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Question
using four quadrant diagram show the effect of the following on equilibrium interest  rate and income
1. Increase in desire to save
2.increased in government spending

Answer
The IS curve
The IS curve  

The IS curve
The IS curve  
Hi Malloba,

Thank you for asking me the question. I am sorry that I was very busy, and so I couldn't answer your question earlier. I understand this is important for you.

As far as I can understand from your question, it is probably something you want to learn in the aggregate demand-aggregate-supply models of income equilibrium in macroeconomics. You have not written anything about your background. So I don't know exactly at what level I should answer it. It could be explained with advanced math, but I don't know of your math background. I assume you have got at least sufficient graphical understanding and a modicum of algebra. With this assumption, I am going to answer your question. Let me tell you, when you answer this question, it means you have got a good grasp of elementary macroeconomics.

Please refer to the four-quadrant diagram in Image 1. Let us call these quadrants NE and NW (the above right and left, respectively) and SE and SW (the below right and left, respectively). Please try to have a good understanding of each of the four quadrants and then all the quadrants in juxtaposition. This presupposes you have studied savings function, investment function, the IS curve (don't worry about LM curve now). You may refer to  any elementary macroeconomics textbook or go to Google.I am sure you know about what we understand by income equal to consumption+investment+government expenditure [Y=c+i+g] and that investment equals saving "at equilibrium." You may also refresh your understanding about the multiplier effect --increase in consumption leads to increase in income by a multiple [which means marginal propensity to save has a negative effect].

Now let's get to the four-quadrant diagram.

The NE quadrant
This is the familiar IS curve. [IS curve shows that as rate of interest, r, goes down, income y goes up, because as interest goes down investment goes up, and multiplier = change in income/change in investment.] IS curve shows the "equilibrium pairs of r and y." If we choose a level of income on the y-axis, we can trace through the three quadrants following the dashed line to locate the equilibrium interest rate [r] for the level of income [y].

The SE quadrant
The straight-line curve gives saving plus tax revenues as a function of income. As IS curve shifts from (IS)1 to (IS)2, income goes down from Y1 to yo [in SE quadrant], "saving plus tax revenues" given by the curve s+t shows a movement towards the north-west direction [in SE quadrant].

The SW quadrant
As you can easily visualize from the 45-degree line [remember how you draw consumption function?] that "investment plus government expenditure," or i+g on the left axis, equals s+t on the down axis [remember we are thinking of this SW quadrant as a "positive" quadrant --or think that it has been rotated 180 degrees anti-clockwise]

The NW quadrant
This is an important quadrant. [Please redraw only this quadrant in your exercise book by rotating it 270 degrees anticlockwise for your better understanding.] You see government expenditure is "autonomous" hence a straight line independent of interest rate. However, government may autonomously increase it from  go to g1, as shown by the arrows. You also see "investment" (as a function of interest rate) or i(r) going downward as interest rate r increases [upward in the NW quadrant and rightward in your exercise book]. Now you add up i(r) and g --that is, put i(r) curve on top of g line, then we have i(r)=g

Your answer
Now you can easily find in the the four-quadrant diagram in Image 1 how an increase in government spending has the effect on equilibrium interest rate and income. This is the answer to your question (2)

Exercise for you: Image 2
You can now easily explain an increase in the desire to save has an impact on equilibrium interest rate and income. Just study the SE quadrant in image 2 --you can now explain the IS curve and the shift in saving.

CONCLUSION
I hope, Malloba, this serves your purpose. I am sorry I could not make it simpler. This is in fact a difficult topic, but I believe you get it right.  Please do not hesitate to write to me in future if you need any help. My best wisher are for you. Keep it up!  

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Eklimur Raza

Expertise

It appears some students in this website are confused about elasticity of demand and the slope of the demand curve when they are trying to figure out why rectangular hyperbola comes up in case of unitary demand curve. First, they don't know that RH can be depicted in a positive quadrant of price,quantity plane. Secondly, they make the mistake that the slope of RH is constant at -1. Two points could help them: first, e=1 at each and every point of the RH, because the tangent at any point shows lower segment=upper segment (another geometric definition of e); yet slopes at different points,dQ/dP, are different; second, e is not slope but [(Slope)(P/Q)]in absolute terms. Caveat: only if we measure (log P) along the horizontal axis and (log Q) up the vertical axis, can we then say slope equals elasticity --in which case RH on P,Q plane is transformed into a straight-line demand curve [with slope= -tan 45 deg] on (log Q),(logP) plane, and e= -d(log Q)/d(log P). [By the way, logs are not used in college textbooks --although that is helpful in econometric estimation of elasticity viewed as an exponent of P, when demand equation is transformed into log-linear form.] I have not found the geometrical explanation I have given in any textbook followed in undergraduate and college classes in Canada (including the book followed in a university where I taught for a short time and in the book followed in George Brown College, Toronto, where I teach.

Experience

About 11 years' teaching economics and business studies, and also English, history and elementary French.Practical experience in a development bank, working with international donor agencies like the World Bank and the ADB. Experience in free-lance journalism, including Canada's "National Post."

Organizations
I teach micro- and macroeconomics at George Brown College (continuing education), Toronto, ON, Canada.

Publications
Many articles and editorials, on different subjects, in English newspapers. Recently an applied Major Research Paper, based on a synthesis of the Solow growth model and the Lewis two-sector model, has be accepted by Ryerson University, Toronto. Professors Thomas Barbiero and Eric Cam, Ryerson University, accepted the paper.

Education/Credentials
Master degree in Interantional Economics and Finance and diploma with honours in Business Administration from Canada.

Awards and Honors
Received First Prize in an inter-university Literary Contest.

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