CHAPTER 4 PROJECT

CHAPTER 4 PROJECT The U.S. Economy

Economic data is quite variable and very complicated, making it difficult to model. The models we use here are rough approximations of the Unemployment Rate and Gross Domestic Product (GDP).

The unemployment rate can be modeled by \[ U = U(t) = \dfrac{5\;\cos \;\dfrac{2t}{\pi}}{2+\sin \dfrac{2t}{\pi}} + 6 \qquad 0 \leq t \leq 25 \]

where \(t\) is in years and \(t = 0\) represents January 1, 1985.

The GDP growth rate can be modeled by \[ G=G(t) = 5\;\cos \;\!\left(\dfrac{2t}{\pi} +5\right)+2 \qquad 0 \leq t \leq 25 \]

where \(t\) is in years and \(t = 0\) represents January 1, 1985. If the GDP growth rate is increasing, the economy is expanding and if it is decreasing, the economy is contracting. A recession occurs when GDP growth rate is negative.

  1. During what years was the U.S. economy in recession?
  2. Find the critical numbers of \(U=U(t).\)
  3. Determine the intervals on which \(U\) is increasing and on which it is decreasing.
  4. Find all the local extrema of \(U\).
  5. Find the critical numbers of \(G=G(t).\)
  6. Determine the intervals on which \(G\) is increasing and on which it is decreasing.
  7. Find all the local extrema of \(G\).
    1. Find all the inflection points of \(G\).
    2. Describe in economic terms what the inflection points of \(G\) represent.
  9. Graph \(U=U(t)\) and \(G=G(t)\) on the same set of coordinate axes.
  10. Okun’s Law states that an increase in the unemployment rate tends to coincide with a decrease in the GDP growth rate.
    1. During years of recession, what is happening to the unemployment rate? Explain in economic terms why this makes sense.
    2. Use your answer to part (a) to explain whether the functions \(U\) and \(G\) generally agree with Okun’s Law.
    3. If there are times when the functions do not satisfy Okun’s Law, provide an explanation in economic terms for this.
  11. What relationship, if any, exists between the inflection points of the GDP growth rate and the increase/ decrease of the unemployment rate? Explain in economic terms why such a relationship makes sense.
  12. One school of economic thought holds the view that when the economy improves (increasing GDP), more jobs are created resulting in a lower unemployment rate. Others argue that once the unemployment rate improves (increases), more people are working and this increases GDP. Based on your analysis of the graphs of \(U\) and \(G\), which position do you support?

For real data on the unemployment rate and GDP, see http://www.bls.gov/data/ and http://www.tradingeconomics.com/United-States/gdp-growth

To read Arthur Okun’s paper, see http://cowles.econ.yale.edu/P/cp/p01b/p0190.pdf