## Macroeconomics – US Private Business Sector Analysis

Macroeconomics – US Private Business Sector Analysis

Order Description

The attached file “EMBA 11_Macro group PW” has the Questions and a set of data coveing the years 1948 – 2001. Please Answer the assignment in a Q&A format showing your calculation work in details.

In Q3 Plot a graph from the data given and don’t download a graph.

EMBA 11

Macroeconomics Core Elective

Group practical work assignment

In the next page you can find measures of productivity for the private business sector in the

U.S., calculated and reported by the Bureau of Labour Statistics (see www.bls.gov). Using this

data:

1.

Find out share of labour in output (i.e. Sl). What is the long-term trend in this variable?

2.

Often, output per person is taken as a measure of productivity. Compare the two

measures (express both in annual growth rates). Which one is higher – on average?

Why? Discuss: are the two measures similar?

3.

Analyse trends in Total Factor Productivity in the last 50 years (a plot would help). Is low

productivity-growth during recessions actually a technological phenomenon?

The word limit for this assignment is 1,500 words

Deadline:

The deadline for submitting this assignment is:

Monday 2nd February 2015 by 12 noon (local time Oxford)

Please submit by uploading the assignment to the practical work system. For more

information, see the EMBA 11 WebLearn Assessment page.

Table 1. Private business sector: Productivity and related measures, 19482001

Indexes 1996=100

Year

Output

per

hour

of all

persons

Output

per

unit of

capital

1948

1949

31.1

32.2

108.5

105.5

51.6

52.2

1950

35.0

111.7

1955

40.9

1960

Multifactor

Productivity

Output

Combined

units of

capital

and

labor

Labor

Input

Capital

Services

Capital

per hour of

all persons

18.6

18.6

51.1

49.4

17.2

17.6

36.1

35.6

28.6

30.5

56.0

20.5

50.3

18.3

36.5

31.3

115.5

62.0

24.9

53.7

21.6

40.2

35.4

45.6

112.0

65.5

27.5

54.0

24.6

42.1

40.7

1965

1966

1967

1968

1969

55.9

58.2

59.5

61.4

61.7

123.3

124.7

119.9

120.8

118.4

76.6

78.9

79.0

81.1

80.6

35.6

38.1

38.8

40.7

42.0

58.0

59.5

59.4

60.3

62.1

28.9

30.5

32.3

33.7

35.5

46.5

48.2

49.1

50.3

52.1

45.3

46.6

49.6

50.8

52.1

1970

1971

1972

1973

1974

63.0

65.8

68.0

70.1

69.0

113.1

112.8

115.4

116.9

109.2

80.5

83.0

85.5

87.8

84.6

42.0

43.6

46.5

49.8

49.0

61.0

60.5

62.6

64.8

65.2

37.1

38.7

40.3

42.6

44.9

52.2

52.5

54.5

56.8

57.9

55.7

58.4

58.9

60.0

63.2

1975

1976

1977

1978

1979

71.4

74.1

75.2

76.1

76.0

104.1

107.8

109.7

111.6

109.8

85.4

88.6

90.0

91.2

90.8

48.5

51.9

54.8

58.2

60.2

62.4

64.2

66.8

70.2

72.4

46.6

48.1

50.0

52.2

54.8

56.8

58.5

60.9

63.9

66.2

68.6

68.7

68.6

68.1

69.2

1980

1981

1982

1983

1984

75.8

77.3

77.2

79.9

82.2

103.3

101.0

94.2

96.2

100.0

88.8

88.9

86.2

88.6

91.5

59.4

61.0

59.3

62.5

68.1

71.9

73.0

71.7

73.4

77.7

57.6

60.5

63.0

65.0

68.1

67.0

68.7

68.8

70.5

74.4

73.4

76.5

81.9

83.0

82.2

1985

1986

1987

1988

1989

83.9

86.5

87.0

88.1

89.0

99.5

99.0

99.2

100.4

101.0

92.4

93.9

94.2

94.8

95.3

71.0

73.6

76.3

79.6

82.4

79.6

80.4

83.1

86.3

88.8

71.3

74.4

76.9

79.2

81.6

76.8

78.4

81.0

83.9

86.4

84.3

87.4

87.7

87.7

88.1

1990

1991

1992

1993

1994

90.2

91.3

94.8

95.4

96.6

99.7

96.5

98.0

98.7

100.4

95.5

94.5

96.7

97.1

98.2

83.6

82.6

85.7

88.5

92.8

89.4

88.3

89.3

91.8

95.6

83.8

85.7

87.5

89.7

92.5

87.5

87.4

88.7

91.1

94.6

90.4

94.6

96.8

96.6

96.2

1995

1996

1997

1998

1999

97.3

100.0

102.2

105.0

107.7

99.8

100.0

100.3

99.3

98.2

98.4

100.0

101.2

102.5

103.4

95.8

100.0

105.2

110.5

115.7

98.0

100.0

103.5

106.1

109.0

96.0

100.0

104.9

111.3

117.9

97.3

100.0

104.0

107.9

111.9

97.5

100.0

101.9

105.8

109.7

2000

2001

111.0

112.4

96.6

92.8

105.0

103.9

120.4

120.2

110.1

109.5

124.5

129.6

114.7

115.7

114.8

121.1

Macroeconomics – US Private Business Sector Analysis

The production function in the Solow growth model is Y = f(K,L), or expressed in terms of

output per worker, y = f(k). If a war reduces the labor force through casualties, the L falls but

