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Please explain this paragraph i have highlighted and how the final formula was derived, thanks ! This equation determines the long-run real interest rate in

Please explain this paragraph i have highlighted and how the final formula was derived, thanks !

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This equation determines the long-run real interest rate in a growing economy. An economy with high growth should have a high real interest rate. Why is this? The reason can be found in the theory of consumption. In a growing economy, consumers expect to have higher income in the future than today. If the real inter- est rate were equal to the subjective discount rate, consumers would prefer to consume the same amount in every period. In a growing economy, this would mean that they would take loans based on their expected future incomes so as to consume more than their income today. But in a closed economy there is nobody else you can borrow from. All consumers behave in the same way. Therefore, the real interest rate has to be such that consumers are satisfied with consuming less today than next year. Consumption must grow at the same pace as income, and this requires a real interest rate that is higher than the subjective rate of discount. Thus we see that an economy with high growth should have a high real interest rate and a high real return on investment. The capital stock per effective worker is determined by f' (k* ) =p+g+s. 1+ /

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