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Consider the basic consumption- savings model under uncertainty where U = log C1 + π(1)β log[C2(1)] + π(2)β log[C2(2)] W1 = Y1 +{p(1)*Y2(1) + p(2)*Y2(2)} / 1+ r (a) Derive the Euler equations and

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Final answer:

The question involves a consumption-savings model with a focus on Keynesian economics, exploring the decisions of an individual based on changing interest rates and their preferences for current versus future consumption.

Step-by-step explanation:

The student's question pertains to the basic consumption-savings model under uncertainty. This model essentially involves the use of Keynesian economics to analyze the decisions an individual, named Yelberton, might make regarding current and future consumption based on changes in the rate of return on savings. Under these conditions, the model posits that even in the absence of income, a base level of consumption will occur. The model further explores the idea that individuals have different preferences and will make varied consumption and savings choices in response to changing interest rates.

The Keynesian model assumes that a proportion of income will always be consumed regardless of total earnings, indicated in the model as a base consumption level when income is zero. If the rate of return on savings increases, Yelverton could choose to save more and increase future consumption, keep savings the same and increase future consumption, increase current consumption with the same future consumption, or a blend of these choices. The actual decision will depend on Yelberton's personal utility maximization.

To find economic equilibrium, one could use the provided guidelines from the Keynesian model to fill out Table D4. According to the model, consumption is calculated as the sum of autonomous consumption (the amount consumed when income is zero) the product of income, and the marginal propensity to consume. Savings are then inferred since they, combined with consumption, must equal total income.

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