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# Economics/Mundell-Flemming Model: How an increase in risk premium causes a righward shift of the LM* curve

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Question
Hi Eklimur,

I am reading Macroeconomics by Mankiw (8th Edition, ISBN: 1-4292-4002-4).

I have a question on the impact of an increase in risk premium to a small open economy. Specifically, it relates to the LM* curve, M/P = L(r* + θ, Y), where:

r* = world interest rate
θ  = the country's risk premium
Y  = the country's income

The author writes:

Now, suppose that political turmoil causes the country's risk premium, θ, to rise. Because r = r* + θ, the most direct effect is that the domestic interest rate r rises. The higher interest rate, in turn, has two effects. First, the IS* curve shifts to the left because the higher interest rate reduces investment. Second, the LM* curve shifts to the right because the higher interest rate reduces the demand for money, which in turn implies a higher level of income for any given money supply.[Recall that Y must satisfy the equation M/P = L(r* + θ, Y).

(Please see file Fig.jpeg for graph of the above problem)

My question:

I don't understand why and how the LM* curve must shift to the right.

Mathematically, I know that given:

M/P = L(r* + θ, Y)

At equilibrium, M/P, supply of real balance, must equal L(r* + θ, Y), demand for real money balance. Since M/P and r* + θ is fixed, when r* + θ rises, Y must increase so that M/P =  L(r* + θ, Y) again (Since increase in r* + θ has a negative effect on the demand for real money balance while increase in Y has a positive effect on the demand for the real money balance).

However, I also know the following:

An increase in r* + θ will cause a fall in investment which will lead to a fall in income. So, I don't know how income can rise again to so that demand for real balance equals supply for real balance.

I tried to find a solution by graphing what is going on in the money market. First, I increase the world interest rate, since the country risk premium increased. Then, I decreased the demand for real money balance, since the higher interest rate will decrease its demand (a movement along the L(r,Y_0) curve). I don't know what is going to happen so that I can move from point A to point B. Please see the file Attempt.jpeg for my attempted solution.

Can you please describe to me the sequence of events that will lead me to move from point B to point C and how this is reflected in the IS* and LM* graph too. Also, I feel I should have decreased income too i.e. draw a curve L(r,Y_1) that is belove L(r,Y_0) since an increase in interest rates will reduce equilibrium income in the IS* curve due to reduction in investments. Please confirm if I should draw this too.

Answer

Derivation of IS and L
Hi Sara,
First of all, I apologize for being a trifle too late in responding to your query because I was busy with the tasks associated with the new academic session. Secondly, I must thank you for asking a very interesting yet very profound question. Finally, before I put forward my explanatory description as an answer to your inquisitiveness about the “sequence of events” that causes a movement “from B to A” in your IS-LM diagram relating to an open economy, I would rather impress upon you a very important double-edged preliminary statement that should make you feel, as a perceptive student of macroeconomic dynamics, you have nothing to worry about your trouble with the diagram.
(A)   THE PRELIMINARY STATEMENT: The diagram in a positive quadrant of r, Y plane, showing IS-LM interaction, whether in a closed economy or in an open economy (we will see that is basically similar in delineation), is something like presenting in a drama the climax scene of Romeo and Juliette rather than showing all the stages about how Romeo gets rejected from Rosaline, gets the suggestion from his friend to take a “new infection” (Juliette) to forget about “the old” (Rosaline), and gets in the tussle before the climax. That final scene would be total nonsense to somebody who doesn’t know of all the events causing that. Quite the same, the one-quadrant IS-LM curve, final and perfect presentation in itself as this is, would be quite confusing even to the most initiated student who has not been confronted with the sequential geometry leading to this set of curves. Therefore, it is quite natural for a bright student like you to get confused with a diagram which conceals behind it rationale for the positions of these two sets of curves. Once the rationale surfaces out of where it is lurking, this would become as clear as the blue sky after the clouds are dispersed. So, Sara, pluck up your heart. Take a little time poring over the attachment giving two four-quadrant diagram, one showing how the IS curve is derived and another how the LM curve is derived.

