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Abstract. This paper revisits the standard multiplier-accelerator model, as advanced by Samuelson. While borrowing on the main assumptions of the multiplier-accelerator, we check the validity of Keynesian theory. Using higher-order difference equations and advanced-level mathematical techniques we solve the tax-augmented multiplier-accelerator model, as well as the open economy one. We find that the values of equilibrium national income are identical to the simple national-income model in the absence of the accelerator. We solve the simple multiplier-accelerator model both in present terms and withprolonged consumption. We solve for equilibrium consumption, tax, and imports which are unaffected by the accelerator. All results conform to Keynesian theory where investment, government spending and exports have a favorable multiplying effect on national income through their respective multipliers. The accelerator coefficient affects neither those multipliers, nor the income and the non-income tax multipliers. Expanding the multiplier-accelerator by the volume of foreign trade, taxation or both does not change the values of Keynesian variables. Adding an accelerator leaves optimal values unaffected but, more importantly, reinforces Keynesian theory.Keywords. Multiplier, Accelerator, Open economy, Difference equations, Keynesian national-income model, Tax multiplier, Exports multiplier.JEL. E12, C02, E21, E22.

We measure the size of the fiscal multiplier using a heterogeneous agents model with incomplete markets, capital and rigid prices and wages. This environment captures all elements that are considered essential for a quantitative analysis. First, output is (partially) demand determined due to pricing frictions in product and labor markets, so that a fiscal stimulus increases aggregate demand. Second, incomplete markets deliver a realistic distribution of the marginal propensity to consume across the population, whereas all households counterfactually behave according to the permanent income hypothesis if markets are complete. Here, poor households feature high MPCs and thus tend to spend a large fraction of the additional income that arises as a result of a fiscal stimulus, assigning a quantitatively important role to the standard textbook Keynesian cross logic. Interestingly, and unlike conventional wisdom would suggest, our dynamic forward looking model reinforces this channel significantly. Third, the model features a realistic wealth to income ratio since we allow two assets, government bonds and capital. We find that market incompleteness plays the key role in determining the size of the fiscal multiplier, which is about 1.5 if deficit financed and about 0.6 if tax financed. Surprisingly, the size of fiscal multiplier remains similar in the Great recession where the economy was in a liquidity trap. Finally, we elucidate the differences between our heterogeneous-agent incomplete-markets model to those featuring complete markets or hand-to-mouth consumers. ; The ADEMU Working Paper Series is being supported by the European Commission Horizon 2020 European Union funding for Research & Innovation, grant agreement No 649396.