suppose that you have the standard Solow model with both labor augmenting productivity growth and population growth. The production function is Cobb-Douglas. The law of motion of capital per efficiency unit of labor is given by

k = 1 [sAk +(1)k]. t+1 (1+z)(1+n) t t

(a) Suppose that the economy initially sits in the steady state. Suppose that at time t there is a surprise increase in z that is expected to last forever. Draw a graph of the law of

motion of capital and show how the change in z will impact the steady state capital stock per efficiency unit of labor.

• (b)Draw a graph of how the capital stock per efficiency unit of labor reacts over time to the increase in z.
• (c)Draw a graph of how consumption per efficiency unit of labor reacts over time to the increase in z.
• (d)Draw a graph of how output per efficiency unit of labor reacts over time to the increase in z.
• (e)Do you think households in the model are better or worse off with the new, higher
• growth rate of labor augmenting productivity z? How does your response relate to the new steady state values of capital, output, and consumption per efficiency unit of labor?