**Macroeconomics EC213**

**Assignment 2**

- Consider a simple Keynesian income-spending model of an economy described by the following equations

C = 210 + 0.75Y_{d}

= 300

= 425

= 120

= 100

M = 0.15Y

= 250

Calculate the equilibrium level of income. At the equilibrium we will have the sum of aggregate expenditure equal to the aggregate income in the economy.i.e. AE = 210+0.75Y_{d}+300+425+250-0.15Y,[Since disposable income Y_{d} =Y-T+TR]i.e. AE = 0.6Y + 1185+15 =0.6Y+1200.AE=Y,i.e. 0.4Y=1200,

Therefore the equilibrium income is 3000.

i.e. Y=12000/4=3000.

i.e. Y=0.6Y+1200,

At equilibrium we have,

i.e. AE = 0.75Y – 0.75(100-120) – 0.15Y +1185,

i.e. AE = 0.75(Y-T+TR)-0.15Y + (210+300+425+250),

Total aggregate expenditure, AE = C+I+G+X-M

Sketch this equilibrium position using a two-dimensional graph.

Suppose the government reduces public expenditure on goods and services by 25. Estimate the change in the equilibrium level of income. What is the new equilibrium level of income?

Now G=425-25=400.

At the equilibrium we will have the sum of aggregate expenditure equal to the aggregate income in the economy.

Total aggregate expenditure, AE = C+I+G+X-M

i.e. AE = 210+0.75Y_{d}+300+400+250-0.15Y,

i.e. AE = 0.75(Y-T+TR)-0.15Y + (210+300+400+250),

[Since disposable income Y_{d} =Y-T+TR]

i.e. AE = 0.75Y – 0.75(100-120) – 0.15Y +1160,

i.e. AE = 0.6Y + 1160+15 =0.6Y+1175.

At equilibrium we have,

AE=Y,

i.e. Y=0.6Y+1175,

i.e. 0.4Y=1175,

i.e. Y=11750/4=2937.5

Therefore the equilibrium income is 2937.5.