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Schweizer Armee Höhere Kaderausbildung der Armee Militärakademie Why External Finance? A Tale of Two Farmers Souvenirs du Caire / 2008-2010 Peter T. Baltes

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2 Schweizer Armee Höhere Kaderausbildung der Armee / Militärakademie Souvenirs du Caire Birmensdorf & Cairo / 2008-2010 PTB Year 1: To farmers, prosperity and ruin may lie close together

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3 Schweizer Armee Höhere Kaderausbildung der Armee / Militärakademie Souvenirs du Caire Birmensdorf & Cairo / 2008-2010 PTB Year 2: Allocating seeds for the new harvest 20406080100 50 100 150 200 250 300 20406080100 50 100 150 200 250 300 expected 1.The production function (x = sacks sown in year 1, E(x) = expected sacks of wheat to be harvested in year 2): 40 2. Farmer 1 has 40 sacks of seed available. 20 3. Due to the bad harvest Farmer 2 has only 20 sacks at his disposal. both Can both farmers be made better off by entering a (sort of) financing contract?

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4 Schweizer Armee Höhere Kaderausbildung der Armee / Militärakademie Souvenirs du Caire Birmensdorf & Cairo / 2008-2010 PTB Diminishing 3.Diminishing marginal product Year 2: The expected marginal product 1.The production function (x = sacks of seed sown, y = sacks of wheat expected to be harvested): marginal 2.The expected marginal product (function): 020406080 2 4 6 8 10 12 14 increases 3a.Each sack of seed sown increases the expected yield. decreasing 3b.However, the contribution of each additional sack sown is decreasing.

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5 Schweizer Armee Höhere Kaderausbildung der Armee / Militärakademie Souvenirs du Caire Birmensdorf & Cairo / 2008-2010 PTB Year 2: The relationship between total output and marginal product 0102030405060 2 4 6 8 10 12 14 102030405060 50 100 150 200 Integrating Integrating the marginal product function results in the original function of total output.

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6 Schweizer Armee Höhere Kaderausbildung der Armee / Militärakademie Souvenirs du Caire Birmensdorf & Cairo / 2008-2010 PTB 6 Year 2: Finding the optimum reallocation combine 4.When the farmers combine their assets, they have in total 60 sacks of seed available.60 0102030405060 5 10 15 20 last all Marginal product of the last sack employed when all sacks are sown on the field of farmer 1. Marginal products development when the corresponding number of sacks are sown exclusively on the field of farmer 1. Development of marginal product when the corresponding number of sacks are sown exclusively on the field of farmer 2. last all Marginal product of the last sack employed when all sacks are sown on the field of farmer 2.

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7 Schweizer Armee Höhere Kaderausbildung der Armee / Militärakademie Souvenirs du Caire Birmensdorf & Cairo / 2008-2010 PTB marginal product much higherfield 2 Reason behind this recommendation: The 60th sack marginal product is much higher when sown on field 2. Thus, the sack should be reallocated to field 2. Year 2: Finding the optimum reallocation combine 4. When the farmers combine their assets, they have in total 60 sacks of seed available. 0102030405060 5 10 15 20 All Starting point: All 60 sacks are sown on the field of Farmer 1. not but Alternative proposal: The 60th sack should not be sown on field 1, but on field 2. 1 2

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8 Schweizer Armee Höhere Kaderausbildung der Armee / Militärakademie Souvenirs du Caire Birmensdorf & Cairo / 2008-2010 PTB Year 2: Finding the optimum reallocation combine 4.If they combine their assets, the two farmers have 60 sacks of seed available. 0102030405060 5 10 15 20 analogy In analogy to the reasoning for the 60th sack, the 59th and the 58th should be sown on field 2. shifting stops equals The shifting of sacks from employment on field 1 to field 2 stops when the marginal product of sowing on field 2 equals the marginal product of sowing on field 1. 1 2 30 sacks

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9 Schweizer Armee Höhere Kaderausbildung der Armee / Militärakademie Souvenirs du Caire Birmensdorf & Cairo / 2008-2010 PTB Year 2: Finding the optimum reallocation 5.An alternative perspective: Total output. 0102030405060 100 200 300 400 A possible misunderstanding? In the constellation here investigated, the two farmers should divide up the total amount of sacks available into equal shares. Reason: By assumption they share the same production function. In contrast, when one of the farmers is more productive, the optimal allocation should then favor him accordingly with a higher share.