(B)   THE “IS CURVE” REPRESENTS THE PAIRS OF r AND y THAT WILL KEEP THE PRODUCT MARKET IN EQUILIBRIUM, IN THE SENSE THAT PLANNED INVESTMENT PLUS GOVERNMENT PURCHASE (i+g) EQUAL SAVING PLUS TAX REVENUE (s+t)

Here r=interest rate. You may consider r=r*+k, where k= the country’s risk premium [you have used theta for k, but Greek scripts are inadmissible on this page, so let’s take theta=k]
i=investment and g=government spending. Then we have

y=c+i+g+X-M       (1)

For simplicity, just take net export, X-M, out so your understanding first becomes clearabout GDP of the country or Income or Output, y, as given in your diagram:

y= c+i+g      (2)

Remember i+g, on the product side, is the amount of real output that does not go to consumer expenditure.

So c+i+g = y in fact gives you, in the CIRCULAR FLOW OF GDP, the upper loop, showing “Household” “buying” goods and services from “Firm” plus the amount that instead of going to consumption goes in part to investment and in part to government spending for building roads, etc. How do they do that? The FIRM gives that in exchange for income=y (which comes to them as rent, wages, interest, profit) that the HOUSEHOLD earn by selling factors of production to FIRM (such as land, labour, capital, enterprise).

Next we have s=saving and t=tax revenues. You also know from your introduction to the circular flow of GDP that equation (2) can equally well be expressed in the lower loop as:

y = c+s+g      [3]

Equation [3], the lower loop, must be equal to equation [2], the upper loop of our circular flow of GDP, giving flow-of-output approach and flow-of-income approach, respectively. In equation [3], on the income side, s+t is the amount of consumer income NOT spent.

So we have

c+i+g = y = c+s+t   [4]

and, invoking the axiom of transformation of equations, [4] yields:

i+g = s+t      [5]

(C)   THE FOUR-QUADRANT DIAGRAM SHOWING HOW THE “IS CURVE” IS DERIVED
Please take a look at Figure 1 of the attachment. We have four quadrants.

Start with the upper left one (the northwest quadrant). This is rotated 90 degrees to the left so that i+g increases as you move along the horizontal axis from the center to the left. Similarly, interest r increases vertically from center upward. Here government expenditure is assumed to be exogenously determined (for simplicity of our explanation). Therefore, g equals the horizontal distance from zero (center) to that marked by the bold-face vertical line, and this distance is shown by the double arrow marked g. This is a straight line, vertical here against r, meaning whatever r is from o upward, g remains unchanged. The investment I which is a function of r, i(r), is added onto  the constant g, to give us i+g measured leftward horizontally as r changes. Can you see that the i(r)+g curve is falling as r is rising? This means, g remaining constant, i(r) is falling as ri increases. This is obvious. Because as interest r goes up, funds become costlier, and entrepreneurs find it more difficult to have funds for investment.

Now come to the upper right-hand quadrant (the northeast quadrant). Let us say, when we have ro, investment and government expenditure plus consumption (i+g+c) add up to income yo on the GDP-axis or y-axis. We will come back to shortly.
Next see what these two s+t curves are. For no take the (s+t)o curve. What does this show? View it like this: Rotate it 180 degrees vertically. Then you have y along horizontal axis, and s+t along vertical axis. This linear curve starts from the origin.  This is natural if there is no income [we assume away consumption for simplicity as in our equation [5]], there will be no s and no t [and, of course, no c]. Then the curve goes “upward” [when you view it that way], when y is zero, s+t equals zero, but as y goes up so goes s+t. This means an increase in y leads to an increase in s+t. This is also natural. The more the income, the more will be s and t [and, of, course, more c]. Now the question comes: By how much. That depends upon what we in economics call the “marginal propensities to save,” etc. That is exactly the slope of the curve. As you can see, (s+t)1 has a GREATER slope than (s+t)o, i. e., (s+t)1 shows the country puts more of the increased y to increase its s and t. Leave this at this stage.

Third, get to the lower left-hand quadrant. The very 45-degree line tells us that all points on the curve are equidistant from s+t axis and i+g axis.  [This is something like what you use in explaining consumption function to show the difference between consumption and saving in a Keynesian positive quadrant of C+S, Y plane.]  Hence the southwest quadrant shown how we measure equal s+t with equal i+g.

Let’s now get down to the dynamics. At yo, via the function in the lower right-hand quadrant, (s+t)o = (i+g)o, as shown in the lower left-hand quadrant. Now, at (i+g)o, via the i(r)+g function in the upper left-hand quadrant, r=ro. And at ro, y=yo. At income yo in equilibrium we have planned s+t at (s+t)o; to generate an equal amount of (i+g)o, the interest rate would have to be at ro. This can be done for any level of y to give a corresponding level of r. Or, conversely, we could take the level of r as given and locate the equilibrium income level associated with that interest rate.

