Feldman-Mahalanobis Model Simulator

"Nehru looked for the magic equations. P.C. Mahalanobis, a quantitative economist with a poor sense of the real economy, supplied these."

The Feldman-Mahalanobis model is an economic growth model independently invented by Soviet economist Grigory Feldman in 1928 and Indian statistician Prasanta Chandra Mahalanobis in 1953, most notable used in India's second five year plan under Nehru's INC. This article will go over the model itself, the assumptions behind it, and the history within.

The Equation

$$Y_t = Y_0\left[1+\alpha_0 \frac{\lambda_k\beta_k+\lambda_c\beta_c}{\lambda_k\beta_k}\left[(1+\lambda_k\beta_k)^t-1\right]\right]$$

$\alpha_0$: The Savings Rate, or fraction of national income set aside for investment

$\beta_k$: The amount of new capital goods produced from $1 worth of investment.

$\beta_c$: The amount of new consumer goods produced from $1 worth of investment.

Feldman-Mahalanobis Model Simulator	Version	v0.1.0
Updated	2025-08-18
Author	Brendan Heaney	Source	Monospace Web

This term reflects the growth of savings. In the Mahalanobis model, this is entirely dependent upon capital goods. The term $\beta_k\lambda_k$ reflects the growth rate of capital. For example, if 30% of investment is set aside for capital and five dollars worth of investment create one dollar of capital, then growth would be $0.3 * 0.2 = 0.06$, or $6\%$ annually. This is, essentially, the interest rate on savings. We add one to get the accumulation factor , then exponentiate it by the number of time periods $t$, and subtract one to get the scaling factor of new growth.

This term is what goes from our growth in savings to growth in output. $\lambda_k$ and $\lambda_c$ "Share" the total savings,

With this, it's easy to see that the term takes the new accumulation factor, and then scales it by one plus the ratio of consumer good production to capital good production. It answers the question "For each dollar of capital goods created, how many dollars of total output are created?" If the consumer goods sector is more efficient(That is, $\beta_c > \beta_k $), then in the short term reallocating capital to consumer goods will boost output, but in the long term the exponential growth function dominates.

This equation tells you for each dollar of savings, how many new dollars of output will be produced at time t. For example, if we set up our equation with $\lambda_k = 0.3, \lambda_c = 0.7, \beta_k = 0.25, \beta_c = 0.4, t = 5$, then one dollar of additional savings produces about $2.06 of output five years down the line.

$$[1+\alpha_0*\frac{\lambda_k\beta_k+\lambda_c\beta_c}{\lambda_k\beta_k}[(1+\lambda_k\beta_k)^t-1]$$

We then scale by $\alpha_0$, our savings rate, to determine just how much growth would come from this. Then, we add one, to figure out how much the economy is scaled by. Using the example from the last section, if savings was 10%, this would result in the economy being rougly 120.6% the size of the economy at $t_o$

$$Y_t = Y_0[1+\alpha_0*\frac{\lambda_k\beta_k+\lambda_c\beta_c}{\lambda_k\beta_k}[(1+\lambda_k\beta_k)^t-1]]$$

Finally, we take our scale factor and multiply it by GDP at the $t_o$ to determine output at $t_k$

$$Y_t = Y_0[1+\alpha_0*\frac{\lambda_k\beta_k+\lambda_c\beta_c}{\lambda_k\beta_k}[(1+\lambda_k\beta_k)^t-1]]$$

Economic Parameters

Initial National Income (Y₀) Initial Investment Rate (α₀) Investment Share (K-sector) (λₖ) Productivity (K-sector) (βₖ) Productivity (C-sector) (β_c) Time Periods Alternative λₖ (for comparison)

Simulation Results

The History and Assumptions of the Feldman-Mahalanobis Model

In 1928, Grigory Feldman created a model to help forecast growth in the Soviet Economy. The model assumed a closed economy, no diminishing marginal product of capital, no constraint from the labor supply, no role for entrepreneurship, and that all growth came from the capital goods sector.

In the Soviet Union, while simplistic, these assumptions were not unreasonable. The Soviet Union could not rely on trade with the capitalist world for industrialization, private enterprise was all but banned, they had a vast rural population that could be moved to the cities to do work, and they had deposits of virtually every natural resource, save potentially for rubber. A heavy industry first, largely self-reliant industrialization campaign, as promoted by the model, was a reasonable course of action given their conditions.

P.C. Mahalanobis's philosophically similar model was much less apt for the Indian situation. The largest industries in India at the time of the Second Five Year Plan were cotton mills, jute mills, and tea plantations, none of which produced capital goods. Emboldened by the Prebisch-Singer hypothesis of the time, stating the price of primary commodities would decrease over time relative to manufactured goods, and as such less developed countries would never be able to catch-up through the export of them, emboldened the hostility to trade.

The Indian Private Sector had little capacity to produce capital goods, such as machine tooling and vehicles, leading to a sense the government needed to step in to promoted their domestic manufacture. Otherwise, they believed, India would be forever dependent on foreign nations for the import of capital goods, whose price would continue to rise relative to their primary exports, keeping them in poverty indefinitely. Following this line of thought prevalent at the time, Mahalanobis concluded that India would never be able to import enough capital goods to industrialize, and thus top priority needed to be given to jumpstarting a domestic capital goods sector. It was feared export-oriented textile industries, which had been performing well under British rule, would siphon away valuable capital goods, and restricted them severely. In 1948, the Cotton Textiles Control Order froze capacity, raised taxes, and forced factories to use hand looms rather than mechanize. This backfired, sending much of the industry underground to small firms that could evade government supervision, emboldening corruption and preventing them from receiving financing for expansion.

Emboldened by his model, Nehru's INC embarked on the second five year plan, shifting focus from agriculture to heavy industry to help jumpstart Indian development.

"Rapid industrialisation and diversification of the economy is thus the core of development. But if industrialisation is to be rapid enough, the country must aim at developing basic industries and industries which make machines to make the machines needed for further development"

This economic policy, rather than creating runaway industrial development, stunted India. As Taiwan, Hong Kong, and Singapore welcomed the development of an export-oriented textile industry, India's hostile policy stunted the growth of valuable export industries without jump-starting industrial growth. India, once one of the most industrialized economies in East Asia, quickly began to stagnate and fall behind.

Perhaps the most crucial failing of P.C. Mahalanobis was, inspired by the Prebisch-Singer hypothesis, assuming the export earnings of India could not be increased. If you remove this false assumption, then the rate of investment does not equal the domestic output of capital goods.

While it is hard to categorize the Indian experience with planning as anything other than an abject failure, and while the Feldman-Mahalanobis model is not used by modern economists, it is of historical significance and an interesting tool for understanding how decolonial planners viewed the world. An alternative model is the Solow-Swan model, which while simpler than cutting-edge economic models, remains used in education on growth modeling.

Citations

Basu, Dipak R., and Victoria Miroshnik. Imperialism and capitalism. volume II, Normative Perspectives. Cham, Switzerland: Palgrave Macmillan, 2020.

Roy, Tirthankar. The economy of South Asia from 1950 to the present. Cham: Springer International Publishing, 2017.

Contact

I've enjoyed putting together this website. Full credit to the Monospace Web, who created the template used for this.