102 Economics Spring 2008 Answers to Homework #3 Due March 31, 2008 On your homework please include at the top of the first page your name, TA name, and the section number for the discussion section you attend. All homeworks should be legible and neat: do a professional looking job!
Question 1. Unemployment. In 2007, there were 2,500,000 adults in China. 1,800,000 of the adults were employed; 500,000 were unemployed; 100,000 were discouraged workers; and 100,000 were not working or seeking jobs in 2007. Among the unemployed, 390,000 were engaged in job search, and 100,000 were in the labor markets where the number of people seeking jobs is more than the number of jobs available. a. What are the labor force and unemployment rates in 2007? Labor force = Employed + Unemployed = 1,800,000 + 500,000 = 2,300,000. Unemployment rate = (Unemployed/Labor force) 100% = (500,000/2,300,000)100% = 21.74% b. What is the frictional, structural, and cyclical unemployment in 2007? What is the natural rate of unemployment in 2007? Frictional unemployment = 390,000 Structural unemployment = 100,000 Natural unemployment = Frictional unemployment + Structural unemployment = 490,000 Cyclical unemployment = Actual unemployment Natural unemployment = 10,000 Natural rate of unemployment = (Natural unemployment / Labor force) 100% = 21.30%
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Diagram A Wage rate Wage rate
Diagram B
W
W
Quantity of labor
Quantity of labor
c. Which of the following diagrams is more appropriate to describe labor markets where the number of people seeking jobs is more than the number of job available? Explain your answer. Diagram B is more appropriate to describe labor markets with positive structural unemployment. When the prevailing wage rate is higher than the equilibrium wage rate, the number of jobs available (the quantity demanded of labor)is smaller than the number of people seeking jobs (the quantity supplied of labor). Question 2. CPI and inflation. In a country, the price index is based upon a market basket consisting of 3 units of rice, 2 units of vegetable, and 1 unit of meat. The prices of these three items in 2005, 2006, and 2007 are presented in the following table. Year 2005 2006 2007 Price per unit of rice $0.5 $0.6 $0.65 Price per unit of vegetable Price per unit of meat $2 $1.5 $2 $3 $2.8 $2.5
a. Use year 2005 as the base year to calculate the price indices for the three years. Year 2005 2006 2007 Cost of Market Basket 3($0.5) + (2)($2) + 1($3) = $8.5 3($0.6) + (2)($1.5) + 1($2.8) = $7.6 3($0.65) + (2)($2) + 1($2.5) = $8.45
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Price index (8.5/8.5)100 = 100 (7.6/8.5)100 = 89.41 (8.45/8.5)100 = 99.41
b. What was the inflation rate from 2005 to 2006 and the inflation rate from 2006 to 2007? Inflation rate from to 2005 2006 = -10.59 Inflation rate from 2006 to 2007 = 11.18 c. If we use 2006 as the base year, will the inflation rates that you calculated in b change? The inflation derived by CPI does not depend on the choice of base year. The inflation rate form year t-1 to t is equal to CPI t - CPI t -1 Inflation ratet = 100 . CPI t -1
By definition of the CPI, Cost of market baskett Cost of market baskett -1 - Cost of market basketbase year Cost of market basketbase year 100 . Inflation ratet = Cost of market baskett -1 Cost of market basketbase year
Since the cost of market basket in the base year can be cancelled out, Cost of market baskett - Cost of market baskett -1 100 . Inflation ratet = Cost of market baskett -1 That is, the choice of base year does not affect the inflation rates.
Question 3. Growth. Suppose the aggregate production function of an economy is Y/L= K/L, where Y is the real GDP, K is the quantity of physical capital, and L is the number of labor employed. Note this production function measures output per worker, Y/L, and not just output, Y. K/L is the capital to labor ratio.
a. Fill in the following table and plot the aggregate production function in a graph. Measure K/L on the horizontal axis and Y/L on the vertical axis.
K/L Y/L
0 0
1 1
4 2
9 3
16 4
25 5
36 6
49 7
64 8
81 9
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Aggregate Productin Function
10 9 8 7 6
Y/L
5 4 3 2 1 0 0 10 20 30 40 50 60 70 80 90
K/L
b. Does this aggregate production function exhibit diminishing returns to physical capital? The aggregate production function exhibits diminishing returns to physical capital. At the point where K/L = 1, we need to increa...