As such, we arrive at exactly what we stated at the beginning under (B).

We can study the effects of changes in exogenous variables like g, or shifts in the investment, saving, or tax functions, on the product market equilibrium r and y levels.

For example, an increase in the desire to save, i. e., a decrease in consumption demand at any given income level, can be shown as a downward rotation of s+t function to (s+t)1 function in Figure 1 of our attachment. This gives a higher s+t for any given y. At the original level of interest rate ro, and planned (i+g)o, this decrease in consumption demand will reduce equilibrium income through the multiplier process. Graphically, at the initial equilibrium ro and thus the initial level of i+g, with the new s+t function we will trace out a new, lower-equilibrium y1 in out attachment.. Thus the increase in the desire to save, reducing total demand at any given interest rate level, has shifted the IS curve to the left, giving a lower equilibrium y for any given r, or lower equilibrium r for any given y.

(D)   THE FOUR-QUADRANT DIAGRAM SHOWING HOW THE “LM CURVE” IS DERIVED
Please take a look at Figure 2 of the attachment. We have four quadrants.

Give some similar reasons to this Figure 2, and you will find that easy.
We have speculative demand = l(r)          [6]
Transactions demand = k(y),  k’ = dk/dy>o.         [7]
The demand function for real balances = M/Y = l(r) +k(y)      [8]
[Note that I have already explained these in detail previously on the AllExpert.com.]

In general, we should recognize that the speculative transactions demands cannot be separated. For example, as the interest rate on bonds rises, we would expect transactions balances to be reduced as people recognize the increasing opportunity cost of holding idle cash balances and squeeze them down. So the amount of transactions balances people hold should be sensitive to the interest rate. Thus the demand-for-money function in general should be written as:

M/P =m(r,y)          [9]

In equation [9], the slope w.r.t. y is positive and the slope w.r.t. r is negative, removing the separation of speculative and transactions demands.

Equating the demand function to the exogenously fixed supply yields the equilibrium condition in the money market:

{M}/P = m(r, y) = l(r) +k(y)          [10]

In equation [10],  {M} stands for a fixed supply of money. In our diagram in the attachment {M} is shown as M with a bar [this font is not available on this page].

In the lower right-hand quadrant we have the line k(y) = transactions demand –and increasing function of income measured downward. In the upper left-hand quadrant is the curve representing the speculative demand as a function of the interest rate. The slope, dl(r)/dr, is negative, because as r goes up, it is wiser to keep money in banks.

The lower left-hand quadrant has a straight line at 45 degrees from the vertical axis as well as from the horizontal axis such that increasing k(y) and decreasing l(r), or vice versa, will leave the result unchanged. Any point on the 45-degree line gives a speculative component l(r) plus a transactions component k(y) which just add up to the total money supply.

Now we can locate in the upper right-hand quadrant the r, y pairs that maintain the money market in equilibrium. At any level of income such as yo we can find transactions component of the demand for money from the k(y) function. This shows us, in turn, the level of interest rate ro that will maintain the money market in equilibrium with income level yo. Having located one money-market equilibrium pair, (ro, yo), we can locate another by beginning with y1.
Repeating the process traces out the line that describes the set of r, y pairs that maintain money-market equilibrium. This is the LM curve in Fig. 2.

WE CAN SEE THAT THE LM CURVE REPRESENTS THE PAIRS OF r AND y THAT WILL KEEP THE MONEY MARKET IN EQUILIBRIUM WITH A GIVEN LEVEL OF THE MONEY SUPPLY, M, AND A GIVEN PRICE LEVEL, M

(E)   NOW APPLY THOSE CONCEPTS TO r*+THETA TO r AND YOU FIND THE SAME REASONING FOR HOW LM CURVE SHIFTS. APPLY THE SHIFTS OF LM AS WELL AS IS CURVES.

When there is insurance premium added, it means r goes up to what I referred to as r1 or, in your question, (r*+theta). The same thing applies in the open economy, and the SEQUENCE can be traced by poring over the two figures in the attachment.

(F)   CONCLUSION
Sara, I have tried to give the sequences of movements of the IS and LM curves as clearly as possible, subject to the constraint of space on the blog. This is basically a very deep concept with lots of abstract, if not very much abstruse, implications that sometimes confound seasoned economics students. If you have further explanation, please do not hesitate to write to me. Wishing you best in your endeavours.

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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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