Homework 3-
1. Consider an economy that has a population of 100,000 people. In this economy 20% of the total population is less than sixteen years old; 10% of the total population is retired and not working; 10% of the total population is not in the labor force; and the number of discouraged workers is equal to the number of cyclically unemployed workers. You are given some other information about this economy.
- This economy is currently not producing at full employment and therefore its unemployment rate is not equal to the natural rate of unemployment.
- You are also told that the number of cyclically unemployed people is equal to 10% of the actual number of unemployed people.
- When this economy produces at full employment and therefore is operating at the natural unemployment rate, the number of frictionally unemployed people is equal to 75% of the naturally unemployed.
- Finally you know that in this economy the number of discouraged workers plus the number of employed workers is equal to 50,000 people.
In answering this question you will find it helpful to use the following symbols:
N = the number of naturally unemployed people in the economy
U = the actual number of unemployed people in the economy
F = the number of frictionally unemployed people in the economy
S = the number of structurally unemployed people in the economy
C = the number of cyclically unemployed people in the economy
D = the number of discouraged workers in the economy
a. Based on the above information, how many people are less than sixteen years old in this economy?
b. Based on the above information, how many people are retired in this economy?
c. Based on the above information, how many people are not in the labor force?
d. Based on the above information, how many people are either in the labor force or are discouraged workers? Write an equation expressing the relationship between the labor force and the number of discouraged workers. Hint: you might find it interesting to see how many variations on this equation you can write.
e. Write an equation using the above symbols for the number of naturally unemployed people. Then, revise this equation using the information you were given at the beginning of this problem.
f. Write an equation using the above symbols for the actual number of unemployed people?
g. What is the actual number of unemployed workers in this economy? Hint: this will take some manipulation of the equations you have written and the information you have been given.
h. What is the number of naturally unemployed workers in this economy? Hint: this will take some manipulation of the equations you have written and the information you were given.
i. What is the number of frictionally unemployed workers in this economy?
j. What is the number of cyclically unemployed workers in this economy?
k. What is the number of structurally unemployed workers in this economy?
l. What is the number of discouraged workers in this economy?
m. What is the number of employed workers in this economy?
n. What is the actual unemployment rate for this economy? Hint: the numbers will be a bit messy here-calculate the unemployment rate to two places past the decimal.
2. Suppose there are 20,000 people 16 years or older in Provincetown. Of this 20,000 people:
- 4,000 are currently working part-time and are satisfied with their jobs;
- 2,000 are currently working part-time and want to work full-time;
- 10,000 are working full-time;
- 1,000 are discouraged workers; and
- The rest of this population is currently not working, but actively looking for work and available for work.
a. What is the current unemployment rate in Provincetown? Calculate this rate to two places past the decimal.
b. What is the unemployment rate if Provincetown classifies discouraged workers as unemployed workers?
c. What is the unemployment rate if Provincetown classifies discouraged workers and part-time workers wanting to work full-time as unemployed workers?
d. Does the way we defined who is unemployed matter? Explain your answer.
3. Consider a community with 50,000 people in the labor force. Of these 50,000 people 5,000 are frictionally unemployed, 4,000 are structurally unemployed, and 2,000 are cyclically unemployed. In addition to the 50,000 people in the labor force this community also has an additional 2,000 people who are considered discouraged workers.
a. What is the current unemployment rate in this community?
b. What is the frictional unemployment rate in this community?
c. What is the structural unemployment rate in this community?
d. What is the cyclical unemployment rate in this community?
e. Does the sum of the frictional, structural, and cyclical unemployment rate equal the overall unemployment rate?
Suppose this community reclassifies discouraged workers and now considers these workers frictionally unemployed.
f. What is the new frictional unemployment rate given this change in the classification of discouraged workers?
g. What is the new structural unemployment rate given this change in the classification of discouraged workers?
h. What is the new cyclical unemployment rate given this change in the classification of discouraged workers?
i. What is the new unemployment rate given this change in the classification of discouraged workers?
j. Compare your answers in (a) and (i). What conclusions do you draw from this comparison?
4. Suppose that the market basket for computing the consumer price index in Salem consists of 5 potatoes, 2 steaks, 10 cookies, and 1 bag of charcoal. You are given the following price data for 2006 through 2011 in Salem.
