Saturday, March 22, 2014

Roundaboutness of Production?: Explaining Austrian Business Cycle Theory with Present Value

What is “roundaboutness” of production? What is a production period? These words are thrown around in Austrian circles, but as Inigo Montoya would say, “I do not think it means what you think it means.” An illustration with present values will make this more clear.

First, a decription of the cycle from Ludwig von Mises in the Theory of Money and Credit

So long as the rate of interest on loans coincides with the natural rate, it will not pay him [the entrepreneur]; to enter upon a longer period of production would involve a loss. On the other hand, a reduction of the rate of interest on loans must necessarily lead to a lengthening of the average period of production. It is true that fresh capital can be employed in production only if new roundabout processes are started. But ever new roundabout process of production that is started must be more roundabout than those already started; new round about processes that are shorter than those already started are not available, for capital is of course always invested in the shortest available roundabout processes of production, because they yield the greatest returns. It is only all the short roundabout processes of production have been appropriated that capital is employed in the longer ones. (360-61)

A precise re-establishment of the old price-ratios between production goods and consumption goods is not possible, on the one hand because the intervention of the banks has brought about a redistribution of property, and on the other hand because the automatic recovery of the loan market involves certain of the phenomena of a crisis, which are signs of the loss of some of the capital invested in the excessively-lengthened roundabout processes of production. It is not practicable to transfer all the production goods from those uses that have proved unprofitable into other avenues of employment; a part of them cannot be withdrawn and must therefore either be left entirely unused or at least be used less economically. In either case there is a loss of value. Let us, for example, suppose that an artificial extension of bank credit is responsible for the establishment of an enterprise which only yields a net profit of 4 per cent. So long as the rate of interest on loans was 4 ½ per cent, the establishment of such a business could not be thought of; we may suppose that it has been made possible by a fall to a rate of 3 ½ per cent which has followed an extension of the issue of fiduciary media. Now let us assume the reaction to begin, in the way described above. The rate of interest on loans rises to 4 ½ per cent again. It will no longer be profitable to conduct this enterprise. Whatever may now occur, whether the business is stopped entirely or whether it is carried on after the entrepreneur has decided to make do with the smaller profits, in either case – not merely from the individual point of view, but also from that of the community - there has been a loss of value. (362)

This can be restated without the confusing language of the roundaboutness of production. It is a simple present value problem. There is a stream of payments that a firm must pay from the moment a certain process of production is begun to the time that the final product of sale is sold. (It will be simpler to imagine that only one firm is involved in this process) and revenue the the firm will receive in the final period. The “problem” can be formalized like this:

π = Profit
C = Cost
R = Revenue
i = period
n = final period
r =  nominal interest rate              0 < r < 1

For those of you not comfortable with math, don’t sweat. This says that the present value – meaning, the value of something when accounting for the interest rate – of the goods of final sale, minus the present value of the costs incurred by the firm over the course of production is equal to the firm’s profit. An increase in the period of production moves n, the period of final sale, away from the present by an additional period. Thus, the addition of a period, ceteris paribus, reduces the present value of profit by a factor of 1/(1 + r). In order for the addition of a period to be profitable, production must increase by a factor of at least (1 + r). That is, gains made from increasing production must exceed the gains a firm can receive by simply investing in an asset whose rate of return is the market rate.

If the rate of interest is depressed, either by a lowering of the reserve ratio or an artificial increase in the stock of base money, longer processes of production can be employed profitably as long as the rate remains depressed. Notice that this is because the payments received in the last period will be discounted at a lower rate. (Remember if r decreases, the present value of the final sale increases!)

If the interest rate increases some time between the start of production, period t = 0, and the final sale,  period t = n, then the company will receive smaller returns than expected, and therefore, smaller or even negative profits. The longer the interest rate remains depressed, the greater the impact will be on the structure of production and the greater the losses will be when the interest rate returns to the natural rate. The bust sets when a large portion of firms’ costs exceed their revenue. This inevitably impacts credit markets as firms revenues cannot cover their debts – a part of their costs – and so demand for money grows alongside a shrinking supply of fiduciary currency. The latter results from an decreased willingness of banks to lend.

Updated @ 4:10 PM EST



  2. "about are distribution of property"

    Isn't that supposed to be "about a re-distribution of property"?

    1. A little magic and the space has been reallocated.

  3. In fact, as Hayek came to note, it is not even necessary for the projects to be longer: some projects that were not profitable at the old rate become profitable at the new one. More projects are kicked off than before, and they are not all supportable.

    1. Yes, and it proves out in the math.

    2. "If the rate of interest is depressed, either by a lowering of the reserve ratio or an artificial increase in the stock of base money, longer processes of production can be employed profitably as long as the rate remains depressed."

      OK, here is what troubles me a little with this: yes, it is true that the final payoff is worth more because it is discounted less, but, it is also true that all costs are "worth more" (negatively) because they too are discounted less. So if a project incurred its cost heavily in far off years, couldn't we get a re-switching type of issue where at a lower interest rate a *shorter* project now appears more profitable? It seems to me it is all in the shape of the cash flows.

    3. I'm not claiming this is always right. I'm describing the theory. Your objection is one that I remember reading in Hawtrey's critique of Hayek's theory. Entrepreneurs will take advantage of any profit opportunity that has come available. If there are short term projects that have become profitable due to a change in the interest rate, then we can expect investment in those projects.

      Which effect dominates? I don't believe one can answer that a priori.