Income Determination: IS-LM Model (Hicks-Hansen Approach)
The IS-LM model, developed by John Hicks (1937) and Alvin Hansen, extends Keynesian theory to show simultaneous equilibrium in both the product market (IS) and the money market (LM). This unit covers the derivation of the IS curve from the product market, the derivation of the LM curve from the money market, and the general equilibrium where both markets clear simultaneously — determining both income (Y) and the interest rate (r).
In this chapter
Introduction to the IS-LM Model
The simple Keynesian cross model determines only income (Y) — it treats investment (I) as autonomous, independent of the interest rate. But in reality, investment depends on the interest rate: when r rises, I falls. The IS-LM model — developed by John Hicks (1937) and popularised by Alvin Hansen — corrects this by determining both income (Y) and the interest rate (r) simultaneously. The IS curve shows equilibrium in the product market (investment = saving), and the LM curve shows equilibrium in the money market (money demand = money supply). Their intersection gives the general equilibrium.
Product Market Equilibrium: Derivation of the IS Curve
The IS curve shows all combinations of interest rate (r) and income (Y) at which the product market is in equilibrium — that is, where investment equals saving (I = S), or equivalently, where aggregate demand equals aggregate supply (Y = C + I). The IS curve slopes downward: a lower interest rate raises investment, which raises income (via the multiplier), so lower r is associated with higher Y. The IS curve shifts right when there is an increase in autonomous consumption, government spending, or a fall in taxes (expansionary fiscal policy).
IS curve — product market equilibrium (I = S)
Money Market Equilibrium: Derivation of the LM Curve
The LM curve shows all combinations of r and Y at which the money market is in equilibrium — where money demand (L) equals money supply (M): L(r, Y) = M. Keynes's liquidity preference theory says money demand has three motives: transactions (proportional to Y), precautionary (proportional to Y), and speculative (inversely related to r). The money supply is fixed by the central bank. The LM curve slopes upward: higher Y raises money demand (for transactions), which raises r (since M is fixed), so higher Y is associated with higher r. The LM curve shifts right when the central bank increases the money supply (expansionary monetary policy).
LM curve — money market equilibrium (L = M)
General Equilibrium: IS and LM Together
The general equilibrium of the economy is at the intersection of the IS and LM curves — the point where both the product market and the money market clear simultaneously. This point determines both the equilibrium income (Y) and the equilibrium interest rate (r). If the economy is not at this point, at least one market is in disequilibrium, and forces push it back. Fiscal policy (changes in G or T) shifts the IS curve; monetary policy (changes in M) shifts the LM curve. The effectiveness of each depends on the slopes of the curves.
Policy Effects in the IS-LM Model
- Expansionary fiscal policy (↑G or ↓T) shifts IS right → Y rises, r rises. The rise in r partly "crowds out" private investment.
- Expansionary monetary policy (↑M) shifts LM right → Y rises, r falls. Lower r stimulates investment.
- Fiscal policy is most effective when LM is flat (liquidity trap) and least effective when LM is vertical (classical case).
- Monetary policy is most effective when IS is steep and least effective in a liquidity trap (LM is horizontal).
Real-Life Example: Nepal Rastra Bank and Monetary Policy
When Nepal Rastra Bank (NRB) cuts the policy rate or reduces the Cash Reserve Ratio (CRR), it increases the money supply — this shifts the LM curve rightward. Lower interest rates encourage businesses to borrow and invest, which raises income. During the COVID-19 pandemic (2020), NRB cut its policy rate to 3% and reduced CRR to inject liquidity — a textbook expansionary monetary policy aimed at shifting LM right and supporting the economy.
Practice Problem
In an IS-LM model: the product market equilibrium condition is Y = 400 + 0.6Y + 200 − 50r, and the money market equilibrium is 0.5Y − 100r = 250 (where money demand L = 0.5Y − 100r and money supply M = 250). (a) Derive the IS curve (express Y as a function of r). (b) Derive the LM curve (express Y as a function of r). (c) Find the equilibrium Y and r.
