Why External Finance? A Tale of Two Farmers

1. Why External Finance?A Tale of Two Farmers Souvenirs du Caire / 2008-2010 Peter T. Baltes

2. Year 1: To farmers, prosperity and ruin may lie close together

3. 300 300 250 250 200 200 150 150 100 100 50 50 20 20 40 40 60 60 80 80 100 100 Year 2: Allocating seeds for the new harvest 1. The production function(x = sacks sown in year 1, E(x) = expected sacks of wheat to be harvested in year 2): 2. Farmer 1 has 40 sacks of seed available. 3. Due to the bad harvest Farmer 2 has only 20 sacks at his disposal. Can both farmers be made better off by entering a (sort of) “financing contract”?

4. 14 12 10 8 6 4 2 0 20 40 60 80 Year 2: The expected marginal product 1. The production function (x = sacks of seed sown, y = sacks of wheat expected to be harvested): 2. The expected marginal product (function): 3. Diminishing marginal product 3a. Each sack of seed sown increases the expected yield. 3b. However, the contribution of each additional sack sown is decreasing.

5. 200 14 150 12 10 100 8 50 6 4 10 20 30 40 50 60 2 0 10 20 30 40 50 60 Year 2: The relationship between total output and marginal product Integratingthe marginal product functionresults in the original functionof total output.

6. 20 15 10 5 0 10 20 30 40 50 60 Year 2: Finding the optimum reallocation 4. When the farmers combine their assets, they have in total 60 sacks of seed available. Development of marginal product when the corresponding number of sacks are sown exclusively on the field of farmer 2. Marginal product’s development when the corresponding number of sacks are sown exclusively on the field of farmer 1. Marginal product of the last sack employed when all sacks are sown on the field of farmer 2. Marginal product of the last sack employed when all sacks are sown on the field of farmer 1. 6

7. 20 15 10 5 0 10 20 30 40 50 60 Year 2: Finding the optimum reallocation 4. When the farmers combine their assets, they have in total 60 sacks of seed available. Starting point:All 60 sacks are sown on the field of Farmer 1. Alternative proposal:The 60th sack should not be sown on field 1, but on field 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. 1 2

8. 20 15 10 5 0 10 20 30 40 50 60 Year 2: Finding the optimum reallocation 4. If they combine their assets, the two farmers have 60 sacks of seed available. The shifting of sacks from employmenton field 1 to field 2 stops when themarginal product of sowing on field 2equals the marginal productof sowing on field 1. In analogy to the reasoning forthe 60th sack, the 59th and the58th should be sown on field 2. 30 sacks 1 2 30 sacks

9. 400 300 200 100 0 10 20 30 40 50 60 Year 2: Finding the optimum reallocation 5. An alternative perspective: Total output. 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.

10. 300 300 250 250 200 200 150 150 100 100 50 50 20 20 40 40 60 60 80 80 100 100 Year 2: Recommendation to reallocate the seed Farmer 1 has 40 sacks of seed available. Farmer 2 has 20 sacks only at his disposal. How can both of them be made better off? In order to maximize total output, Farmer 1 should transfer some 10 sacks of seed to Farmer 2.

11. Year 2: Determining the conditions of reallocation If Farmer 1 keeps all 40 sacks to himself, he can expect to harvest: If Farmer 1 transfers 10 sacks to Farmer 2, he is still able to harvest by sowing the remaining 30 sacks (on average): Thus, in order to make the transfer attractive to Farmer 1, he must at least be compensated by:

12. Year 2: Determining the conditions of reallocation If Farmer 2 only sows his own20 sacks, he can expect to harvest in year 2: 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: Thus, in comparison to a situation without support by Farmer 1, Farmer 2 increases his expected output by: 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:

13. Conclusion Thus, we have shown how – when external sources are employed to “support” investment projects – both sides … • Farmer 1 = party A: “The external source” = Financier • Farmer 2 = party B: “The original investor” … can be made better off. 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).

14. Conclusion Two basic types of compensation: Contract version A: The financier becomes a “partner in investment”. By this she / he acquires a claim on the project’s surplus proportional to his / her share of investment. Equity 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

15. Feedback Many thanks to:Odilo Gwerder, Daniel Lätsch and Maximilian Zangger Questions? Flaws? Hints or Critique? Contact: peter.baltes.bp “ad” vtg.admin.ch

16. 300 300 250 250 200 200 150 150 100 100 50 50 20 20 40 40 60 60 80 80 100 100 Year 2 (Allocating seeds for the new harvest) – Hyperlink (refer to slide No 6) 1. The production function (x = sacks of seed sown, y = sacks of wheat to be harvested next year): 2. Farmer 1 has 40 sacks of seed available. 3. Due to the bad harvest Farmer 2 has only 20 sacks at his disposal.