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Homework 1 Solutions for Intermediate Macroeconomic Theory | ECON 302, Assignments of Macroeconomics

University of Wisconsin (UW) - MadisonMacroeconomics

Material Type: Assignment; Class: Intermediate Macroeconomic Theory; Subject: ECONOMICS; University: University of Wisconsin - Madison; Term: Spring 2008;

Typology: Assignments

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Economics 302
Spring 2008
Homework #1
Homework will be graded for both content and neatness. This homework requires the
use of Microsoft Excel.
1) The following table is taken from the Bureau of Economic Analysis data release on
quarterly GDP from 1/30/2008.
Figures in Billions of Dollars 2007-I 2007-II 2007-III 2007-IV
Gross domestic product 13552 13768.9 13970.4 14081
Personal consumption expenditures 9540.5 9674 9785.7 9928
Durable goods 1074 1074.7 1081.6 1088
Nondurable goods 2759.4 2822.7 2846.3 2903.7
Services 5707.1 5776.6 5857.8 5936.3
Gross private domestic investment 2117.3 2139.1 2162.9 2109.8
Fixed investment 2118.9 2133.9 2127.5 2118.3
Nonresidential 1431.4 1469.1 1500.2 1532.1
Residential 687.5 664.9 627.3 586.2
Change in private inventories -1.6 5.1 35.4 -8.5
Net exports of goods and services -714.1 -714.2 -694.7 -727.5
Ex ports 1549.9 1598.7 1685.7 1727.1
Imports 2264 2312.9 2380.4 2454.6
Government expenditures 2608.3 2670 2716.5 2770.7
Federal 946.6 969.5 990.3 997.1
Stat e and local 1661.7 1700.5 1726.2 1773.6
a) Fill in all the blanks in the table. (While this can be done by hand, you will find it
easier to use Excel). Don’t forget to calculate GDP.
Answers are shown in the table in bold. In each case, we simply sum the appropriate
values.
Consumption = Durables + Nondurables + Services
Investment = Fixed Investment + Change in inventories
(and Fixed Investment = Non-residential fixed investment+ Residential fixed investment)
Net Exports = Exports – Imports
Government Expenditures = Federal Expenditures + State and Local Expenditures
GDP = C + I + G +NX
b) In their release, the BEA points out that their GDP data is “seasonally adjusted at
annual rates”. Why is it important to seasonally adjust quarterly data? What patterns
might emerge in US quarterly GDP data if it is not seasonally adjusted?
Measuring GDP using the expenditure approach, we might be worried that people have
different spending patterns during different quarters. In the U.S., 4th quarter GDP is
generally higher than the other three quarters because of consumer spending on winter
holidays, and 1st quarter GDP is often a bit lower due to consumers using their income
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Download Homework 1 Solutions for Intermediate Macroeconomic Theory | ECON 302 and more Assignments Macroeconomics in PDF only on Docsity!

Economics 302

Spring 2008

Homework

Homework will be graded for both content and neatness. This homework requires the

use of Microsoft Excel.

1) The following table is taken from the Bureau of Economic Analysis data release on

quarterly GDP from 1/30/2008.

Figures in Billions of Dollars 2007-I 2007-II 2007-III 2007-IV Gross domestic product 13552 13768.9 13970.4 14081 Personal consumption expenditures 9540.5 9674 9785.7 9928 Durable goods 1074 1074.7 1081.6 1088 Nondurable goods 2759.4 2822.7 2846.3 2903. Services 5707.1 5776.6 5857.8 5936. Gross private domestic investment 2117.3 2139.1 2162.9 2109. Fixed investment 2118.9 2133.9 2127.5 2118. Nonresidential 1431.4 1469.1 1500.2 1532. Residential 687.5 664.9 627.3 586. Change in private inventories -1.6 5.1 35.4 -8. Net exports of goods and services -714.1 -714.2 -694.7 -727. Exports 1549.9 1598.7 1685.7 1727. Imports 2264 2312.9 2380.4 2454. Government expenditures 2608.3 2670 2716.5 2770. Federal 946.6 969.5 990.3 997. State and local 1661.7 1700.5 1726.2 1773.

a) Fill in all the blanks in the table. (While this can be done by hand, you will find it

easier to use Excel). Don’t forget to calculate GDP.

Answers are shown in the table in bold. In each case, we simply sum the appropriate

values.

Consumption = Durables + Nondurables + Services

Investment = Fixed Investment + Change in inventories

(and Fixed Investment = Non-residential fixed investment+ Residential fixed investment)

Net Exports = Exports – Imports

Government Expenditures = Federal Expenditures + State and Local Expenditures

GDP = C + I + G +NX

b) In their release, the BEA points out that their GDP data is “seasonally adjusted at

annual rates”. Why is it important to seasonally adjust quarterly data? What patterns

might emerge in US quarterly GDP data if it is not seasonally adjusted?

