Question

Consider the following model of a very simple economy:

C = 100 + 0.6Yd

Yd = Y-T

T = 500

I = 200

G = 500

Y = C + I + G

(a) what are the equilibrium levels of GDP (Y), consumption(C), and disposable

income (Yd)

(b) What is the government spending multiplier

(c) If government spending increases by 250, by how much would GDP increases?

And what would be the new GDP

Answer 1

The three sector model have the equations as , , , , and .

(a) The equilibrium level of GDP is where the aggregate demand is equal to Y. The AD is , and the last equation is the equilibrium solution. Hence, for , we have . The consumption function can be simplified as for , we have , and as , we have , putting which in equilibrium equation, we have or or or or or , is the equilibrium level of GDP. The equilibrium level of consumption, since is , hence , ie or . The equilibrium disposable income, since is , hence , ie or .

(b) The equilibrium equation of the economy can be written as , ie , as in this case, the mpc is 0.6, while the investment is just autonomous investment. Further, as , we have or or or or , which is the equilibrium level of GDP/output. Now, suppose the government spending increases from G to G', and we term the change as , then the new output is , where output is increased to Y', with a change of . The change in output can be expressed as since , then or or , ie , or . Thus, the government spending multiplier is , meaning for a unit change in government spending, the output will increase by , as mpc is less than one and 1-mpc is a fraction less than 1.

(c) Suppose , then as , we have or or , ie Y will increase by 625 if government spending increase by 250. The New GDP can be calculated as since , we have , or , which is the new GDP.