$($Complexico mine$)$ Consider the Complexico mine and assume a $10\%$ constant interest rate; also assume the price of gold is constant at $$400/$oz

$($a$)$ Find the value of the mine $($not a $10-$year lease$)$ if the current deposit is

xo$.$ In particular, how much is the mine worth initially when xo $=50,000$ ounces? $[$Hint: Consider the recursive equation for nk as k $->\backslash$infty $.]$

$($b$)$ For the $10-$year lease considered in the text, how much gold remains in

the mine at the end of the lease; and how much is the mine worth at that time?

$($c$)$ If the mine were not leased, but instead operated optimally by an owner,

what would the mine be worth after$10$ years?