Capital-labor ratio k = K/L rises. The production function tells us that total output falls

because there are fewer workers. Output per worker increases, however, since each worker

has more capital.

b) The reduction in the labor force means that the capital stock per worker is higher after the

war. Therefore, if the economy were in a steady state prior to the war, then after the war the

economy has a capital stock that is higher than the steady-state level. This is shown in the

figure below as an increase in capital per worker from k1 to k2. As the economy returns to the

Steady state, the capital stock per worker falls from k2 back to k1, so output per worker also

Falls.

Suppose the economy begins with an initial steady-state capital stock below the Golden Rule

Level. The immediate effect of devoting a larger share of national output to investment is that the

economy devotes a smaller share to consumption; that is, “living standards” as measured by

consumption fall. The higher investment rate means that the capital stock increases more quickly,

so the growth rates of output and output per worker rise. The productivity of workers is the

average amount produced by each worker – that is, output per worker. So productivity growth

rises. Hence, the immediate effect is that living standards fall but productivity growth rises.

k = K/L

y = Y/L

y = f(k)

sy

(n+d)k

k1 k2

y2

y1

In the new steady state, output grows at rate n+g, while output per worker grows at rate g. This

means that in the steady state, productivity growth is independent of the rate of investment. Since

we begin with an initial steady-state capital stock below the Golden rule level, the higher

investment rate means that the new steady state has a higher level of consumption, so living

standards are higher

Thus, an increase in the investment rate increases the productivity growth rate in the short run but

has no effect in the long run. Living standards, on the other hand, fall immediately and only rise

over time. That is, the quotation emphasizes growth, but not the sacrifice required to achieve it.

Chapter 9, #2

To solve this problem, it is useful to establish what we know about the U.S. economy:

• A Cobb-Douglas production function has the form y = k? , where ? is capital’s share

of income. The question tells us that ? = 0.3, so we k now that the production

function is y = k??

• In the steady state, we know that the growth rate of output equals 3%, so we know

that (n+g) = .03

• The depreciation rate ? = .04

• The capital-output ratio K/Y = 2.5. Because k/y = [K/(LxE)]/[Y/(LxE)] = K/Y, we

also know that k/y = 2.5. (That is, the capital-output ratio is the same in terms of

effective workers as it is in levels.)

a) Begin with the steady-state condition, sy = (? + n + g)k. Rewriting this equation leads

to a formula for saving in the steady state:

s = (? + n + g)(k/y)

Plugging in the values from above: s = (0.04 + 0.03)(2.5) = .175

The initial saving rate is 17.5%.

b) We know from Chapter 3 that with a Cobb-Douglas production function, capital’s

share of income ? = MPK(K/Y). Rewriting, we have:

MPK = ?/(K/Y)

Plugging in the values from above: MPK = 0.3/2.5 = .12

c) We know that at the Golden Rule steady state:

MPK = (n + g + d)

Plugging in the values from above: MPK = (.03 + .04) = .07

At the Golden Rule steady state, the marginal product of capital is 7%, whereas it is 12%

in the initial steady state. Hence, from the initial steady state we need to increase k to

achieve the Golden Rule steady state.

d) We know from Chapter 3 that for a Cobb-Douglas production function,

MPK = ?(Y/K). Solving this for the capital-output ratio, we find:

K/Y = ?/MPK

We can solve for the Golden Rule capital-output ratio using this equation. If we plug in

the value 0.07 for the Golden Rule steady-state MPK, and the value 0.3 for a, we find:

K/Y = 0.3/0.07 = 4.29

In the Golden Rule steady state, the capital-output ratio equals 4.29, compared to the

current capital-output ratio of 2.5.

e) We know from part (a) that in the steady state

s = (n + g + ?)(k/y)

where k/y is the steady-state capital-output ratio. In the introduction to this answer, we

showed that k/y = K/Y, and in part (d) we found that the Golden Rule K/Y = 4.29.

Plugging in this value and those established above:

s = (0.04 + 0.03)(4.29) = 0.30

To reach the Golden Rule steady-state, the saving rate must rise from 17.5% to 30%.

How do differences in education across countries affect the Solow Growth Model?

