Introduction. Short mentions of the history of Samuelson Multiplier-Accelerator Model or the Hansel-Samuelson Model and the idea of the paper.
Thesis statement. Models based on the interaction between the accelerator and multiplier are models of Keynesian sense and describe the process of economic transition from one equilibrium state to another when exogenous parameters change. Samuelson Multiplier-Accelerator Model is a model of the business cycle, in which the mechanisms of market fluctuations are explained on the basis of the principle of acceleration and the multiplier concept.
Main body.
Basis of the Samuelson Multiplier-Accelerator Model:
Samuelson Multiplier-Accelerator Model includes only the market of goods, and therefore the price level and the interest rate is assumed to be constant, the volume of supply of goods is perfectly elastic.
The volume of household consumption in the current period depends on the size of its income in the previous period
Ct = Ca, t + Cyyt-1
where Ca - autonomous consumption.
Entrepreneurs exercise autonomous investment, the volume of which is fixed for a given rate of interest, and induced investment, depending on the growth of aggregate demand in the previous period
It = Ia, t + (yt-1 - yt-2).
For a fixed value of autonomous expenditure (At = A = const) the dynamic equilibrium is achieved in the economy when the volume of the national income has stabilized at a certain level, which is yt = yt-1 = yt-2 = = yt-n =, where n - the number of periods with constant size of independent costs.
5. Citations from economic journals:
“The acceleration principle is a theory which states that small changes in the demand for consume goods can generate large changes in the demand for investment (capital) goods needed for their production In (Samuelson, 1939), he derived a second-order difference equation which describes the model of the combination of those two principles. In his interaction model, he assumes that the national income Y is dependent on the following three expenditure streams: Induced investment I, autonomous investment G (government expenditure), and consumption C” (Bohner, Gelles, & Heim, 2010).
“The multiplier effect also models how investment into savings accounts can increasemonetary circulation. When the Federal Reserve sets the reserve requirement to a certain amount, the money supply is altered” (Ashley, Chapman, & Inaamullah, 2009).
“Matching the movements of the savings rate in real life, though the values our model predicts for the savings rate differ somewhat from the pbserved values” (Ashley, Chapman, & Inaamullah, 2009).
6. Application of the Samuelson Multiplier-Accelerator Model.
Economic development can take place uniformly, but usually this does not happen. There are lifting periods, alternating with periods of slowing down, and this alternation takes place in a certain rhythm. The sequence of movements of the economy from one state to another economic conditions such as the state is called the business or economic cycle.
Economic development and income relate primarily to changes in consumption and investment, and both are going to have multiplier effects (Ma & Gao, 2009). With the growth of independent expenditures in equilibrium multiple increase in national income occurs during the transition of the economy from one equilibrium to another. If changing both consumption and investment, the multiplier has a stabilizing effect on revenue as falling investment will be repaid by an increase in consumption. However, this impact will be manifested in a single increase or a decrease in investment. Consequently, periodic fluctuations in market conditions are caused by fluctuations in investment. These fluctuations are determined by the changes induced by investments.
Increase in income as a result of the multiplier effect leads to the growth of consumer spending, which requires an increase in production, but the increase in production is possible only due to the effect of the accelerator.
Vibrations caused by the mechanism of acceleration, are divided as follows: damped, explosive, and uniform. This is due to the value of the accelerator and its combination with the marginal propensity to consume. If the marginal propensity to consume and the accelerator are large quantities, they can cause a permanent increase in the national income, if their value is low, then at some point the growth of capital and income growth are reduced. Sustainable reduction in income growth will cause a drop in investment and income. However, the decline does not occur usually for a long time. First, there is a slowdown in the fall, and then the increase in income. If the marginal propensity to consume and the accelerator are very small, the fluctuation of income does not occur at all.
7. Conclusion.
References
Ashley, A., Chapman, S., & Inaamullah, M. (2009). The Accelerator‐Multiplier Model.
Bohner, M., Gelles, G., & Heim, J. (2010). Multiplier-accelerator Models on Time Scales.International Journal Of Statistics And Economics, 4(S10), 1-12.
Junhai Ma and Qin Gao. (2009) “Stability and Hopf bifurcations in a business cycle model with delay.” Applied Mathematics and Computation, Vol 215 (2): 829‐834. (http://www.sciencedirect.com/science/article/B6TY8‐4WGF0X4‐ 3/2/e12302954a764d01c69ac11511dd1aaa)
