Macroeconomics Homework 6: Analyzing Global Economic Relationships

This document provides a comprehensive solution to Macroeconomics Homework 6, analyzing the economic relationship between the US and China. The assignment explores key macroeconomic concepts, including savings, investment, trade balance, and real interest rates. It calculates equilibrium interest rates, determines which country is 'spending beyond its means,' and examines the impact of changes in output and interest rates on trade balances and consumption. The solution includes detailed calculations, diagrams, and explanations of economic principles. The assignment covers topics such as the money multiplier, liquidity traps, and the effects of changes in inflationary expectations, providing a thorough understanding of macroeconomic theory and its application to real-world scenarios. The analysis considers the effects of government spending and the money market, offering insights into economic policies and their impact on various economic indicators. The document presents a clear and concise analysis of the macroeconomic concepts in the assignment.

Running head: MACROECONOMICS HOMEWORK 6
Macroeconomics Homework 6
Name of the Student
Name of the University
Student ID

1MACROECONOMICS HOMEWORK 6
Table of Contents
Answer 1..........................................................................................................................................2
Answer 2..........................................................................................................................................8
Reference.......................................................................................................................................15

2MACROECONOMICS HOMEWORK 6
Answer 1
(a) It is know from macroeconomic theory that difference between total savings and total
investment is zero.
Therefore, savings in the US and China is given as
For US,
S=Y −Cd−G
¿ , S=1000−300−0.4 ( Y −T ) +200 rw−275
¿ , S=1000−300−0.4 ( 1000−200 ) +200 r w−275
¿ , S=1000−300−0.4 ( 1000−200 ) +200 r w−275
¿ , S=200 r w+105
For China,
S=Y F −CF
d −GF
¿ , S=1500−450−0.4 (Y F −T F ) + 300r w−300
¿ , S=1500−450−0.4 ( 1500−300 ) +300 rw−300
¿ , S=1500−450−0.4 ( 1500−300 ) +300 rw−300
¿ , S=300 r w+270
Therefore,
[ S ( US ) +S (Ch ) ]− [ I ( US ) + I ( Ch ) ]=0

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¿ , [ 200 rw +105+300 rw +270 ]− [ 200−200 rw +250−300 rw ]=0
¿ , [ 375+500 rw ] − [ 450−500 rw ] =0
¿ , 375+500 rw−450+500 rw=0
¿ , 1000 rw−75=0
¿ , rw=0.075
(b) For US,
Savings:
Sd =200 rw +105
¿ , Sd =(200 × 0.075)+105
¿ , Sd =15+105
¿ , Sd =120
Investment:
I d=200−200 rw
¿ , I d=200−( 200× 0.075)
¿ , I d=200−15
¿ , I d=185
Net exports:
NX US=Y −C−I−G

4MACROECONOMICS HOMEWORK 6
¿ , NXUS =1000−605−185−275
¿ , NXUS =−65
For China,
Savings:
SF
d =300 r w+270
¿ , SF
d =(300 ×0.075)+270
¿ , SF
d =292.5
Investment:
I F
d =250−300r w
¿ , I F
d =250−(300 ×0.075)
¿ , I F
d =227.5
Net exports:
NXCh=Y −C−I −G
¿ , NXCh=1500−907.5−227.5−300
¿ , NXCh=65
(c) The US is running from trade deficit of -65 and on the other hand, China is running trade
surplus of 65. The US has total income of 1000 and it is consuming1065 (C+I+G). Therefore,
absorption is total consumption irrespective of the total produce (Gu et al., 2018). In this case,

5MACROECONOMICS HOMEWORK 6
the US borrows from China. On the other hand, China consumes 1435 (C+I+G) which is less
than its total produce of 1500. Therefore, it is evident that that US is spending beyond its means.
(d)
Figure 1: US and China
Source: (Created by the Author)
(e) Output of China falls to 1400
Savings:
S=1400−450−0.4 (1400−300 ) +300 rw−300
¿ , S=300 r w+210
Now,
¿ , [ 200 rw +105+300 rw +210 ]− [ 200−200 rw +250−300 rw ]=0

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¿ , rw=0.135
For US,
Savings:
Sd =200 rw +105
¿ , Sd =(200 × 0.135)+105
¿ , Sd =27+105
¿ , Sd =132
Investment:
I d=200−200 rw
¿ , I d=200−( 200× 0.135)
¿ , I d=200−27
¿ , I d=173
For China,
Savings:
SF
d =300 r w+270
¿ , SF
d =(300 ×0.135)+270
¿ , SF
d =310.5
Investment:

7MACROECONOMICS HOMEWORK 6
I F
d =250−300r w
¿ , I F
d =250−(300 ×0.135)
¿ , I F
d =209.5
(f) After change in interest rate, total consumption of the US is 1095 and that of China is 1440.
Both the countries have consumed more than the amount they have produced. Thus, it is evident
that both the US and China have negative trade balance (Chiu and Ren 2019). Initially the trade
balance of the US was -65 and now the trade balance is -95. The country is thus spending more
beyond its means than before and thus the US is not going to AA.

