Heterodox
Figure 1: Probability a Random Economy Will Be Viable I have begun working towards replicating certain simulation results reported by Stefano Zambelli's. At this point, I have implemented a capability to generate a random economy, where such an economy is characterized by a single technique. A technique is specified by a row vector of labor coefficients and a corresponding square Leontief input-output matrix. The labor coefficients are randomly generated from a uniform distribution on (0.0, 1.0]. Each coefficient in the Leontief input-output matrix is randomly generated from a uniform distribution on [0.0, 1.0). The random number generator is as provided by the class java.util.Random, in the Java programming language. I am running Java version 1.8. A Monte Carlo simulation, in the
Topics:
Robert Vienneau considers the following as important: Example in Mathematical Economics
This could be interesting, too:
Robert Vienneau writes The Production Of Commodities And The Structure Of Production: An Example
Robert Vienneau writes A Derivation Of Prices Of Production With Linear Programming
Robert Vienneau writes Reswitching Pattern In Corn-Tractor Model
Robert Vienneau writes Goal: Perturb Special Case Of Steedman’s Corn-Tractor Model
|
| Figure 1: Probability a Random Economy Will Be Viable |
I have begun working towards replicating certain simulation results reported by Stefano Zambelli's.
At this point, I have implemented a capability to generate a random economy, where such an economy is characterized by a single technique. A technique is specified by a row vector of labor coefficients and a corresponding square Leontief input-output matrix. The labor coefficients are randomly generated from a uniform distribution on (0.0, 1.0]. Each coefficient in the Leontief input-output matrix is randomly generated from a uniform distribution on [0.0, 1.0). The random number generator is as provided by the class java.util.Random, in the Java programming language. I am running Java version 1.8.
A Monte Carlo simulation, in the results reported here, tests each random economy for viability, where the technique, for each economy, is used to produce a specified number of commodities. A viable economy can reproduce the inputs used up in producing the outputs. If the economy is just viable, nothing is left over to pay the workers and the capitalists. The Hawkins-Simon condition can be used to check for viability.
Table 1 reports the results. The number of Monte Carlo runs, for each row, is 1,000,000,000. The seed is reported so I can replicate my results, if I want. I think I can provide a symmetry argument for why the probability for the first row should be 1/2. I reran the simulation for the last row with 2,000,000,000 runs and the same seed. I still found zero viable economies.
| Seed for Random Generator | Number of Commodities |
Number of Viable Economies | Probability |
| 46,576,889 | 2 | 499,967,476 | 49.9967476% |
| 89,058,538 | 3 | 50,198,690 | 5.019869% |
| 7,586,338 | 4 | 372,339 | 0.0372339 |
| 784,054 | 5 | 99 | 0.0000099% |
| 568,233,269 | 6 | 0 | 0% |
Zambelli suggests randomly specifying a rescaled output, in some sense, for the technology so as to ensure viability. I have a rough conceptual understanding of this step, but I need a better understanding to reduce it to source code. I think I'll go on to further analyses before revisiting the issue of viability. The above results certainly suggest that my analyses will be limited, in the mean time, to economies that produce only two, three, or maybe four commodities.
I think that Zambelli's approach is worthwhile for pursuing the results in which he is interested. One limitation arises with applying a probability distribution to one particular description of technology. In practice, coefficients of production evolve in a non-random manner. Pasinetti's structural dynamics is a good way of exploring technical progress in the tradition of Sraffa.
References- Stefano Zambelli (2004). The 40% neoclassical aggregate theory of production. Cambridge Journal of Economics 28(1): pp. 99-120.