Ramsey model, COVID-19 shocks. Government expenditures and TFP

1.a.-Government expenditures: Assume that the economy is converging to its long

term steady state along the saddle path. At time t=0, it has a level of capital per

effective worker given by k(0), which is half of the steady state level of capital, k*.

At time t=0 it is learned that the government expenditure changes from 0 to a level G(1)>0,

and that the change will take place for T periods, and back to 0 thereafter.

Show the qualitative dynamics of consumption and capital.

How is T affecting the dynamics?

1.b.- TFP.- Assume that the economy is converging to its long term steady state

along the saddle path. At time t=0, it has a level of capital per effective worker given

by k(0), which is half of the steady state level of capital, k*.

At t=0 it is learned that

total factor productivity drops temporarily from z to z' and that the change will take

place for T periods, and back to z thereafter. Show the qualitative dynamics of

consumption and capital.