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Item
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Price in 2006
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Price in 2007
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Price in 2008
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Price in 2009
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Price in 2010
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Price in 2011
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1 Potato
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$0.20
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$0.20
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$0.30
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$0.40
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$0.40
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$0.60
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1 Steak
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$5.00
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$5.50
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$5.50
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$6.00
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$6.00
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$6.00
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1 Cookie
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$0.10
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$0.10
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$0.10
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$0.15
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$0.20
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$0.20
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1 Bag of Charcoal
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$4.00
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$4.00
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$4.00
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$5.00
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$5.00
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$5.00
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a. Using the above data compute the cost of each market basket. Put your answers in the following table.
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Cost of Market Basket in 2006
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Cost of Market Basket in 2007
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Cost of Market Basket in 2008
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Coat of Market Basket in 2009
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Cost of Market Basket in 2010
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Cost of Market Basket in 2011
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b. Now, calculate the CPI for 2006 through 2011 using 2006 as the base year. Enter your results in the following table. Use a 100 point scale for the CPI. Carry your answer out to two places past the decimal.
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Year
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CPI
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2006
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2007
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2008
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2009
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2010
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2011
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c. Now, using the answers you got in part (b) calculate the annual rate of inflation in this economy from 2007 through 2011. Enter your answers in the table provided. Carry your answer out to two places past the decimal.
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Year
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Rate of Inflation
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2007
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2008
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2009
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2010
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2011
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d. Now, redo the CPI you found in part (b) with 2009 as the base year. Enter your results in the following table. Use a 100 point scale for the CPI. Carry your answer out to two places past the decimal.
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Year
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CPI
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2006
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2007
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2008
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2009
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2010
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2011
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e. Now, using the answers you got in part (d) calculate the annual rate of inflation in this economy from 2007 through 2011. Enter your answers in the table provided. Carry your answer out to two places past the decimal.
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Year
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Rate of Inflation
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2007
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2008
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2009
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2010
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2011
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f. Compare your answers in (b) and (d). Are they the same? If they are the same, explain why you got this result. If they are different, explain why you got this result.
g. Compare your answers in(c) and (e). Are they the same or different? Explain your results.
5. Suppose an economy's aggregate production function can be expressed as
Y = AKαL1-α
where Y is real GDP, A is a measure of the available technology, K is the number of units of capital available, L is the number of units of labor available, and α is a constant between zero and one that measures capital's share of total product or total income (recall from the circular flow diagram that total production equals total income in the aggregate economy).
Suppose that A = 10, K = 81, and L varies. In addition, you know that α is equal to .5. Use this information to answer the following questions. You might find it helpful to use excel to answer this question since a spreadsheet program will simplify the calculations and, in addition, the program can graph the data you submit.
a. Given the above information fill in the following table. In the real GDP and marginal product of labor columns carry your answer out to two places past the decimal.
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Units of Labor
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Units of Capital
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Real GDP
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Marginal Product of Labor
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0
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-----
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1
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2
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.....
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All the way to 36
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b. Given your results in(a), describe what is happening to the marginal product of labor as the number of units of labor is increasing?
c. Draw a graph of your aggregate production function with real GDP on the vertical axis and labor on the horizontal axis.
d. Now, suppose that the level of technology changes in this economy so that the value of A is now equal to 30. Redraw the graph of this economy's new aggregate production function on a new graph. On this new graph represent the economy's original aggregate production function as well as the economy's new aggregate production function. What happens to the aggregate production function when the level of technology increases?
e. Given your work in part (d), what happens to labor productivity when the level of technology increases holding everything else constant?
6. Suppose that the supply and demand curves for labor for an economy are given by the following equations:
Demand for Labor: w = 10 - (1/50)L
Supply of Labor: w = 1 + (1/400)L
where w is the wage rate per unit of labor and L is the quantity of labor. Furthermore, you now that aggregate production, Y, in this economy is determined by the following aggregate production function:
Y = f(K, L) = AKαL1-α
where A is a measure of the available technology, K is capital, and L is labor. Suppose the value of A is 10, K is 100, and α is .5.
a. Given the above information, what is the equilibrium quantity of labor and the equilibrium wage rate?
b. What is labor's total income in this economy?
c. Assume the labor market is in equilibrium. What is the value of full employment for this economy?
d. Suppose there is no change in this economy's labor market but that the level of capital increases to 256 units. Describe what happens to the full employment level of output for this economy.
e. Returns to scale describes what happens to output when all inputs are changed by the same proportion. Recall from your microeconomics class decreasing returns to scale (e.g., all inputs doubled and output less than doubled), constant returns to scale (e.g., all inputs doubled and output doubled), and increasing returns to scale (e.g., all inputs doubled and output more than doubled). Identify the type of returns to scale this economy has and provide a proof of this answer.