8MACROECONOMICS HOMEWORK 6
Answer 2
(a) For home country.
S=Y −Cd−G
¿ , S=1500−480−0.4 ( Y −T ) +300 r w−300
¿ , S=1500−480−0.4 ( 1500−300 ) +300 rw−300
¿ , S=300 r w+240
For foreign country,
S=Y F −CF
d −GF
¿ , S=1000−320−0.4 (Y F −T F ) +200 rw−275
¿ , S=1000−320−0.4 ( 1000−200 ) +200 r w−275
¿ , S=200 r w+ 85
Therefore,
[ S ( H ) +S ( F ) ]− [ I ( H )+ I ( F ) ]=0
¿ , [ 300 rw +240+200 rw +85 ] − [ 225−300 r w+150−200 rw ] =0
¿ , [ 500 rw +325 ]− [ 375−500 rw ]=0
¿ , 1000 rw−50=0

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¿ , rw=0.05
(b) For home country,
Savings:
Sd =300 rw +240
¿ , Sd =(300 × 0.05)+240
¿ , Sd =255
Investment:
I d=225−300 rw
¿ , I d=225−(300 × 0.05)
¿ , I d=210
Net exports:
NX H =Y −C−I−G
¿ , NXH =1500−945−210−300
¿ , NXH =45
For Foreign country:
Savings:
SF
d =200r w+85
¿ , SF
d =(200 ×0.05)+85

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¿ , SF
d =95
Investment:
I F
d =150−200r w
¿ , IF
d =150−(200 ×0.05)
¿ , I F
d =140
Net exports:
NX F =Y −C−I−G
¿ , NXF =1000−630−140−275
¿ , NXF =−45
(c) The total consumption of home country is 1455 and that of foreign country is 1045. It is
evident from the calculations that the income of home country is 1500 and that of foreign
country is 1000. Therefore, it can be clearly observed that the foreign country is consuming more
than it produces (Fornero and Krichner 2018). Thus, the foreign country absorbing all of its
produce. To reiterate absorption can be defined as demand for all of the goods and services
produced in an economy.

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(d)
Figure 2: Home and Foreign Country
Source: (Created by the Author)
(e) Increase in G of foreign country to 325,
S=1000−320−0.4 ( 1000−200 )+ 200 rw−325
¿ , S=200 r w+35
Therefore, interest rate is
[ 300 rw +240+200 rw +35 ]− [ 225−300 r w+150−200 rw ]=0
¿ , rw=0.1
For home country,
Savings:
Sd =300 rw +240

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¿ , Sd =270
Investment:
I d=225−300 rw
¿ , I d=195
For Foreign country:
Savings:
SF
d =200r w+85
¿ , SF
d =105
Investment:
I F
d =150−200r w
¿ , I F
d =130
(f) Foreign country,
NX F =Y −C−I−G
¿ , NX F =1000−630−130−325
¿ , NXF =−85
The trade balance has further declined for foreign country due to increase in G. Before
the increase in G, the amount of trade balance was -45 but after increase in G, the trade balance

13MACROECONOMICS HOMEWORK 6
declined by 40 and the current trade balance is -85. In addition that, the increase in G crowds out
10 units of investment and it declined to 130.
(g) There will be no change ‘S’ function of home country due to the government spending
multiplier with value 1.
The change in S function of foreign country is
S=1050−320−0.4 ( 1050−200 )+ 200 rw−325
¿ , S=200 r w+ 65
Interest rate:
[ 300 rw +240+200 rw +65 ]− [ 225−300 r w+150−200 rw ]=0
¿ , rw=0.07
For home country,
Savings:
Sd =300 rw +240
¿ , Sd =261
Investment:
I d=225−300 rw
¿ , I d=204

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Net exports:
NX H =Y −C−I−G
¿ , NXH =1500−939−204−300
¿ , NXH =57
For Foreign country:
Savings:
SF
d =200r w+85
¿ , SF
d =99
Investment:
I F
d =150−200r w
¿ , I F
d =136
Net exports:
NX F =Y −C−I−G
¿ , NXF =1050−646−136−325
¿ , NXF =−57
The Government spending multiplier effect improves the trade balance of foreign
country. Previously, the trade balance was -85 and now it is -57. Therefore, the trade balance has

15MACROECONOMICS HOMEWORK 6
improved but the amount is still negative (Bernardini and Peersman 2018). Hence, it can be said
that the country is going to AA as the trade balance improved by 28 units. However, the foreign
country has not reached the point AA.
Reference
Bernardini, M. and Peersman, G., 2018. Private debt overhang and the government spending
multiplier: Evidence for the United States. Journal of Applied Econometrics, 33(4), pp.485-508.
Chiu, Y.B. and Ren, R., 2019. Trade Balance, Savings Rate, and Real Exchange Rate: Evidence
from China and Its Trading Partners. Emerging Markets Finance and Trade, 55(2), pp.351-364.
Fornero, J. and Kirchner, M., 2018. Learning about Commodity Cycles and Saving-Investment
Dynamics in a Commodity-Exporting Economy. International Journal of Central Banking, 14(2),
pp.205-262.
Gu, S., Huang, X., Liu, D., He, C. and Ai, X., 2018. Effect of matrix modifiers on determination
of cadmium in dried aquatic products by graphite furnace atomic absorption
spectrometry. Journal of Food Safety and Quality, 9(10), pp.2379-2383.

16MACROECONOMICS HOMEWORK 6