(4 pts) The sale and export of ivory from African elephant tusks is illegal under CITES. Nevertheless, there is a black market for ivory. Suppose the annual demand per unit of ivory is given by Qtd=abPt where a=1000 (in tons) and b=1. The annual supply is an upward function of price such that QtS=1000XtPt where Xt is the stock of wild African elephants. Assume that X0=1,500. The reproduction of elephants is such that the stock evolves according to Xt+1=Xt+XtQt with =0.15, which is the growth rate of elephants. Here the variable Qt signifies the market quantity of ivory extracted from one elephant. a. Use the information to fill in the following table. (1 pt) b. Using a supply and demand graph, show what the market for poached ivory looks like in periods t=0,t=1 and t=2. (1pt) c. Suppose the government of Tanzania has 900 tons of ivory stockpiled. It is allowed to sell an annual quota of its ivory stockpile in each time period equal to Q=300 on t=0,t=1 and t=2. Recalculate the prices, quantities, and stock by filling in the table below. (Assume that stockpiled ivory is a perfect substitute for poached ivory. )(0.5pt) (4 pts) The sale and export of ivory from African elephant tusks is illegal under CITES. Nevertheless, there is a black market for ivory. Suppose the annual demand per unit of ivory is given by Qtd=abPt where a=1000 (in tons) and b=1. The annual supply is an upward function of price such that QtS=1000XtPt where Xt is the stock of wild African elephants. Assume that X0=1,500. The reproduction of elephants is such that the stock evolves according to Xt+1=Xt+XtQt with =0.15, which is the growth rate of elephants. Here the variable Qt signifies the market quantity of ivory extracted from one elephant. a. Use the information to fill in the following table. (1 pt) b. Using a supply and demand graph, show what the market for poached ivory looks like in periods t=0,t=1 and t=2. (1pt) c. Suppose the government of Tanzania has 900 tons of ivory stockpiled. It is allowed to sell an annual quota of its ivory stockpile in each time period equal to Q=300 on t=0,t=1 and t=2. Recalculate the prices, quantities, and stock by filling in the table below. (Assume that stockpiled ivory is a perfect substitute for poached ivory. )(0.5pt)