#1. (12 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 Q=+22. Assume the marginal cost of extraction in each period is constant, a = . Also, assume a tax, T, is levied on profits in each period. Demand is inverse linear and given as pe = a -l+by+Bpop, where y is income. Assume income grows at a rate p such that y2 = (1+phy and population grows at a rate o such that popa = (1 + a) pop. a. (4 pts) Find expressions for . 2. P and p. b. (4 pts) Solve for expression that explain what happens when (1) p increases, Gil) increases, (ii) Q increases, and (iv) r decreases. Explain what your results indicate. (HINT: This is a comparative statics exercise.)