Sample Answers

Answer: The profit of the first period must be equal to the present value of thep2− 2profit of the second period: p1− 2 =1+1 34 84 2p1− + 2 = p2thus p2= p1−3 33 3(b) By using the resource constraint, 10 = q 1 + q 2 , find the first and secondprices.Answer: From the demand function, we have4 2 32 4q1 = 10 − p 1and q2= 10 − ( p1− ) = − p1.3 3 3 3Because that the total amount is 10, we have32 410 = q1+ q2= 10 − p1+ − p13 37 323p = 1332p1= = 4. 57 .7And4 2 4 32 2 38p2= p1− − = − = = 5.43 .3 3 3 7 3 7Thus,32 3838 32q1= 10 − = = 5.43 and q2= 10 − = = 4. 57 .7 77 7(c) What is the total profit in the present value?Answer: The profit in each period is32 38 18x38684π1= p1q1− MC q1= ( − 2) = = = 13.967 7 49 49and38 32 24x32768π2= p2q2− MC q2= ( − 2) = = = 15.67 .7 7 49 49Thus, the total profit is684 768 1 1260π1+ π2= + × = = 25.71.49 49 1+1/ 3 49This is smaller than the profit in the unlimited total amount case in Q2-1. Thus,it is more profitable for the mine firm to charge the monopoly price in eachperiod and extact only 8 units, instead of 10 units.2