solving real-world problems in economics and beyond.

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Most popular questions from this chapter

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