Question

Consider the Economy of Rwanda. The consumption function is given by 𝐶=200+0.75[𝑌−𝑇] while the

investment function is 𝐼=200−25𝑟. Government purchases and taxes are both 100.

The money demand function of Rwanda is [𝑀𝑃⁄]𝑑=𝑌−100𝑟. The nominal money supply is 100 and the

price level P is 2.

i

i) Derive the IS curve equation.

ii

ii) Draw a well labeled diagram of the IS Curve.

iii

iii) Derive the LM curve equation.

iv

iv) Draw a well labeled diagram of the LM Curve.

v

v) Determine the equilibrium level of income and equilibrium interest rate

Answer 1

i).

The IS equation is derived as follows:

$Y = C +I + G$

$Y = 200 + 0.75 (Y -T) + 200 -25r + 100$

$Y = 200 + 0.75 (Y -100) + 200 -25r + 100$

$Y = 500 + 0.75Y - 75 -25r$

$0.25Y = 425 - 25r$

$Y = 1700 - 100r$

ii).

Below is a graph of IS curve

iii).

Derivation of the LM equation

$Money \space Demand = Money \space Supply$

$Y - 100r = 100/2$

$Y - 100r = 50$

$Y = 50 + 100r$

iv)

The LM curve is drawn below;

v)

The equilibrium level of income is calculated by solving IS and LM equations. It can be solved as follows:

$1700 - 100r = 50 + 100r$

$1650 = 200r$

$R = 1650\div200$

$=8.25\%$

$Y = 50 + 100 × 8.25$

$= 875$

The equilibrium level of real GDP is $ 875 while the equilibrium level of interest rate is 8.25%