Education is one factor affecting the Efficiency of labor, which we denoted by E. (Other

Factors affecting the efficiency of labor include levels of health, skill and knowledge.) Since

Country 1 has a more highly educated labor force than country 2, each worker in country 1 is

More efficient. That is E1>E2. We will assume that both countries are in steady state.

a. In the Solow Growth model, the rate of growth of total income is equal to n+g, which is

independent of the work force’s level of education. The two countries will, thus, have the

same rate of growth of total income because they have the same rate of population

growth and the same rate of technological progress.

b. Because both countries have the same saving rate, the same population growth rate, and

the same rate of technological progress, we know that the two countries will converge to

the same steady-state level of capital per efficiency unit of labor k*. This is shown in the

figure below.

sy

(? + n + g)k

k2* Capital per efficiency unit

Investment

Hence, output per efficiency unit of labor in the steady state, which is y* = f(k*) is the

same in both countries. But y* = Y/(L*E) or Y/L = y*E. We know that y* will be the

same in both countires, but that E1>E2. Therefore y*E1>y*E2. This implies that

(Y/L)1>(Y/L)2. Thus, the level of income per worker will be higher in the country with

the more educated labor force.

c. We know that the real rental price of capital r equals the marginal product of capital

(MPK). But the MPK depends on the capital stock per efficiency unit of labor. In the

steady state, both countries have k*1 = k*2 = k* because both countries have the same

saving rate, the same population growth rate, and the same rate of technological progress.

Therefore, it must be true that r1 = r2 = MPK. Thus, the real rental price of capital is

identical in both countries.

d. Output is divided between capital income and labor income. Therefore, the wage per

efficiency unit of labor can be expressed as:

w = f(k) – MPK * k

As discussed in parts (b) and (c), both countries have the same steady-state capital stock k and the

same MPK. Therefore, the wage per efficiency unit in the two countries is equal.

Workers, however, care about the wage per unit of labor, not the wage per efficiency

unit. Also, we can observe the wage per unit of labor but not the wage per efficiency unit. The

wage per unit of labor is related to the wage per efficiency unit of labor by the equation:

Wage per Unit of L = wE

Thus, the wage per unit of labor is higher in the country with the more educated labor force.

Year

1948 31.1 108.5 51.6 18.6 51.1 17.2 36.1 28.6

1949 32.2 105.5 52.2 18.6 49.4 17.6 35.6 30.5

1950 35 111.7 56 20.5 50.3 18.3 36.5 31.3

1955 40.9 115.5 62 24.9 53.7 21.6 40.2 35.4

1960 45.6 112 65.5 27.5 54 24.6 42.1 40.7

1965 55.9 123.3 76.6 35.6 58 28.9 46.5 45.3

1966 58.2 124.7 78.9 38.1 59.5 30.5 48.2 46.6

1967 59.5 119.9 79 38.8 59.4 32.3 49.1 49.6

1968 61.4 120.8 81.1 40.7 60.3 33.7 50.3 50.8

1969 61.7 118.4 80.6 42 62.1 35.5 52.1 52.1

1970 63 113.1 80.5 42 61 37.1 52.2 55.7

1971 65.8 112.8 83 43.6 60.5 38.7 52.5 58.4

1972 68 115.4 85.5 46.5 62.6 40.3 54.5 58.9

1973 70.1 116.9 87.8 49.8 64.8 42.6 56.8 60

1974 69 109.2 84.6 49 65.2 44.9 57.9 63.2

1975 71.4 104.1 85.4 48.5 62.4 46.6 56.8 68.6

1976 74.1 107.8 88.6 51.9 64.2 48.1 58.5 68.7

1977 75.2 109.7 90 54.8 66.8 50 60.9 68.6

1978 76.1 111.6 91.2 58.2 70.2 52.2 63.9 68.1

1979 76 109.8 90.8 602 72.4 54.8 66.2 69.2

1980 75.8 103.3 88.8 59.4 71.9 57.6 67 73.4

1981 77.3 101 88.9 61 73 60.5 68.7 76.5

1982 77.2 92.2 86.2 59.3 71.7 63 68.8 81.9

1983 79.9 96.2 88.6 62.5 73.4 65 70.5 83

1984 82.2 100 91.5 68.1 77.7 68.1 74.4 82.2

1985 83.9 66.5 92.4 71 79.6 71.3 76.8 84.3

1986 86.5 66 93.9 73.6 80.4 74.4 78.4 87.4

1987 87 66.2 94.2 76.3 83.1 76.9 81 87.7

1988 88.1 100.4 94.8 79.6 86.3 79.2 83.9 87.7

1989 89 101 95.3 82.4 88.8 81.6 86.4 88.1

1990 90.2 99.7 95.5 83.6 89.4 83.8 87.5 90.4

1991 91.3 96.5 94.5 82.6 88.3 85.7 87.4 94.6

1992 94.8 98 96.7 85.7 89.3 87.5 88.7 96.8

1993 95.4 98.7 97.1 88.5 91.8 89.7 91.1 96.6

1994 96.6 100.4 98.2 92.8 95.6 92.5 94.6 96.2

1995 97.3 99.8 98.4 95.8 98 96 97.3 97.5

1996 100 100 100 100 100 100 100 100

1997 102.2 100.3 101.2 105.2 103.5 104.9 104 101.9

1998 105 99.3 102.5 110.5 106.1 111.3 107.9 105.8

1999 107.7 98.2 103.4 115.7 109 117.9 111.9 109.7

2000 110 96.6 105 120.4 110.1 124.5 114.7 114.8

2001 112.4 92.8 103.9 120.2 109.5 129.6 115.7 121.1