Shifts in IS and LM Curves
The IS curve shifts right when there is an increase in autonomous consumption, government spending, or a cut in taxes — all of these raise aggregate demand at every interest rate. The IS curve shifts left when taxes rise, government spending falls, or consumer confidence drops. The LM curve shifts right when the central bank increases the money supply — more money means lower interest rates at every income level. The LM curve shifts left when money supply falls or money demand rises (e.g., due to financial uncertainty). These shifts are the mechanism through which fiscal policy (shifting IS) and monetary policy (shifting LM) affect the economy.
Policy Effects in the IS-LM Model
| Policy Action | Curve Shift | Effect on Y | Effect on r |
|---|---|---|---|
| Expansionary fiscal (↑G) | IS right | Y rises ↑ | r rises ↑ |
| Contractionary fiscal (↓G) | IS left | Y falls ↓ | r falls ↓ |
| Expansionary monetary (↑M) | LM right | Y rises ↑ | r falls ↓ |
| Contractionary monetary (↓M) | LM left | Y falls ↓ | r rises ↑ |
Crowding Out Effect
Crowding out occurs when expansionary fiscal policy (↑G) raises the interest rate, which reduces private investment. The mechanism: ↑G shifts IS right → Y rises → money demand rises (for transactions) → r rises → investment falls. So part of the increase in government spending is offset by a decrease in private investment — the government "crowds out" private spending. Crowding out is complete (full crowding out) when the LM curve is vertical (classical case) — then fiscal policy has no effect on Y. It is zero when LM is horizontal (liquidity trap) — then fiscal policy is most effective.
Liquidity Trap
A liquidity trap is a situation where the interest rate is so low that everyone expects it to rise (and bond prices to fall). Everyone prefers to hold money rather than bonds, so money demand becomes perfectly elastic — the LM curve is horizontal. In this situation, monetary policy is completely ineffective: increasing the money supply does not lower the interest rate further (it's already at the floor), so investment and income do not rise. However, fiscal policy is extremely effective: the IS curve shift translates fully into higher income with no crowding out (because r doesn't rise). Keynes argued the 1930s Great Depression was a liquidity trap — which is why monetary policy alone could not revive the economy.
Real-Life Example: NRB Monetary Policy
During COVID-19 (2020), Nepal Rastra Bank aggressively cut interest rates and reduced CRR to inject liquidity. This was expansionary monetary policy — shifting LM right. Lower interest rates made borrowing cheaper, encouraging businesses to invest. However, with lockdowns and uncertainty, private investment was unresponsive (a near-liquidity-trap situation). The government's fiscal package (relief spending) — shifting IS right — was more effective in supporting incomes. This illustrates the IS-LM insight: when monetary policy hits its limits, fiscal policy becomes crucial.
Key Terms and Definitions
- IS curve: Combinations of r and Y where product market clears (I = S) — IS वक्र: उत्पादन बजार सफा हुने r र Y का संयोजन।
- LM curve: Combinations of r and Y where money market clears (L = M) — LM वक्र: मुद्रा बजार सफा हुने r र Y का संयोजन।
- General equilibrium: IS and LM intersect — both markets clear simultaneously — सामान्य सन्तुलन: IS र LM प्रतिच्छेदन।
- Fiscal policy: Changing G and T to shift IS curve — राजकोषीय नीति: G र T परिवर्तन गरी IS सराउने।
- Monetary policy: Changing M to shift LM curve — मौद्रिक नीति: M परिवर्तन गरी LM सराउने।
- Crowding out: ↑G raises r, reducing private investment — भीड निकाल्ने: ↑G ले r बढाउँछ, निजी लगानी घटाउँदै।
- Liquidity trap: LM horizontal; monetary policy ineffective — तरलता जाल: LM तेर्सो; मौद्रिक नीति अप्रभावकारी।
- Liquidity preference: Keynes's money demand (3 motives) — तरलता प्राथमिकता।
- Hicks-Hansen: Developers of the IS-LM model — हिक्स-ह्यान्सेन: IS-LM मोडेलका विकासकर्ता।
Practice Problem
In an IS-LM model, the equilibrium is Y = 1,000 and r = 5%. The MPC = 0.75. (a) If the government increases spending by ΔG = 40, calculate the change in Y using the government multiplier (assuming no crowding out). (b) If crowding out reduces the actual change in Y to 60% of the theoretical multiplier effect, what is the actual new Y? (c) What is the implied change in r that caused the crowding out?