## 12 July 2015

### Social Economics 101

If you haven't already seen this video, watch it now before I to assess its economic validity:

Before I begin my analysis of the economics in the video, I would like to  point out that the video complains about one thing and then goes on to argue about another. It begins with Reagan saying that wealth redistribution is bad and went on to (implicitly) deal with the entirely different economic problem of workers and wages.

The whole "everybody gets the same grade" experiment is akin to a firm deciding to pay all of its workers the same wage regardless of differences in productivity. The video claims that, in this situation, high skill workers, call them $H$, and low skill workers, $L$, would all end up working less than if their wages were independently determined. Of course, this result is not consistent with either profit maximizing behavior.

If the assumption of profit maximization for firms holds, then all inputs (in this case $H$ and $L$) are given wages equal to there marginal products. So, if the production technology for this firm takes the form
$$(1) \: Y = H^\alpha L^{1-\alpha} \: \alpha > 0.5$$
then the wage given to the high skill workers would be $W_H = \alpha H^{\alpha -1}L^{1-\alpha}$ and the wage given to the low skill workers would be $W_L = (1-\alpha)H^\alpha L^{-\alpha}$. Since the firm has agreed to pay each firm the same wage, the ratio of high skill workers to low skill workers (or effort from the smart and not so smart students, if you like) can be easily determined.
$$(2) \: H = \frac{\alpha}{1-\alpha}L$$
Because of the fact that $\alpha > 0,5$, it becomes clear that firms end up demanding more labor from the high skilled workers than the low skilled workers; something that would be the case regardless of same wage and/or same grade policy.

The key problem with this video is that it relies on examples ill suited for analogy to economics. Classroom dynamics have very little power in explaining the ideal level of government redistribution or the behavior of neoclassical firms. Yes, I know it's only there to further a political ideology and its makers are not economists, but after seeing this video on social media for the umpteenth time, I think its economic assertions need to be kept in check with some actual economics.