Consider a two-period model of optimal resource depletion.

Suppose market demand is P = 120-8Q and market supply is P = 40 + 2Q (assume that these represent social benefits and costs). a) State the efficiency condition and calculate the efficient level of consumption and production, Q*, and the associated NB. Calculate P* and verify that CS + PS = NB in this case. b) Illustrate your answers to (@) in a clearly labeled diagram. c) Explain why Q = 5 is not efficient. Illustrate your answer using the diagram from (b ).Consider a two-period model of optimal resource depletion. Suppose that copper deposits are 800 tonnes, demand in each period is Pt = 4000 -10qt, MCt = $600/tonne, and r = 10%. [P is in S/tonne and q is in tonnes]. a) Calculate the efficient extraction path. What are the optimal prices and MUCs? For the remaining parts, suppose that copper deposits are 420 tonnes. b) Set up the Lagrangian for this problem and solve for the efficient extraction path. What is the interpretation of the Lagrange multiplier? c) What are the optimal prices and undiscounted MUCs? What are their growth rates? d) Illustrate your answers to (b) and (c) in a clearly labeled diagram. e) Supposer = 5%. Without recalculating anything, explain what happens to the efficient extraction path. Be sure to clearly explain your reasoning