Use the Solow-Swan growth model to anser the following questions.

Suppose that a government purchases goods in the amount of per worker every year; with L_t workers in year t, total government ourchases are L_t.. The government has a balanced budget so that its tax revenue in year t,T_t, equals total government purchases. National saving is given by

S_t=s(Y_t-T_t) - wK_t,

where Y is total output and s is the saving rate (o

Y_t = K_tL_t^1- ,

where is constant, 0<<1, and physical capital depreciated at rate >0. Finally, population growth rate is n>0.

(a) Find the steady-state condition for this economy, and graphically show the steady-state values of per-worker capital (K*) and output (y*).

(b) Suppose that the government permanently increases its purchases per worker. What are the effects on the steady-state levels of capital per worker, output per worker, and consumption per worker?