/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 51 During 2008 the US economy stopp... [FREE SOLUTION] | 91Ó°ÊÓ

91Ó°ÊÓ

During 2008 the US economy stopped growing and began to shrink. Table \(1.25^{48}\) gives quarterly data on the US Gross Domestic Product (GDP), which measures the size of the economy.(a) Fstimate the relative growth rate (percent per year) at the first four times in the table. (b) Economists often say an economy is in recession if the GDP decreases for two quarters in a row. Was the US in recession in \(2008 ?\) $$\begin{array}{c|c|c|c|c|c} \hline t \text { (years since 2008) } & 0 & 0.25 & 0.5 & 0.75 & 1.0 \\ \hline \text { GDP (trillion dollars) } & 14.15 & 14.29 & 14.41 & 14.2 & 14.09 \\\ \hline \end{array}$$

Short Answer

Expert verified
Annual growth rates were 4%, 3.4%, and -5.7%, indicating recession in last two quarters of 2008.

Step by step solution

01

Calculate GDP Changes

First, determine how the GDP changes from quarter to quarter for the first four times in the given table. We have GDPs for 0 to 0.75 years: - From 0 to 0.25 years: 14.29 - 14.15 = 0.14 trillion dollars increase. - From 0.25 to 0.5 years: 14.41 - 14.29 = 0.12 trillion dollars increase. - From 0.5 to 0.75 years: 14.20 - 14.41 = -0.21 trillion dollars decrease.
02

Compute Quarterly Growth Rates

Calculate the relative growth rate for each of these changes:- For 0 to 0.25 years: \(\frac{0.14}{14.15} \times 100 = 0.99\%\).- For 0.25 to 0.5 years: \(\frac{0.12}{14.29} \times 100 = 0.84\%\).- For 0.5 to 0.75 years: \(\frac{-0.21}{14.41} \times 100 = -1.46\%\).
03

Convert Quarterly Rates to Annual Rates

Assume that these quarterly rates compound for four quarters in a year to convert them into annual growth rates. Approximate the annual rate using the formula \((1 + r)^{4} - 1\) where \(r\) is the quarterly rate in decimal:- Annual rate from 0 to 0.25 years: \((1 + 0.0099)^{4} - 1 \approx 0.040\) or \(4.0\%\).- Annual rate from 0.25 to 0.5 years: \((1 + 0.0084)^{4} - 1 \approx 0.034\) or \(3.4\%\).- Annual rate from 0.5 to 0.75 years: \((1 - 0.0146)^{4} - 1 \approx -0.057\) or \(-5.7\%\).
04

Check for Recession

Check if the GDP decreases for two consecutive quarters, indicating a recession. The GDP at 0.5 years is 14.41 trillion, and at 0.75 years is 14.20 trillion, and at 1.0 years it is 14.09 trillion. The GDP indeed falls for two consecutive quarters (0.5 to 0.75 and 0.75 to 1.0 years), confirming a recession in 2008.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91Ó°ÊÓ!

