# Economic Equations and Calculations

Economic Equations and Calculations
a.)
C= 200+c(Y-T)
T=25
Y= C +I+G+NX+T
c= 200+ 0.6(Y- 25)
C= 200+ 0.6Y- 15
Y= 200+ 0.6Y- 15 +100
0.4Y= 285
Y= 712.5

c= 200+ 0.75(Y- 25)
C= 200+0.75Y-18.75
Y= 200+0.75Y-18.75 + 100
0.25Y=281.25
Y= 1005

c= 200+ 0.9(Y- 25)
Y= C+G+I+NX+T
C= 200+0.9Y-22.5
Y= 200+0.9Y-22.5+100
0.1Y= 277.5
Y= 2775
b.) A county’s GDP is directly proportional to the MPC, an increase in the MPC results in an increase in the GDP of a country.
c.) 1050 (Y) = C +I+G+NX+T
Where C = 200 + 0.75(Y-T)
C = 200+787.5-0.75T
C = 987.5 – 0.75T
1050 = 987.5 -0.75T+75+T
1.75T =1050 -912.5
1.75T = 137.5
T = 78.6
Increase = 53.6
d) GDP abbreviation represents Gross Domestic Product which is the sum of all private consumption, available investments, net exports and overall government expenditure. It is calculated by subtracting total imports from total exports whereas the Marginal Propensity to consume refers to the relationship between consumption and income which is expressed as a ratio between the change in consumption and the change in income.
e). Getting the government expenditure the government need to close output gap
Multiplier analysis for government expenditure,
Where Y= 1050
M= 0.75
1050/DG =1/0.25
DG = 1050/4
DG = 262.5
The government will have to increase its expenditure by 262.5 to close the recession gap.
f). Getting the changes that the government will make in taxation to close the output gap.
Multiplier analysis for taxation,
Where Y = 1050
M = 0.75
1050/DT= -0.75/1-0.75
1050/DT =-0.75/1-0.75
1050/3 =350
DT =350
The government will decrease taxes y 350 to close the output gap.
g). the difference between the magnitude when the government decide to use taxation or its expenditure occurs because changing government expenditure will cause expansionary changes that will affect the GDP directly while changing taxation will cause cotractionary changes that affects the GDP indirectly.
2.
Y= 1/ 1-c (1-t) +m (C=I=G=NX
C= 0.8
Autonomous spending = 100
i). m= 0.1 t=0.2
Y= 1/1-0.8(1-0.2) +0.1 (0.8 + 100)
Y=219.2

ii) m =0.15 t=0.3
Y=1/1-0.8(1-0.3) +0.15 (C+I+G+NX)
Y= 1/1-0.56+0.15
Y= 1/0.59 (0.8 +100)
Y=170.8

iii) m= 0.25 t=0.4
Y= 1/1-c(1-t)+m (C+ I +G+ NX)
Y= 1/1 -0.8 (1-0.4) +0.25 (C+ I +G+ NX)
Y= 1/1-0.48+0.25
=130.9
b.)To close the output gap government should increase its total spending in all the three scenarios.
In the first case the government should increase its spending by \$281
Government spending 500 – GDP 219 = 281
In the second scenario it should increase by 329
Government spending 500 – GDP 171= 329
In the second scenario it should increase by 369
Government spending 500 – GDP 131= 369
c.) Increased taxation as well as induced imports would result in less money in circulation and increased government revenue, thus enabling the government to reduce any existing output gaps.
3.) (a) Expression relating output expenditure to output to the rate of interest
Ynominal = C+I +G+NX
Y-C-G-NX = I(-)(r)
(Y-T-C) + (T-G) + (-NX)= I(R)
(b) Output if real rate is 10%
C= 1000+0.8(Y-T)- 1000r
Y= C+I+G+T+NX
Y= 1000+0.8(Y-2000)- 1000r +4000-5000r +2000-1000
Y= 1000+0.8Y- 1600- 100 +4000-500+1000
0.2Y= 3500
Y= 17500
c). T eliminate the output gap the bank of Canada shoul;d ensure the country GDP is at equilibrium of 80000
17500 = 10% interest rate
80000 = 45.71%
Interest rate should be increased to 45.71%
4.). In order to lower the nominal interest rates, the bank on Canada should sell its debts to the central bank in order to increase its circulatory cash reserves in their accounts. They can also borrow additional reserves from the central bank in order to increase their credit and to meet the required reserves to lend loans. This way they will maintain lower nominal interest rates which will encourage borrowing.
The bank of Canada can close a recessionary gap by using monetary policies where it can increase its rate of interest to decrease the rate of borrowing; this will decrease investments and outputs which will lead to fall in prices consequently controlling inflation. On the other hand, when faced with a deflation, the bank can decrease their interest rates which will discourage borrowing leading to reduced investments and output levels which will eventually lead to higher prices.
5). Autonomous investments are those investments that are not dependant on the level of profits or production whereas induced investments depends on current profits and production levels. Again, autonomous investments may rise or fall in different times whereas the induced investments are continuous without any changes. Additionally, autonomous investments are comes as a result of government activities while induced investments comes as a result of private business activities. Finally, the interest and profits of autonomous investments are inelastic while those of the induced investments are elastic.
b). Marginal propensity to consume and the multiplier are related since when investments levels are multiplied, people tend to have more cash to and the marginal propensity to consume is increased. Thus an increase in multiplier investments will lead to an increase in marginal propensity to consume.
c). The multiplier has significantly reduced in current years compared to how it was in the past. This if due to the depreciating economic natures where people lack enough money left to increase investments. The nature of the current economy has lead to inflation levels that has reduced people’s marginal propensity to consume as well as the ability to get into any kind of investments which has led to a reduced multiplier.
6.
c= 1000 + 0.8(Y-T) – 1000r
I= 1000- 5000r
G= 200
T= 250
NX= 0
(a) Expression relating output Y to the rate of interest
Ynominal = C+I +G+NX
Y-C-G-NX = I(-)(r)
(Y-T-C) + (T-G) + (-NX)= I(R)
(b). GDP and Output
Real interest rate is 10% (0.1)
Y*= 400

Y= C+I=G
C= 1000+0.8(Y-T)-1000(r)
Y= 1000+0.8(y-250)-1000(0.1) +1000-5000(0.1) +200
Y= 1000+0.8Y-200-100+1000-500+200
0.2Y= 1400
Y=7000

If the Y* IS 400 the bank should change is rate of interest by by 1.75 percent which is achieved by comparing the two GDP’s 7000/4000