Consider the following solutions in the model for quantity demanded $D_n$ and quantity supplied $P_n$ :

$P_n=\frac{1}{2}(D_0+P_0)+\frac{1}{2}(P_0-D_0)(1-2k{)}^n,$

$D_n=\frac{1}{2}(D_0+P_0)+\frac{1}{2}(D_0-P_0)(1-2k{)}^n$

where $P_n$ is the level production after $n$ time intervals, $D_n$ is the quantity demanded by the consumer and $k$ is a constant.

Which of the following gives the best description of the behaviour of the quantity demanded and level of production when $k=0\mathrm{.}7?$

A The level of production oscillates with an increasing amplitude. The quantity demanded also oscillates with an increasing amplitude. The level of production and quantity demanded diverge from each other as the number time steps $n$ goes to infinity.

B The level of production oscillates with a decreasing amplitude. The quantity demanded also oscillates with a decreasing amplitude. The level of production and quantity demanded diverge from each other as the number time steps $n$ goes to infinity.