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Base effort Optimized effort 10.91 Los Angeles 5.00 % change in effort 118.2% 56.2% 119.7% Optimized net margin 3043 % change in margin 41.4% San Francisco 4.00 Base net margin 2 153 1 371 6.25 Los Angeles San Francisco Seattle 3.00 6.59 1 512 10.3% 45.7% Seattle 2 605 3796 4.00 7.42 85.6% 2 724 3 687 35.3% 5.00 8.12 62.4% 1 637 1 851 13.1% Boston Philadelphia Cleveland Atlanta Nashville 4.00 7.73 93.2% 2 653 4030 51.9% 3.00 7.39 146.5% Boston Philadelphia Cleveland Atlanta Nashville High Point 1 716 3 003 3.00 5.94 98.0% 75.0% 37.5% 1 937 2 662 4.00 6.07 51.8% 915 1 291 41.1% High Point Dallas 3.00 7.15 138,4% Dallas 1 439 2 235 55.3% Chicago 5.00 7.35 46.9% Chicago 3 157 3782 19.8% Cincinnati 3.00 6.18 Cincinnati 2 288 2 790 106.1% % 69.7% 21.9% 29.1% St. Louis 3.00 5.09 St. Louis 1 504 1 941 3.00 67.2% Twin Cities 2 629 2973 13.1% Twin Cities Total 5.02 97.22 52.00 87.0% Total 28 728 38 597 34.4% Comparison of effort in unconstrained optimization, Comparison of net margin in unconstrained optimization Los Angeles San Francisco Seattle Current number of reps Current sales (5000) Cost per sales rep (5000) Margin Cost of effort 5.00 8 250 147.00 0.35 735 4.00 5 598 147.00 0.35 588 3.00 8 703 147.00 0.35 441 4.00 9464 147.00 0.35 588 Gross margin Net margin 2 888 2 153 1959 1371 3 046 2605 3 312 2 724 5.00 6777 147.00 0.35 735 2 372 1 637 4.00 9 260 147.00 0.35 588 3 241 2653 Boston Philadelphia Cleveland Atlanta Nashville High Point Dallas 3.00 6 163 147.00 0.35 441 2157 1 716 3.00 6 793 147.00 0.35 441 2 378 1937 4.00 4 294 147.00 0.35 588 1 503 915 3.00 5372 147.00 0.35 441 1 880 1439 Chicago 5.00 11 119 147.00 0.35 735 3892 3157 Cincinnati 3.00 147.00 0.35 441 2 729 2 288 St. Louis 3.00 7798 5 557 8 772 147.00 0.35 441 1 945 1 504 Twin Cities 3.00 147.00 0.35 441 3070 2629 Total 52.00 103 920 7 644 36 372 28 728 Base scenario table, Question 1: Public debt sustainability Consider two different countries, A and B. They are very similar, given that they share lots of characteristics, as: - the growth rate of GDP between t and t+1, equal to 2%, - the interest rate in t and t+1, constant and equal to 2% - the tax-to-GDP ratio, constant and equal to 0.1. Moreover, they display also the same: - initial GDP, i.e. Yat = Ype = 100 - previous level of debt, Bat-1 = BBt-1 = 50. They differ only regarding the composition of their population: - in year t, both countries have an old population-to-total population ratio equals to art = apt = 0.2 - in year t+1 these ratios are anc+1 = 0.8 for country A and Bt+1 = 0.2 for country B. Some studies have shown that the total public expenditure depends positively on the portion of old people living in a country; assume for simplicity that Git = air Yit and it is valid in any country I in any period. Find the level of public debt att and t+1 for both country A and country B, and then compare their growth rates