Please help with the Solow-Swan calculator question in question 5. and 6. if possible please. I have included a picture of the example graph that question 6 mentions and the link to the Madison Database data needed for question 6. Thank you!
5. We will new build a SolowSwan calculator using the Euler algorithm discussed in lecture. An example of my Excel versiOn of this calCulator is shown below. Yen can use your preferred platform (e.g., Python, Matlab, Octave, Mathematica, etc.), but the steps presented below will given in terms of Excel. .8 8 C D E F G H .I K I. M N 1 z kappa' kappa[t) BaP{tl Balanced Actual ' 2.0 so 11 i a 1.5 35 1' 30 a E 1.0 g 25 10 E g 11 E 0.5 :520 1' 8 5T15 13 a 0.0 11 10 15 16 415 5 1? 18 ~1.0 0 19 -10 10 20 30 40 50 -10 0 10 20 TIME {years} TIME (years: 21 22 23 shack-a 2 1 1 l 1 1 1 21 yrs-shock 111 (103 0.02 one (13 initial mm 5 some] :5 tin: swing rm LE g_L delta alpha w W1] we: gaps) Em summed Actud 25 -10 0.1 0.03 0.02 0.08 0.3 0.68? 0.68? 0.0!!) 0.0:!!! 5.00 4.4682 4.4682 2? -9 0.1 0.03 0.02 0.08 0.3 0.68? 0.68? 0.000 0.00011 5.15 4.6043 4.6043 23 -s 0.1 0.03 0.02 0.08 0.3 0.68? 0.68? 0.0m 0.0000 5.31 43445 4.1445 29 -? 0.1 0.03 0.02 0.1! 0.3 0.68? 0.68? 0.01] 0.0000 5.4? 4.8890 4.8890 an -6 0.1 0.03 0.02 0.\" 0.3 0.68? 0.68? 0.11\" 0.0000 5.64 50379 5.031'9 31 -5 01 0.03 0.02 one 03 0.68? 0.68? 0.013 0.0000 5.81 5.1914 5.1914 32 -4 0.1 0.03 0.02 0.08 0.3 0.68? 0.68? 0.003 0.0000 5.99 5.3495 5.3495 33 -3 0.1 0.03 0.02 0.08 0.3 0.68? 0.68? none 0.0001: 6.1? 5.5124 5.5124 34 -2 0.1 0.03 0.02 0.08 0.3 0.68? 0.68? 0.1113 coma 6.36 5.6803 5.6803 35 -1 0.1 0.03 0.02 0.13 0.3 0.68? 0.68? 0.01) 0.0000 6.55 5.8532 5.8532 36 0 0.2 0.03 0.02 0.1! 0.3 1.850 0.68? 0.089 -0.?692 6.?5 8.11?8 6.0315 3? 1 0.2 0.03 0.02 0.\" 0.3 1.850 0.??? 0.084 -0.?CIJ5 6.95 8.3650 6.44?3 311 2 0.2 0.03 0.02 can 0.3 1.850 0.861 0.0?9 -0.63?8 ?.1? 86198 6.8525 39 3 0.2 0.03 0.02 0.13 0.3 1.850 0.940 0.0?4 c.5305 ?.38 8.8823 ?.2502 o In column A, create a time range running from -10 to 50 in steps of l. o In column B, create the saving rate, 3, as a function of time: To include a shock at t = 0, put the pre-shock value for s of 0.1 in cell B24. Set cell B26 equal to cell B24. For cells B2? to B86 set the value in each row to be equal to the value in the previous row (e.g., the equation in cell B27 is = B26). We introduce a shock at t = 0 by (i) adding a shock multiplier (the value of 2 in this case) in cell B23 and then (ii) multiplying the value in cell B36 by it: i.e., the equation in cell B36 is = B35 a: B23. At this point your values for the saving rate should look like those in the gure above. To verify that this is working, if you (i) change the value in cell B23 to 1 then all of the saving rates should be 0.1 and (ii) if you change the value in cell B3 to 3 then all saving rates before t = 0 should be 0.1 and the rest should be 0.3. 0 COpy cells B23 to B86 into columns C, D, E, and F, and change the pre-shock values in row 24 and the column headings in row 25 as shown in the gure above. 0 Populate cells G26 to G86 with values of 5* s m It: 2 h: (9E+9L+5) [8) using the value of the variables in each row. Note how the shock to 3 changes 5' at t = 0 c To initialize and evolve am: Set the initial condition 5(t = 10) = a\" in cell H26 and in cell 126 put the result of dn _ a J (itSK: (93+9L+ )5 with the time derivative calculated using values at t = 10. Evolve ah?) with the Euler algorithm (in n(t+ At) = 5(1'?) + X dt dt with the equation in cell H27 of =H26+I26*1. for our time step of 1 year. Calculate ds/dt in cell 127 in the same way that you calculated the value in cell I26. Complete the evolution for all times by copying the equations in cells H27 and 127 into all cells below to cells H86 and I86. 0 Calculate the gap in column J using the values for 5*, 5.05), and o: in columns G, H, and F. Note how the economic is initially in steady state (gap = D), has a negative gap in response to the shock at t = 0, and how the gap relaxes after the shock as a result of 5(t) moving toward 5' for t > 0. 0 Calculate EU) in column K in a manner similar to the way that you set up the saving rate. First enter the shock, column heading and initial value in cells K23 to K26. Then model the evolution of E(t) in cells K27 though K86 using: E(9) = E(1o)e9E' with, for example, the value in cell K27 given by = K26 a: EXP(026 * 1) and similarly for the remaining cells in column K. a Add the ability to incorporate the shock to E(t) at t = 0 with the equation =K35*EXP (C35*1) *K23 in cell K36. o The shock to E(t) at t = 0 will also impact a(t). In addition, a shock to K(t)/L(t) at t = 0 will also impact 5(t). We will incorporate the shocks to E(0) and K(0)/L(O) through the use of factors that we will refer to as g and fm, respec- tively. At t = 0 we have that \"(ii = 333%) = () (%) into which we can introduce the shock factors as follows \"(13) _,. (W) (fir/L >K.(t) >
