#1. (15 points) Consider a simple two period model of production of a depletable resource. The sum of production in each period is equal to the total resource endowment, or a = qr1 + q,. Assume the marginal cost of extraction in each period is constant, c, = F . Also, assume a tax, I , is levied on prots in each period. Demand is inverse linear and given as p, = a bq, + 5y, + 6,0019r , where y is income. Assume income grows at a rate p such that y2 = (1+ p) )21 and population grows at a rate 0' such that pop2 = (1+ 0')p0p1. a. (5 pts) Find expressions for qr1 , qz, p1 and p2 . b. (5 pts) Solve for expressions that explain what happens when (i) p decreases, (ii) a increases, (iii) 5 increases, and (iv) r increases. Explain what your results indicate