2. Consider an economy in which output, Y(f), is produced according to the production function Y (t) = K(t)" A(t)] -, (4) where 0 0 and let the level of technology, A(t), grow over time according to A (t ) = gA (t) , (7) g > n >0. 2.1. Using equations (4)-(7), derive the growth rate for output-per- worker on a balanced growth path. Would government policy be able to influence long-run growth in this economy? Show your work- ing. [25%] 2.2. Suppose the economy is on a balanced growth path when at date to the government implements a policy that permanently increases the saving rate from s to s'. Use three separate figures to characterize the paths that output, output-per-worker, and growth in output-per- worker follow over time as the economy adjusts back to a balanced growth path. Explain your figures. [25%]