28 Apr 2008

More on Inequality, Inflation, and Trade

I got some complaints (why do people email, isn’t it easier to comment?) that my algebra leaved something to be desired in my previous post on this. I thought the details were rather obvious, and I left H and L as being the real expenditure for a single unit of a high and low quality good. Everything falls out anyway, but we can include prices and show the ratios and how they behave. The inequality literature largely makes the claim that, for the past 20-30 years:

\dfrac{\partial}{\partial t} \dfrac{w_p}{w_r} < 0 (1a)

I_w = \dfrac{1}{\frac{w_p}{w_r}} > 0 (1b)

That is, wage inequality, I_w, is increasing. The claim of the paper discussed is that the inflation rate of high quality goods is higher than low quality goods:

\dfrac{\partial}{\partial t} \dfrac{\pi_h}{\pi_l} > 0 (2)

Namely, that these two rates are about equal to offset the ratio of the purchasing power of the rich and poor to buy high and low price goods, respectively:

\dfrac{PP_r^H}{PP_p^L} = \dfrac{\dfrac{Hp_h \pi_h}{w_r}}{\dfrac{Lp_l \pi_l}{w_p}} = \left( \dfrac{H}{L}\dfrac{p_h}{p_l} \right) \left(\dfrac{\pi_h}{\pi_l} \dfrac{w_p}{w_r}\right) (3)

has been about constant, using data for the past 10 years.

But, as I said before, that is not a particularly relevant measure of inequality. So the poor can still buy the stuff the poor buy while the rich buy the stuff the rich buy at about the same rate. That doesn’t tell us how capable the poor are of participating in this ‘higher’ society. That we get with the ratio of the buying power of the rich of high quality goods to the poor of high quality goods:

\dfrac{PP_r^H}{PP_p^H} = \dfrac{ \dfrac{Hp_h \pi_h}{w_r}}{\dfrac{Hp_h \pi_h}{w_p}} = \dfrac{w_p}{w_r}

Of course, we saw above that this is decreasing, (1a), overtime. This was my point. The author’s points, I think, are that things could be much worse. Namely, if cheap imports weren’t helping to drive (2), (3) would not be stable, or probably more importantly, PP_p^L, would decreasing.

I still haven’t seen the results that are scream from the top of the hill that inequality isn’t as bad as thought.

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