Question

Let the IS and LM relations be given as in class but suppose that investment is now increasing in the interest rate i; that is, when i increases, I(Y,i) increases. All other functions and relations remain the same.

1. (a) Graphically derive the IS curve using a Keynesian cross; explain why, given the unusual assumption for investment, it is upward sloping.

2. (b) Draw an arbitrary LM curve (based on standard assumptions about the financial market) along with your IS curve from (a). Make your LM curve flatter than your IS curve. Suppose the government increases G. Show the impact this has on Y and i in the short run equilibrium.

Answer 1

Answer to the question no. a:

Derivation of the IS curve is shown in the following figure:

Here, the PE is the planned expenditure which is the sum of Consumption expenditure, Investment expenditure and government expenditure (closed economy model). E1 is the first equilibrium point where PE is equal to the Actual expenditure (AE). Keeping the consumption and government expenditure as constant, when investment expenditure is increased from I1 to I2 (as a result of fall in the rate of interest from r1 to r2), the PE curve shifts upward from PE1 to PE2. This will increase the Income and output (through multiplier effect) from Y1 to Y2. Since, IS curve shows the equilibrium in real market, and shows the relationship between interest rate and income (the IS curve depicts the set of all levels of income (GDP) and interest rates at which saving equals the investment), we can get the IS curve by joining the different level of rate of interest corresponding with different level of income.

Answer to the question no. b:

An increase in government expenditure shift the IS curve to the right.Given the LM curve, this rise in government expenditure raises the Income/output of the economy and on the otherhand it also lead to a higher interest rate. Refer the following diagram:

The increase in government expenditureshifts the IS curve to the right from IS1 to IS2. this shifts the equilibriumpoint upward from E1 to E2 and income increases from Y1 to Y2. The amount of crowding out is Y2 Y3. Crowding out is the situation when the government raises its expenditure, the rate of interest increases which offset the private investment by some amount.

More flatter the LM curve, lesser will be the crowding out and thus, more effective will be the fiscal policy.

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Y=AE -- PEx=C+lz+G Planned Expenditure & PE:= C+12+G Actual Expenditure Y2 Output/Real Income Rate of Interest Investment Y Y Output/Real Income Investment

LM Rate of Interest IS2 IS V1 V2 Ya Output/Real Income

Y=AE -- PEx=C+lz+G Planned Expenditure & PE:= C+12+G Actual Expenditure Y2 Output/Real Income Rate of Interest Investment Y Y Output/Real Income Investment

LM Rate of Interest IS2 IS V1 V2 Ya Output/Real Income

YEAE PE2=C+Iz+G Ez --- Planned Expenditure & PEA= C+1+G Actual Expenditure Output/Real Income Investment V1 V2 Output/Real Income Investment

LM Rate of Interest IS2 IS V1 V2 Ya Output/Real Income