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

(a) Find the value of the mine (not a 10 -year lease) if the current deposit is $x_{0}$. In particular, how much is the mine worth initially when $x_{0}=50,000$ ounces? [Consider the recursive equation for $K_{k}$ as $k \rightarrow \infty$.]

(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?