Consider a firm that extracts a depletable resource and acts as a monopolist. Assume that production costs are given as (c0 c1 Rt )qt . (Note that is must be that c0 > c1 Rt always, so that costs are strictly positive.)

The firm must also allocate expenditures to the development of domestic infrastructure (such as roads, bridges, hospitals and schools) such that it is indexed to the firm's total production at a cost qt ,where is the marginal cost of the firm's contribution to infrastructure. The quantity of resource remaining at any point in time is equal to the remaining resource from last period minus last period's production, qt , plus new

discoveries, Nt , so that Rt+1= Rt -qt+ Nt . The firm must bear a cost for new discoveries given as c2 N^2 t

Demand is given as pt = a - bqt . Find and interpret the first order conditions for the firm operating in this market.What is the impact of on the firm's production?