Accompanying this problem is a spreadsheet called Excel problem set 1 - renewables The first columns A through G are identical to the spreadsheet we have been using in class. This will be the "base case by which we compare subsequent results. Next to these calculations, starting in column I are four additional sets. In each case we are changing a parameter in our competitive model of resource extraction: a. Here we are reducing the choke price from 6 to 2, implying a more competitive substitute have become available. b. Here we are increasing the steepness of the inverse demand curve, implying that consumers are more sensitive to price changes. c. Here we are increasing the starting Stock level from 40 to 50, perhaps due to new discoveries. d. Here we are decreasing the discount rate. For each case: 1. Use Excel and first set of columns of the spreadsheet to fill in each of the 4 cases' cells (for example, fill in columns J through O for part a, etc.) 2. Calibrate the model by adjusting the value of lamda results in a case where the "sum of q' cell equals (get as close as you can to) the available stock level S. Analyze the results in each case by comparing your results with the base case by addressing: The length of mining activity t ii. The extraction levels and path, qt iii. The price levels and path, Rt iv. The value of lamda In your analysis, recall we are dealing with a competitive extraction market. So make sure you analysis involve ECONOMIC rationales for the changes in price, output and cost patterns (i.e. don't just say that qt is lower rather explain WHY it's lower) 4. In Excel, create 4 different charts that plot the extraction paths (at) for each change 2a, 2b, 2c, and 2d. On each chart, plot both the new qt and the original qt as provided for you in column c. E F H K L N P R S T V X Z AA AB AC AD AE AF AH AL AJ AK AL AM 1 a lamda lamda AG d lamda 2 lamda a 6 B D Base case competitive market lamda 279833 true lamda 279833 6 b 0.4 S 40 0.1 sum of a 40.00036 b S 2 0.4 40 0.1 0 b S b S 4 5 6 7 8 b S 6 0.4 50 0.1 0 40 0.1 0 6 0.4 40 0.01 0 sum of a sum of a sum of a sum of a Hotelling 96 at' St St Hotelling 96 at St st" t 0 Hotelling at qt St St" pt' Hotelling at qt' St St pt" Hotelling 0 7.305 1 2 3 0 1 2 3 Z 3 9 10 11 12 13 14 15 16 17 18 19 4 5 6 4 5 t 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 75 16 17 20 21 22 23 24 4 5 6 7 A 9 10 11 12 13 14 15 16 17 18 19 7 A 9 10 11 17 13 14 15 16 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0. 0.0003 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 gt 8.004 7.305 6.535 5.689 4.757 3.733 2.606 1.367 0.004 -1496 -3.145 -4.960 -6.956 -9.151 - 11.567 -14.223 -17.146 -20.360 -23.896 -27.786 -32.064 -36.771 -41.948 -47.643 -53.907 -60.798 -68.377 -76.715 -85.887 -95.975 -107.073 - 119.280 - 132.708 -147.479 -163.727 -181.600 -201.260 -222.886 -246.674 -272.842 -301.626 -333.288 -368.117 -406.429 -448.572 -494.929 -545.922 -602.014 -663.716 -731.587 -806.246 at" St St 8.004 31.996 31.996 24.691 24.691 6.535 18.156 18.156 5.689 12.468 12.468 4.757 7.710 7.710 3.733 3.977 3.977 2.606 1371 1.371 1.367 0.003 0.003 0.004 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.0000.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 #VALUE! #VALUE! 2.798 3.078 3.386 3.725 4.097 4.507 4.957 5.453 5.998 6.000 6.000 6.000 6.000 6.000 6.000 6.000 6.000 6.000 6.000 6.000 6.000 6.000 6.000 6.000 6.000 6.000 6.000 6.000 6.000 6.000 6.000 6.000 6.000 6.000 6.000 6.000 6.000 6.000 6.000 6.000 6.000 6.000 6.000 6.000 6.000 6.000 6.000 6.000 6.000 6.000 6.000 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 19 20 21 22 23 24 25 26 27 28 29 21 22 23 24 25 26 27 28 29 30 31 32 33 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 0 0 0 0 0 0 0 0 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 0 0 0 0 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 0 40 41 42 43 44 45 46 47 48 49 50 0 0 0 11 