Consider a fully additive model with two consumption goods, $U\left(c_{1, i}, c_{2, i}\right)$, where $i$ indexes time. Suppose in the first period, $i=0, U\left(c_{1,0}, c_{2,0}\right)=u\left(c_{1,0}\right)+u\left(c_{2,0}\right)$ and $\frac{u^{\prime}\left(c_{1,0}\right)}{u^{\prime}\left(c_{2,0}\right)}=k$, then which of the following is an assumption of the fully additive model?
A) $\frac{u^{\prime}\left(c_{1,2}\right)}{u^{\prime}\left(c_{2,2}\right)}=2 k$
B) $\frac{u^{\prime}\left(c_{1,2}\right)}{u^{\prime}\left(c_{2,2}\right)}=k$
C) $\frac{u^{\prime}\left(c_{1,2}\right)}{u^{\prime}\left(c_{2,2}\right)}=k^{2}$
D) $\frac{u^{\prime}\left(c_{1,2}\right)}{u^{\prime}\left(c_{2,2}\right)}=k+2$

Question

Quizplus · Accepted Answer

In a fully additive model, the marginal rate of substitution between any two goods remains constant over time, implying that the ratio of the marginal utilities of these goods does not change with time. Therefore, if $\frac{u^{\prime}\left(c_{1,0}\right)}{u^{\prime}\left(c_{2,0}\right)}=k$ in period 0, it remains $k$ in any other period, including period 2.

Consider a Fully Additive Model with Two Consumption Goods U(c1,i,c2,i)U\left(c_{1, i}, c_{2, i}\right)U(c1,i​,c2,i​)

Consider a Fully Additive Model with Two Consumption Goods $U\left(c_{1, i}, c_{2, i}\right)$