a F.6 econ question

If good X is free of charge, assuming no other real-world constraint, the budget line would be horizontal, because one is not required to forgo any unit of good Y in order to consume more good X. If X remains a good forever, the consumption of X would be indefinite and we have to specify other constraints (like limited resources) or consider market competition in order to determine the equilibrium. If good X may turn to a bad after a certain quantity (i.e. the IC may become bowl-shaped over a large quantity of X), the equilibrium will be at the satiation threshold where the horizontal budget line touches the minimum of the IC, which implies people consume good X until its MRS of X is zero and further consumption will turn X to be a bad.

If good Y is free of charge, assuming no other real-world constraint, the budget line would be vertical, because one is not required to forgo any unit of good X in order to consume more good Y. If Y remains a good forever, the consumption of Y would be indefinite and we have to specify other constraints (like limited resources) or consider market competition in order to determine the equilibrium. If good Y may turn to a bad after a certain quantity (i.e. the IC may become "C"-shaped over a large quantity of Y), the equilibrium will be at the satiation threshold where the vertical budget line touches the leftmost point of the IC, which implies people consume good Y until its MRS of Y (or 1 / MRS of X) is zero and further consumption will turn Y to be a bad.