Key Concepts

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

Economic Recession
An economic recession is a period when a country's economy experiences a significant decline. It's like when someone is not feeling well and slows down. In terms of the economy, this means that activities such as employment, company profits, and production of goods start going down.
A common way to detect a recession is by observing the Gross Domestic Product or GDP. If GDP falls for two back-to-back quarters (a total period of six months), economists usually agree that the country is in a recession. In 2008, the US faced such a scenario.
During 2008, GDP numbers showed a decrease over successive quarters, indicating that the economy was indeed shrinking. This situation is similar to how a person might catch a cold and feel less energetic over a few days. The only difference here is that GDP is the thermometer that checks the economy's health.
Quarterly Growth Rate
The concept of a quarterly growth rate refers to how much a particular economic indicator, like the GDP, changes over a three-month period. Each quarter is a part of the year, and observing changes in these smaller periods helps economists spot trends and make comparisons.
To calculate this rate, you compare the GDP values of two quarters. For example, if the GDP increases from 14.15 trillion to 14.29 trillion, you'd calculate the change to find the growth rate. You do this by dividing the change by the initial value and multiplying by 100 to get a percentage. Formally, this formula is:
  • Growth rate = \( \frac{{\text{{Change in GDP}}}}{{\text{{Starting GDP}}}} \times 100 \)
In our example, from 0.00 to 0.25 years, the GDP changed by 0.14 trillion dollars, leading to a quarterly growth rate of 0.99%.
Such calculations help in understanding the short-term health of an economy and is like checking your progress in a task every few days.
Annual Growth Rate
The annual growth rate takes the quarterly growth rate and projects it over a full year, assuming the conditions remain constant throughout the year. This helps to understand how an economy might grow or shrink if it follows the same trends for an entire year.
To calculate this, we use the formula, \( (1 + r)^{4} - 1 \), where \( r \) is the quarterly growth rate expressed as a decimal. For instance, if you have a quarterly growth rate of 0.99%, you would convert that to decimal form (0.0099) and then plug it into the formula.
This calculation is somewhat like looking ahead in a game to predict your final score if you continue scoring at the same rate. It helps economists prepare and make policies that can adjust for upcoming challenges or make the most of expected opportunities.
This annual perspective can be particularly telling, especially when quarterly rates fluctuate, as it offers a big-picture view of economic health.
Gross Domestic Product
Gross Domestic Product, or GDP, is like the report card for a country’s economy. It sums up the value of all the goods and services produced over a specific time.
Think about everything produced in an economy \( e.g., \) cars, healthcare, technology. The total monetary value of these products and services gives the GDP.
Monitoring the GDP is crucial because it gives insight into whether an economy is growing or shrinking. A growing GDP indicates a healthy economy where businesses flourish, more jobs are available, and people usually earn more money. Conversely, a shrinking GDP suggests economic issues such as falling production and potential unemployment.
The GDP data is usually reported on a quarterly basis, allowing for frequent check-ins regarding the economy's state. In 2008, the US GDP data showed a decrease over time, hinting at the impending recession.
So, GDP works as a comprehensive measure, helping everyone, from economists to policymakers, understand the productive health of a country. It strategizes ways to sustain growth or combat recession.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

In Example \(8,\) the demand and supply curves are given by \(q=100-2 p\) and \(q=3 p-50,\) respectively; the equilibrium price is $$ 30\( and the equilibrium quantity is 40 units. A sales tax of \)5 \%$ is imposed on the consumer. (a) Find the equation of the new demand and supply curves. (b) Find the new equilibrium price and quantity. (c) How much is paid in taxes on each unit? How much of this is paid by the consumer and how much by the producer? (d) How much tax does the government collect?

Delta Cephei is one of the most visible stars in the night sky. Its brightness has periods of 5.4 days, the average brightness is 4.0 and its brightness varies by \(\pm 0.35 .\) Find a formula that models the brightness of Delta Cephei as a function of time, \(t,\) with \(t=0\) at peak brightness.

A quantity \(P\) is an exponential function of time \(t .\) Use the given information about the function \(P=P_{b} a^{t}\) to: (a) Find values for the parameters \(a\) and \(P_{0}\). (b) State the initial quantity and the percent rate of growth or decay. \(P=1600\) when \(t=3\) and \(P=1000\) when \(t=1\)

Soybean production, in millions of tons $$\begin{array}{c|c|c|c|c|c|c} \hline \text { Year } & 2000 & 2001 & 2002 & 2003 & 2004 & 2005 \\ \hline \text { Production } & 161.0 & 170.3 & 180.2 & 190.7 & 201.8 & 213.5 \\ \hline \end{array}$$ Whooping cough was thought to have been almost wiped out by vaccinations. It is now known that the vaccination wears off, leading to an increase in the number of cases. w, from 1248 in 1981 to 18,957 in 2004 (a) With \(t\) in years since \(1980,\) find an exponential function that fits this data. (b) What does your answer to part (a) give as the average annual percent growth rate of the number of cases? (c) On May \(4,2005,\) the Arizona Daily Star reported (correctly) that the number of cases had more than doubled between 2000 and \(2004 .\) Does your model confirm this report? Explain.

Values of a function are given in the following table. Explain why this function appears to be periodic. Approximately what are the period and amplitude of the function? Assuming that the function is periodic, estimate its value at \(t=15,\) at \(t=75,\) and at \(t=135\). $$\begin{array}{|c|c|c|c|c|c|c|c|c|c|}\hline t & 20 & 25 & 30 & 35 & 40 & 45 & 50 & 55 & 60 \\\\\hline f(t) & 1.8 & 1.4 & 1.7 & 2.3 & 2.0 & 1.8 & 1.4 & 1.7 & 2.3 \\\\\hline\end{array}$$

See all solutions

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.