{"id":366,"date":"2021-11-06T23:20:10","date_gmt":"2021-11-06T23:20:10","guid":{"rendered":"https:\/\/www.economic-instability.com\/?p=366"},"modified":"2024-06-03T14:33:06","modified_gmt":"2024-06-03T14:33:06","slug":"out-of-the-beaten-path-lundbergs-take-on-instability","status":"publish","type":"post","link":"https:\/\/www.economic-instability.com\/?p=366","title":{"rendered":"Out of the beaten path: Lundberg\u2019s take on instability"},"content":{"rendered":"

      The idea that the economy can be fluctuating even if markets are at equilibrium (all which is produced is sold) was built into early macro-dynamic models. This is apparent in the models developed by Tinbergen (1934), Kalecki (1935) or Samuelson (1939a,b), where at any point of time the whole production is sold; instead, the movement of the economy stems from the existence of various delays responsible for keeping the economy away from its stationary state. Erik Lundberg pointed to another direction when he published his Studies in the Theory of Economic Expansion <\/i>(1937). The question he asked was: How would the economy behave when pushed outside of its market equilibrium? At a time when this approach was still exploratory in economic models, his was a groundbreaking study.<\/p>\n

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Lundberg illustrated in this figure (1937: 183) the necessary condition for the “dynamic equilibrium”: the development of economic variables must be exponential rather than linear<\/figcaption><\/figure>\n

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      With that aim in mind, Lundberg examined the conditions for which an economy may grow steadily and then wondered what would happen if these conditions were not fulfilled. His first step was to show on the basis of a small model (Lundberg, 1937: 185, reproduced hereafter) that the development of investment and capital was necessarily exponential, and that a linear development would lead to imbalances in the economy. Consider a model where a fraction \"\Lambda\" of income is saved at every moment. Assume that \"\Lambda\" is equal to 0.2, and that production \"Y\" is equal to 100 units. Then, if 80 units are consumed, for the equilibrium to be obtained, 20 units need to be invested. Suppose now that there is a fixed relationship between investment and the variations of production such that \"I=\mu \dot Y\" with for instance \"\mu=2\". Assuming no depreciation of the stock of capital, we have \"K=\mu Y\". With the condition that \"I=S\" at each point in time, we obtain the differential equation \"\dot Y= \frac{\Lambda}{\mu} Y\" which represents the model economy, and the solution \"Y=ce^{\frac{\Lambda}{\mu}t}\", where \"c\" is a constant determined by the initial conditions of the economy. With the values \"\Lambda=0.2\" and \"\mu=2\", this means that the economy will grow at a rate of \"\frac{\Lambda}{\mu}=0.10\", a “dynamic equilibrium.” <\/p>\n