$2.(3$ points$)$ Consider an economy described by the following production function:

Y $=$ F$($K$,$L$)=$ K$1/4$ L$3/4.$

$($a$)$ Calculate the per$-$worker production function.

$($b$)$ Assuming no population growth or technological progress, find the steady

state level of capital per worker, output per worker, consumption per worker as a function

of the savings and depreciation rates.

$($c$)$ What savings rate maximizes steady state consumption? $[$Hint: Use the Golden

Rule Condition to solve for the Golden Rule Capital Stock and then the steady state

condition to solve for the Golden Rule Savings Rate$]$