IS-LM model 2

Question 1

The interest rate, investment and the IS Curve

Answer 1

In the Keynesian cross, planned investment I is treated as exogenous. This ignores one of the most important macroeconomic relationships: investment spending depends negatively on the interest rate. I=I(r),I′(r)<0. A higher interest rate increases the cost of borrowing and the opportunity cost of using internal funds. Firms invest less when r rises, and more when r falls. Planned expenditure now depends on both Y and r. For each value of the interest rate, the Keynesian cross determines an associated level of income. The set of (Y, r) pairs consistent with goods-market equilibrium forms the IS curve.

Question 2

Deriving the IS curve

Answer 2

↑r→↓I
↓I→↓PE
↓PE→↓Y
The IS curve gives us the combination of r and Y at which planned expenditure equals to income — equilibrium in the goods market!

Question 3

Fiscal policy- Shifts in the IS curve

Answer 3

For any interest rate r , the IS curve shows the level of income Y that clears the goods market. It is drawn for a given fiscal policy: government spending Gˉ and taxes Tˉ. In the Keynesian cross, higher G shifts the planned-expenditure line upward. At a given interest rate rˉ, equilibrium income rises from Y1​ to Y2. Therefore, every point on the IS curve now corresponds to a higher level of income. Expansionary fiscal policy raises aggregate demand.
Goods-market equilibrium now occurs at higher income for any given interest rate

Question 4

Theory of liquidity preference: Money Supply

Answer 4

Keynes’s idea: In the short run, the interest rate adjusts to equilibrate the supply and demand for the most liquid asset, money.
* Real money balances supply= (M/P)^s=M(bar)/P(bar). M is the nominal money supply, set exogenously by the central bank. P is the price level, taken as fixed in the short run. Therefore, the supply of real money balances is fixed. Implications: Because both M and P are exogenous in IS–LM, M/P=constant. Money supply does not depend on the interest rate.

Question 5

Theory of Liquidity Preference: Money Demand

Answer 5

Holding money yields convenience but no interest. Holding bonds yields interest r. Therefore, when r rises, the cost of holding money rises. Real money balances demand = (M/P)^d = L(r). L(r) is the liquidity-preference (money-demand) function. It is downward-sloping. r↑⇒L(r)↓. Higher interest rate ⇒ people hold less money and more interest-bearing assets.

Question 6

Equilibrium in the money market

Answer 6

The interest rate adjusts to ensure (M/P)^s=(M/P)^d

Question 7

Adjustment in the money market

Answer 7

If r is too high, (M/P)^s > (M/P)^d. People hold more money than they want → they buy bonds. Bond issuers face excess demand for interest-bearing assets → lower r. If r is too low (M/P)^s < (M/P)^d. People want more money → sell bonds. Bond issuers must attract scarce funds → raise r.

Question 8

How central banks change interest rates

Answer 8

Central bank reduces the money supply (M↓). Real money balances fall: M/P shifts left. At the old interest rate r1​, money demand exceeds money supply. People try to obtain money by selling bonds. Bond prices fall → interest rate rises. Central bank increases the money supply (M↑). Real money balances increase: M/P shifts right. At the ongoing interest rate there is excess money supply. Excess supply of money leads people to buy bonds. Bond prices rise → interest rate falls.

Question 9

Income, money demand and the LM curve

Answer 9

Money demand depends on both the interest rate and income:(M/P)^d = L(r) with Lr​<0, LY​>0. Higher income ⇒ higher money demand: More income → more spending → more transactions → greater need for liquidity. The supply of real money balances is exogenously determined: (M/P)^s=M(bar)/P(bar). If income increases, money demand rises above the fixed supply at the initial interest rate. To restore equilibrium, the interest rate must rise: Y↑⇒L(r,Y)↑⇒r↑. This positive relationship between income and the interest rate is the basis of the LM curve.