Question

Suppose the demand for real money balances is M^d/P = L(Y, i), where L(Y, i) is an increasing function of income Y and a decreasing function of the nominal interest rate i. Assume that the interest elasticity of money demand is infinite when the nominal interest rate is zero. Money-market equilibrium is represented by the equation M^s/P = L(Y, i), where Ms is the money supply controlled by the central bank and P is the price level. The LM curve relationship between Y and i represents money-market equilibrium for given values of Ms and P. In the IS-LM model, the price level P is assumed to be fixed in the short run.

(a) [5 marks] Show how the LM curve is derived, paying careful attention to its shape where i is zero.

The IS curve represents goods-market equilibrium. Consumption depends positively on disposable income; investment depends negatively on the real interest rate; tax and government spending are exogenous. Following a large negative shock to confidence, investment demand falls and the IS curve shifts to the left, intersecting the LM curve at i = 0.

(b) [8 marks] Use the IS-LM model to analyse the effects on GDP of each of the following policy options. Which policies does the model predict are effective in avoiding a recession?

i. The central bank increases the money supply by buying more short-term government bonds (‘quantitative easing’);

ii. Higher government expenditure paid for by increasing taxes;

iii. A tax cut paid for by printing money (a ‘helicopter drop’ of money);

iv. The central bank raises its inflation target (assume this is credible and increases inflation expectations π e ).

Answer 1

a)

Figure-1 and 2 combinedly illustrate the derivation of the LM curve from the money or loanable funds market equilibria involving money demand or Md/P or L(Y, i) where L is an increasing function of Y(aggregate income) and a decreasing function of i(nominal interest rate) and money supply or Ms/P or L(Y,i) which is controlled and administered by the Central Bank with P representing the price level of goods and services in the economy. Figure-1 in the document attached represents the money or loanable funds market with Md/P and Ms/P curves. The y-axis and the x-axis denote the interest rate and the quantity of money or M respectively. The various equilibria in the money market are labeled as E1, E2, and E3 which all correspond to the equality or intersection between the Md/P and Ms/P curves. The money market equilibrium E1 corresponds to the intersection of Md/P1 curve and Ms/P curves with the equilibrium interest rate and quantity of money as i1 and M* and E2 is established by the intersection of Md/P2 and Ms/P curves with the equilibrium interest rate and quantity of money as i2 and M* respectively. The equilibrium point E3 corresponds to the intersection of Md/P3 and Ms/P curves with the equilibrium interest rate and money quantity of i3 and M* respectively.

Now, with assumption that the interest elasticity of real money demand or Md/P is perfectly elastic or infinite when the interest rate i is equal to 0, the derivation of the LM curve has been presented in figure-2 in the same attached document where figure-1 is illustrated. The LM curve basically shows the relationship between Y and i based on the money market equilibria. In figure-2, the y-axis and the x-axis represent the interest rate i and the aggregate income Y respectively. In this context, note that corresponding to the point E1 in figure-1, when the interest rate is i1, the aggregate income in the economy would be Y1 as indicated in figure-2 and referring to the equilibrium point E2, at the interest rate of i2 the aggregate income in the economy would be Y2. Based on the equilibrium point E3, when the interest rate is i3 the aggregate income becomes Y3 as pointed in figure-2. Now, by joining all these points corresponding to respective is and the Ys, the LM curve can be derived as shown in figure-2. The shape of the LM curve is upward sloping implying that as the interest rate increases the aggregate income also increases implying that the aggregate income is an increasing function of the interest rate. One important point to consider in figure-2 is the shape of the LM curve when the interest rate or i is equal to 0. Based on the assumption of the perfect interest rate elasticity of Md/P when i is 0, the shape of the LM curve would be completely flat when i is 0 as indicated in figure-2. The direction of the LM curve as the i increases has been pointed out by the arrow signs in figure-2 implying that when i is 0, the LM curve is completely flat at the x-axis due to the perfect interest elasticity of money demand at this point and as i gradually increases the LM curve becomes upward sloping based on the respective money market equilibria points. The higher the interest elasticity of money demand in the money or loanable funds market, the flatter the shape of the LM curve denoting the relationship between i and the Y.

b)

IS-LM Model:

This model show that how the IS and LM interact to balance the rate of interest arte and total output (GDP). In this model IS stand for investment-saving and LM stand for Liquidity preference-money supply. This is a macroeconomic model.

i)

When central bank increase money supply by buying more short-term government then its decrease the rate of interest. Lower interest rate increase the demand for money and increase investment and consumptions. Increasing investment and consumptions boost the economic growth and GDP grow fast. So, its increase GDP growth rate.

ii)

Higher government spending paid for by increasing tax is a combination of expansionary and Contractionary Fiscal Policies. Here, one side a government is increasing that `will increase which in turn increases the production of goods and services and other side government is increasing tax rate that will negatively affect the the investment and which in turn increases the production of goods and services. So, here, the change in investment affects the aggregate demand in precisely the same manner as a change in government purchases. Higher spending and lower tax positively affect the the investment and which in turn increases the production of goods and services that will increased the GDP growth rate and vice versa. So, here the impact of higher government spending paid for by increasing tax on GDP will depend upon the spending level and increasing tax rate.

iii)

A tax cut paid by for by printing money is a tool that is use during the recession. A helicopter drop of money is a tool of increasing money supply without create

more debt. It is a non-repayable money transfer from the central bank to the government. It does not affect the Interest rate. It boost the economic growth and increase GDP.

iv)

When a central bank increase its inflation target then its increase the money supply buy quantity easing or helicopter drop of money then its decrease the interest rate and increase the the demand of money that positively affect the consumption and investment and increase the economic growth and GDP.

Effective policy in avoiding recession:

In all these four option option one is better because here a central bank use the OMO tool (purchasing short-term government bonds) to increase the money supply and decrease the the interest rate that boost the investment and consumption and boost economic growth or increase GDP. In option two strategy and its impact is not clear because a mixed fiscal policy is taking in use, In third option central bank use  a helicopter drop of money that can increase the inflation rapidly and negatively affect the exchange rate also. In long run it will negatively affect the economy. In forth option central bank is only focusing on inflation target that is not a suitable idea to recover from recession.

I have attached graphs where you can see that how a increasing money supply (LM to LM1) decrease the interest rate and increase GDP (Y to Y1). How a  Increasing IS curve (IS to IS1) Increase the interest rate and GDP (Y to Y1) both.

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