1. Suppose that you have a standard Solow model with a Cobb-Douglas production function and both labor augmenting productivity growth and population

growth. The central equation of the model is:

kt+1 = (1/((1 + z)(1 + n)))[s(kt)^() + (1 )kt].

(a) Suppose that the economy initially sits in a steady state. Suppose that

at time t there is a surprise increase in z that is expected to last forever.

Use the main diagram to show how this will impact the steady state

capital stock per efficiency unit of labor.

(b) Plot out a diagram showing how the capital stock per efficiency unit of

labor ought to react dynamically to the surprise increase in z.

(c) Plot out diagrams showing how consumption and output per efficiency

unit of labor will react in a dynamic sense to the surprise increase in z.

(d) Do you think agents in the model are better o or worse o with a higher

z? How does your answer square with what happens to the steady state

values of capital, output, and consumption per efficiency unit of labor?

How can you reconcile these findings with one another?