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Determining the nonnegative interest rate

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Consider a Samuelson model with two commodities, 1 and 2, respec- tively, in each period. Each consumer is endowed with one unit of each commodity in youth and none in old age. The utility function of each consumer is u(x01, x02, x11, x12) = 2 ln(x01) + ln(x02) + ln(x11) + 2 ln(x12).

(a) Compute a stationary spot price equilibrium, (x0 , x1, P(r), r , G, T), with nonnegative interest rate r and with P1(r) + P2(r) = 1.

(b) Does the ratio P1(r)/P2(r) increase, decrease, or remain constant as r increases? Give an intuitive explanation for what occurs.

Reference no: EM13888048

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