Can indifference curves slope up and to the right when both goods are inferior goods? Just a general question related to Micro. I always thought they sloped down to the right. Thanks!
The negativity of slope of the indifference curve depends on the monotonicity of utility function and non-satiation, not on whether the goods are inferior or normal goods. Inferior goods are goods which are consumed less when income increases but that is not the same as saying that the utility is not monotonically increasing in both goods or that non-satiation is violated.
However, the above being said there are cases where indifference curve can be upward sloping. Those are cases when some good creates disutility (so the utility function is no longer monotonically increasing in all arguments). For example, in case where we have utility of the form:
$$U(x,y) = \sqrt{x}  - y $$
Where $x$ can be considered some standard consumption good and $y$ is treated as a 'bad good' (e.g. pollution - but note this is not the same as being an inferior good). In this case we would get an indifference curve that would have positive slope and it would be 'slope up and to the right'. This is because in such case person would be only willing to increase the consumption of dirty good if at the same time the person is compensated by higher consumption of the good $x$.
Also more generally, indifference curves can have various shapes. For example, if we assume that satiation is possible indifference curves become circles. However, if there is tradeoff between consuming $x$ and $y$ (when they both monotonically increase utility) and when people are non-satiated (more is always better) the indifference curves will be downward sloping, since indifference curve represents a collection of all points where the utility from consuming different bundles of $x,y$ is constant. If person likes to consume both goods then a persons utility when you reduce $x$ will remain same only when you give person more $y$. Only when utility stays constant when you increase consumption of both goods will indifference curve have positive slope, and that will generally happen when consuming more of one good creates disutility.