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10 Schweizer Armee Höhere Kaderausbildung der Armee / Militärakademie Souvenirs du Caire Birmensdorf & Cairo / 2008-2010 PTB Year 2: Recommendation to reallocate the seed 20406080100 50 100 150 200 250 300 20406080100 50 100 150 200 250 300 40 Farmer 1 has 40 sacks of seed available. 20 Farmer 2 has 20 sacks only at his disposal. both How can both of them be made better off? 10 sacks In order to maximize total output, Farmer 1 should transfer some 10 sacks of seed to Farmer 2.

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11 Schweizer Armee Höhere Kaderausbildung der Armee / Militärakademie Souvenirs du Caire Birmensdorf & Cairo / 2008-2010 PTB Year 2: Determining the conditions of reallocation Farmer 1all 40 sacks If Farmer 1 keeps all 40 sacks to himself, he can expect to harvest: 10 sacksFarmer 2 If Farmer 1 transfers 10 sacks to Farmer 2, he is still able to harvest by sowing the remaining 30 sacks (on average): attractiveat least Thus, in order to make the transfer attractive to Farmer 1, he must at least be compensated by:

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12 Schweizer Armee Höhere Kaderausbildung der Armee / Militärakademie Souvenirs du Caire Birmensdorf & Cairo / 2008-2010 PTB Year 2: Determining the conditions of reallocation own20 If Farmer 2 only sows his own 20 sacks, he can expect to harvest in year 2: receiving 10 additional sacks By receiving 10 additional sacks from Farmer 1 in year 1, for Farmer 2 the total output in year 2 is expected to increase to: increases Thus, in comparison to a situation without support by Farmer 1, Farmer 2 increases his expected output by: additional yield After paying at least 25.42 sacks to farmer 1 in year 2 (as a compensation for receiving 10 sacks in year 1), Farmer 2 expects to keep hold of an additional yield of:

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13 Schweizer Armee Höhere Kaderausbildung der Armee / Militärakademie Souvenirs du Caire Birmensdorf & Cairo / 2008-2010 PTB Conclusion both Thus, we have shown how – when external sources are employed to support investment projects – both sides … opportunity cost Because financiers could always use their assets in their own projects instead of supporting external projects, they must be compensated for providing resources (opportunity cost). FinancierFarmer 1 = party A: The external source = Financier investorFarmer 2 = party B: The original investor … can be made better off.

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14 Schweizer Armee Höhere Kaderausbildung der Armee / Militärakademie Souvenirs du Caire Birmensdorf & Cairo / 2008-2010 PTB Conclusion basic types Two basic types of compensation: Equity Capital Contract version A: The financier becomes a partner in investment. By this she / he acquires a claim on the projects surplus proportional to his / her share of investment. Equity Capital Debt Capital Contract version B: The financier is compensated by an ex ante determined fixed amount (exception: case of bankruptcy). No further claims beyond this level of compensation do exist. Debt Capital

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15 Schweizer Armee Höhere Kaderausbildung der Armee / Militärakademie Souvenirs du Caire Birmensdorf & Cairo / 2008-2010 PTB Questions? Hints or Critique? Contact: peter.baltes.bp ad vtg.admin.ch Feedback Flaws? Many thanks to: Odilo Gwerder, Daniel Lätsch and Maximilian Zangger

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16 Schweizer Armee Höhere Kaderausbildung der Armee / Militärakademie Souvenirs du Caire Birmensdorf & Cairo / 2008-2010 PTB Year 2 (Allocating seeds for the new harvest) – Hyperlink (refer to slide No 6) 20406080100 50 100 150 200 250 300 20406080100 50 100 150 200 250 300 1.The production function (x = sacks of seed sown, y = sacks of wheat to be harvested next year): 40 2. Farmer 1 has 40 sacks of seed available. 20 3. Due to the bad harvest Farmer 2 has only 20 sacks at his disposal.

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