Schweizer Armee Höhere Kaderausbildung der Armee Militärakademie Why External Finance? A Tale of...

Schweizer ArmeeHöhere Kaderausbildung der ArmeeMilitärakademie

Why External Finance?A Tale of Two Farmers

Souvenirs du Caire / 2008-2010

Peter T. Baltes

2Schweizer ArmeeHöhere Kaderausbildung der Armee / Militärakademie

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Birmensdorf & Cairo / 2008-2010PTB

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


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Year 2: Allocating seeds for the new harvest

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1. The production function(x = sacks sown in year 1, E(x) = expectedexpected sacks of wheat to be harvested in year 2):

2. Farmer 1 has 4040 sacks of seed available.

3. Due to the bad harvest Farmer 2 has only 2020 sacks at his disposal.

Can bothboth farmers be made better off by entering a (sort of) “financing contract”?


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3. DiminishingDiminishing 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):

2. The expected marginalmarginal product (function):

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3a. Each sack of seed sown increasesincreases the expected yield.

3b. However, the contribution of each additional sack sown is decreasingdecreasing.


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Year 2: The relationship between total output and marginal product

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200IntegratingIntegratingthe marginal product functionresults in the original functionof total output.


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Birmensdorf & Cairo / 2008-2010PTB 6

Year 2: Finding the optimum reallocation

4. When the farmers combinecombine their assets, they have in total 60 sacks of seed available.

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Marginal product of the lastlast sack employed when allall sacks are sown on the field of farmer 1.

Marginal product’s 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.

Marginal product of the lastlast sack employed when allall sacks are sown on the field of farmer 2.


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Reason behind this recommendation:The 60th sack’ marginal productmarginal product is much highermuch higher when sown on field 2field 2. Thus, the sack should be reallocated to field 2.


4. When the farmers combinecombine their assets, they have in total 60 sacks of seed available.

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20Starting point:AllAll 60 sacks are sown on the field of Farmer 1.

Alternative proposal:The 60th sack should notnot be sown on field 1, butbut on field 2.

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4. If they combinecombine their assets, the two farmers have 60 sacks of seed available.

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In analogyanalogy to the reasoning forthe 60th sack, the 59th and the58th should be sown on field 2.

The shiftingshifting of sacks from employmenton field 1 to field 2 stopsstops when themarginal product of sowing on field 2equalsequals the marginal productof sowing on field 1.

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30 sacks

30 sacks


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5. An alternative perspective: Total output.

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400A 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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Year 2: Recommendation to reallocate the seed

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Farmer 1 has 4040 sacks of seed available.

Farmer 2 has 2020 sacks only at his disposal.

How can bothboth of them be made better off?

In order to maximize total output, Farmer 1 should transfer some 10 sacks10 sacks of seed to Farmer 2.


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Year 2: Determining the conditions of reallocation

If Farmer 1Farmer 1 keeps all 40 sacksall 40 sacks to himself, he can expect to harvest:

If Farmer 1 transfers 10 sacks10 sacks to Farmer 2Farmer 2, he is still able to harvest by sowing the remaining 30 sacks (on average):

Thus, in order to make the transfer attractiveattractive to Farmer 1, he must at leastat least be compensated by:


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Year 2: Determining the conditions of reallocation

If Farmer 2 only sows his ownown 2020 sacks, he can expect to harvest in year 2:

By receiving 10 additional sacksreceiving 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 increasesincreases 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 yieldadditional yield of:


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Conclusion

Thus, we have shown how – when external sources are employed to “support” investment projects – bothboth sides …

Because financiers could always use their assets in their own projects instead of supporting external projects, they must be compensated for providing resources (opportunity costopportunity cost).

• Farmer 1 = party A: “The external source” = FinancierFinancier

• Farmer 2 = party B: “The original investorinvestor”… can be made better off.


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Conclusion

Two basic typesbasic 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 CapitalEquity 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 CapitalDebt Capital


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Questions?Questions?

Hints or Critique?Hints or Critique?

Contact: peter.baltes.bp “ad” vtg.admin.chContact: peter.baltes.bp “ad” vtg.admin.ch

Feedback

Flaws?Flaws?

Many thanks to:Many thanks to:

Odilo GwerderOdilo Gwerder, , Daniel LätschDaniel Lätsch and and Maximilian ZanggerMaximilian Zangger


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Year 2 (Allocating seeds for the new harvest) – Hyperlink (refer to slide No 6)

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1. The production function (x = sacks of seed sown, y = sacks of wheat to be harvested next year):

2. Farmer 1 has 4040 sacks of seed available.

3. Due to the bad harvest Farmer 2 has only 2020 sacks at his disposal.

Schweizer Armee Höhere Kaderausbildung der Armee Militärakademie Why External Finance? A Tale of...

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