This content is meant for BBA macroeconomics.

1. General Equilibrium
IS-LM Framework
By
Khemraj Subedi
Associate Professor
M.Phil in Economics
PhD Scholar in Economics
Tikapur Multiple Campus
Far Western University

2. General Equilibrium of Product and
Money Markets (4)
 1 Derivation of IS curve
 2 Derivation of LM curve
 3 General Equilibrium of product and money
 markets

3. General Equilibrium of Product and Money
Markets or IS-LM Model
 What is the IS-LM model?
 The IS-LM model, which stands for “investment-saving” (IS) and
“liquidity preference-money supply” (LM) is a
Keynesian macroeconomic model that shows how the market for
economic goods (IS) interacts with the loanable funds market (LM)
or money market.
 It is represented as a graph in which the IS and LM curves
intersect to show the short-run equilibrium between interest
rates and output.
 The IS-LM model describes how aggregate markets for real goods
and financial markets interact to balance the rate of interest and
total output in the macroeconomy.

4. 12.1 Derivation of IS curve
 What is IS curve?
 IS curve is an abbreviation of investment and saving curve. In
general equilibrium analysis, IS curve shows equilibrium in
the product market.
 The IS curve depicts the set of all levels of interest rates and
national income (Y) at which total investment (I) equals total
saving (S). At lower interest rates, investment is higher,
which translates into more total output or national income
(Y), so the IS curve slopes downward and to the right.
 Therefore, IS curve refers to the locus of various
combinations of interest rates (i) and national income (Y)
which shows the product market equilibrium of any economy.

5. Conditions for the Product Market
Equilibrium:
 The product market is in equilibrium when desired
savings and investments are equal. Saving is a direct
function of the level of income, S= f (Y) … (1)
 Investment is a decreasing function of the interest rate,
I= f (r) … (2)
 From (1) and (2), we have S=I.
 The IS schedule reflects the equilibrium of the product
market. It shows the combinations of interest rate and
income levels where saving-investment equality takes
place so that the product market of the economy is in
equilibrium. It is also known as the “real sector”
equilibrium.

7. 7

8.  In the diagram given on the previous page, in panel-A, it has been
shown that with a certain amount of investment at the i2 rate of
interest, the determined income level of income is 0Y2. The
combination between the same rate of interest and the income level
is represented by point B in panel-B. Now let us suppose that there
is a fall in the rate of interest from i2 to i1. Consequently, there is
an increase in investment which causes the AD curve to shift
upward where the 0Y3 income level gets determined as shown in
Panel-A.
 The interest-income combination, 0i1 and 0Y3 represented by the
point C as shown in Panel-B. Similarly, with the rise in interest rate
from i2 to i3, there is a fall in investment resulting in a fall in
income level from 0Y2 to 0Y1. The interest-income combination 0
i3 and 0Y1 is represented by point A as shown in Panel B. When
all these interest-income combinations A, B, and C are joined
together with a smooth line, we get a downward-sloping curve
called the IS curve, as shown in Panel B.

9.  Problem 1:
 Given C= 10+0.5Y; I=200-2000i,
then find (i)IS equation.
(ii) Income (Y) when interest rate (i) is 0.10
Solution: We know, at equilibrium,
Y=C+I
 Y = 10+0.5Y+200-2000i
 Or, Y-0.5Y =210-2000i
 Or, 2(0.5Y) = 2(210-2000i) (multiplying both sides by 2)
 ∴ Y = 420 -4000i (IS equation)

 (ii) Income (Y) when interest rate (i) is 0.10
 Y = 420-4000(0.10)=420-400=20
 ∴ Y = 20

10. What is LM curve?
 LM curve is an abbreviation of the money demand(liquidity
preference, L) and money supply(M) curve. In general equilibrium
analysis, the LM curve shows equilibrium in the money market.
 The LM curve depicts the set of all levels of national income (Y)
and interest rates (r) at which money supply equals money
(liquidity) demand. The LM curve slopes upward because higher
levels of national income (Y) induce increased demand to hold
money balances for transactions, which requires a higher interest
rate to keep money supply and liquidity demand in equilibrium.
 Therefore, LM curve refers to the locus of various combinations of
interest rates (i) and national income (Y) which shows the money
market equilibrium of any economy.

11. Conditions for the Money Market
Equilibrium:
 The money market is in equilibrium when the
demand and supply of money are equal. Denoting L
for money demand and M for the money supply, the
money market is in equilibrium when L=M. The
demand for money L=L1+L2 where L1 is the
transaction demand for money and precautionary
demand for money which is a direct function of the
level of income, L1 = f(Y). The L2 is the speculative
demand for money which is a decreasing function of
the rate of interest, L2=f(r). Thus in money market
equilibrium, M= L1 (Y)+ L2 (r).

12. Deriving the LM Curve:
 The LM curve shows all combinations of interest rate and levels
of income at which the demand for and supply of money are
equal. In other words, the LM schedule shows the combinations
of interest rates and levels of income where the demand for
money (L) and the supply of money (M) are equal such that the
money market is in equilibrium.
 The LM curve is derived from the Keynesian formulation of
liquidity preference schedules and the schedule of supply of
money. A family of liquidity preference curves L1Y1 L2Y2 and
L3Y3 is drawn at income levels of Rs100 crores, Rs200 crores,
and Rs300 crores respectively in Figure 4 (A). These curves
together with the perfectly inelastic money supply curve MQ
give us the LM curve.

14.  In the previous page, the panel A diagram vertical axis shows the
rate of interest ( R) and the horizontal axis shows the demand and
supply of money. In this panel, the MQ curve shows money
supply and R1, R2 and R3 depict the rate of interest whereas
L1Y1 (100), L2Y2 (200), and L1Y2 (300) show corresponding
money demand accompanied by national income(Y). This figure
clearly shows that with the increase in national income, there is a
corresponding increase in money demand. Likewise, the increase
in money demand causes an increase in the rate of interest.
national increases.
 Likewise, panel B shows the locus of various combinations of the
rate of interest (R ) in the vertical axis and the level of national
income(Y) in the horizontal axis. After joining the locus points
K,S, and T we derive a positively slopped LM curve. In
conclusion, we can say that with the increase in GDP or national
income, money demand increases. The increase in money demand
causes increases in rate of interest.

15.  Problem 2:
 Given the following data about the monetary sector of the economy:
Md = 0.4 Y – 80i
Ms = 1200 crores.
 where Md is demand for money, Y is level of income, ‘i’ is the rate of
interest and MS is the supply of money
 Derive the equation for the LM function
 What will be the rate of interest for income level Y=4000 crore and
Y=4400 crore
 Give the economic interpretation of the LM curve. Draw the LM curve
from the above data.
 Solution:
For the money market to be in equilibrium:
Md = Ms
0.4 Y – 80 i = 1200
80 i = 0.4 Y – 1200
i = (
𝟎.𝟒𝒀
𝟖𝟎
) – (
𝟏𝟐𝟎𝟎
𝟖𝟎
) (PTO)

16. i = (
𝟏
𝟐𝟎𝟎
)Y – 15 ….. (i)
Thus we get the following LM function:
i = (
𝟏
𝟐𝟎𝟎
)Y – 15
Alternatively, the LM equation or function
equation(1) above can also be stated as:
Y = 200i + 3000

17. Thank You!
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