Measuring GDP using the expenditure approach, we might be worried that people have

different spending patterns during different quarters. In the U.S., 4th quarter GDP is

generally higher than the other three quarters because of consumer spending on winter

holidays, and 1st quarter GDP is often a bit lower due to consumers using their income

to pay off credit card debt accumulated during last year’s 4th quarter rather than

purchasing new goods and services. If we did not seasonally adjust GDP, we would

expect to see this pattern in our quarterly GDP numbers. Of course, no one actually

believes that the economy grows every October and shrinks every January, so seasonally

adjusting the data eliminates this trend and helps make GDP numbers more comparable

across quarters.

2) Consider the following table of data for an economy.

Year 1960 1970 1980 1990 2000 GDP 220 228 236.595 245.8179 255. C 125 131.25 137.8125 144.7031 151. I 20 22 24.2 26.62 29. G 50 51 52.02 53.0604 54. NX 25 23.75 22.5625 21.43438 20.

a) Using Excel, calculate the growth rates of GDP, C, I, G, and NX and present them in a

table such as the one below. Put the growth rates in percentage terms.

GDP growth ------------- 3.636364 3.769737 3.89818 4. C growth ------------- 5 5 5 5 I growth ------------- 10 10 10 10 G growth ------------- 2 2 2 2 NX growth ------------- -5 -5 -5 -

Answers are shown in the table in bold. We use the percentage growth formula.

% Growth = [(new value – old value)/(old value)]*

b) Now that we have the growth rates for all variables, approximate the growth rates for

the share of each variable in GDP (C/Y, I/Y, G/Y, and NX/Y) using the technique

discussed in class and in Mankiw. Present your answers in a table as below.

C share growth (approx) ------------- 1.363636 1.230263 1.10182 0. I share growth (approx) ------------- 6.363636 6.230263 6.10182 5. G share growth (approx) ------------- -1.63636 -1.76974 -1.89818 -2. NX share growth (approx) ------------- -8.63636 -8.76974 -8.89818 -9.

Answers are shown in the table in bold. To get the approximations, we use the formula

Approx % growth of C/Y = % growth of C - % growth of Y.

c) To check the accuracy of these approximations, compute the actual share of each

variable in GDP and find the actual growth rates. Present your answers in a table as

below. Put the growth rates in percentage terms.

GDP (A=4, K=10) 0 5 10 15 20 25 30 35 40 45 1 2 3 4 5 6 7 8 9 10 Labor GDP GDP (A=4, K=10)

Note the curvature in the graph – each unit of labor adds less to GDP than the unit

before it. This function exhibits a diminishing marginal product of labor.

c) Now assume that the technology level increases, so A = 6, but K remains fixed at 10.

Recalculate GDP as labor ranges from 1 to 10, and report your results in a table similar to

the one above. You should change your GDP variable name to “GDP (A=6, K=10)”.

See part a above.

d) Now keep A=4, but assume that the capital stock increases, so K = 15. Recalculate

GDP as labor ranges from 1 to 10, and report your results in a table similar to the one

above. You should change your GDP variable name to “GDP (A=4, K=15)”.

See part a above.

e) Graph all three GDP calculations [(A=4, K=10), (A=6, K=10), and (A=4, K=15)] on

the same graph with GDP on the vertical axis and labor on the horizontal. Make sure

your graph has labels so that it is clear which line corresponds to each measure of GDP.

GDP with various levels of A and K

0 10 20 30 40 50 60 70 1 2 3 4 5 6 7 8 9 10 Labor GDP GDP (A=4, K=10) GDP (A=6, K=10) GDP (A=4, K=15)

Note that in each case, increasing A or K causes the aggregate production function to

shift upward, and all functions exhibit a diminishing marginal product of labor.

f) When we changed the value of A and K, we increased each by 50%. However, as our

tables and graphs show, GDP increased more when we increased A by 50% than when

we increased K by 50%. Looking at the Cobb-Douglas production function, why is this

true? You may give either an intuitive or mathematical answer.

Mathematically, we see that if we increase A by 50%, we get

Y 1 = 1.5AK0.6L0.4^ =1.5Y, where Y = AK0.6*L0.4.

However, if we increase K by 50%, we get

Y 2 = A(1.5K)0.6L0.4^ = A(1.5)0.6K0.6L0.4^ = (1.5)0.6Y, where Y = AK0.6*L0.4.

As 0.6 < 1, (1.5)0.6^ < 1.5, so Y 1 > Y 2. Thus, increasing K by 50% increases total output

less than increasing A by 50%.

Intuitively, for a fixed level of labor, our Cobb-Douglas production function exhibits a

diminishing marginal product of capital, while the marginal product of additional

technology is constant. Thus, when we add 50% more capital, we do not get 50% more

output due to the effect of the diminishing returns. However, adding 50% more

technology does yield 50% more output, as there are constant returns to increases in

technology.