Accompanying this problem is a spreadsheet called Excel problem set 1 - renewables The first columns A through G are identical to the spreadsheet we have been using in class. This will be the "base case by which we compare subsequent results. Next to these calculations, starting in column I are four additional sets. In each case we are changing a parameter in our competitive model of resource extraction: a. Here we are reducing the choke price from 6 to 2, implying a more competitive substitute have become available. b. Here we are increasing the steepness of the inverse demand curve, implying that consumers are more sensitive to price changes. c. Here we are increasing the starting Stock level from 40 to 50, perhaps due to new discoveries. d. Here we are decreasing the discount rate. For each case: 1. Use Excel and first set of columns of the spreadsheet to fill in each of the 4 cases' cells (for example, fill in columns J through O for part a, etc.) 2. Calibrate the model by adjusting the value of lamda results in a case where the "sum of q' cell equals (get as close as you can to) the available stock level S. Analyze the results in each case by comparing your results with the base case by addressing: The length of mining activity t ii. The extraction levels and path, qt iii. The price levels and path, Rt iv. The value of lamda In your analysis, recall we are dealing with a competitive extraction market. So make sure you analysis involve ECONOMIC rationales for the changes in price, output and cost patterns (i.e. don't just say that qt is lower rather explain WHY it's lower) 4. In Excel, create 4 different charts that plot the extraction paths (at) for each change 2a, 2b, 2c, and 2d. On each chart, plot both the new qt and the original qt as provided for you in column c. E F H K L N P R S T V X Z AA AB AC AD AE AF AH AL AJ AK AL AM 1 a lamda lamda AG d lamda 2 lamda a 6 B D Base case competitive market lamda 279833 true lamda 279833 6 b 0.4 S 40 0.1 sum of a 40.00036 b S 2 0.4 40 0.1 0 b S b S 4 5 6 7 8 b S 6 0.4 50 0.1 0 40 0.1 0 6 0.4 40 0.01 0 sum of a sum of a sum of a sum of a Hotelling 96 at' St St Hotelling 96 at St st" t 0 Hotelling at qt St St" pt' Hotelling at qt' St St pt" Hotelling 0 7.305 1 2 3 0 1 2 3 Z 3 9 10 11 12 13 14 15 16 17 18 19 4 5 6 4 5 t 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 75 16 17 20 21 22 23 24 4 5 6 7 A 9 10 11 12 13 14 15 16 17 18 19 7 A 9 10 11 17 13 14 15 16 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0. 0.0003 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 gt 8.004 7.305 6.535 5.689 4.757 3.733 2.606 1.367 0.004 -1496 -3.145 -4.960 -6.956 -9.151 - 11.567 -14.223 -17.146 -20.360 -23.896 -27.786 -32.064 -36.771 -41.948 -47.643 -53.907 -60.798 -68.377 -76.715 -85.887 -95.975 -107.073 - 119.280 - 132.708 -147.479 -163.727 -181.600 -201.260 -222.886 -246.674 -272.842 -301.626 -333.288 -368.117 -406.429 -448.572 -494.929 -545.922 -602.014 -663.716 -731.587 -806.246 at" St St 8.004 31.996 31.996 24.691 24.691 6.535 18.156 18.156 5.689 12.468 12.468 4.757 7.710 7.710 3.733 3.977 3.977 2.606 1371 1.371 1.367 0.003 0.003 0.004 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.0000.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 #VALUE! #VALUE! 2.798 3.078 3.386 3.725 4.097 4.507 4.957 5.453 5.998 6.000 6.000 6.000 6.000 6.000 6.000 6.000 6.000 6.000 6.000 6.000 6.000 6.000 6.000 6.000 6.000 6.000 6.000 6.000 6.000 6.000 6.000 6.000 6.000 6.000 6.000 6.000 6.000 6.000 6.000 6.000 6.000 6.000 6.000 6.000 6.000 6.000 6.000 6.000 6.000 6.000 6.000 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 19 20 21 22 23 24 25 26 27 28 29 21 22 23 24 25 26 27 28 29 30 31 32 33 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 0 0 0 0 0 0 0 0 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 0 0 0 0 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 0 40 41 42 43 44 45 46 47 48 49 50 0 0 0 11