Binary operation broadcasting across multiindex - pandas

Question

can anyone explain why broadcasting across a multiindexed series doesn't work? Might it be a bug in pandas (0.12.0)?
x = pd.DataFrame({'year':[1,1,1,1,2,2,2,2],
'country':['A','A','B','B','A','A','B','B'],
'prod':[1,2,1,2,1,2,1,2],
'val':[10,20,15,25,20,30,25,35]})
x = x.set_index(['year','country','prod']).squeeze()
y = pd.DataFrame({'year':[1,1,2,2],'prod':[1,2,1,2],
'mul':[10,0.1,20,0.2]})
y = y.set_index(['year','prod']).squeeze()
From the description of matching/broadcasting behavior from the pandas docs I would expect to be able to multiply x and y and have the values of y broadcast across each country, giving:
>>> x.mul(y, level=['year','prod'])
year country prod
1 A 1 100.0
2 2.0
B 1 150.0
2 2.5
2 A 1 400.0
2 6.0
B 1 500.0
2 7.0
But instead, I get:
Exception: Join on level between two MultiIndex objects is ambiguous
(Note that this is a variation on the theme of this question.)

Answer 1

As discussed by me and #jreback in the issue opened to deal with this, a nice workaround to the problem involves doing the following:
Move the non-matching index level(s) to columns using unstack
Perform the multiplication/division
Put the non-matching index level(s) back using stack
Make sure the index levels are in the same order as they were before.
Here's how it works:
In [112]: x.unstack('country').mul(y, axis=0).stack('country').reorder_levels(x.index.names)
Out[112]:
year country prod
1 A 1 100.0
B 1 150.0
A 2 2.0
B 2 2.5
2 A 1 400.0
B 1 500.0
A 2 6.0
B 2 7.0
dtype: float64
I think that's rather good, and should be pretty efficient.