We are given that Jane's DEMAND for caviar is price INELASTIC.

It means that she likes caviar quite a lot and would want to consume it even when prices go up.

In particular, it means that when the price of caviar goes up as a result of a decreased supply caused by Chernobyl accident, Jane's quantity of caviar demanded would decrease (the law of demand still holds) but by less than the price increase.

For example, if caviar is now 5% more expensive than before, Jane's quantity demanded (consumption) of caviar would go down by a number LESS than 5% (maybe 4%, maybe 2.5%, maybe 1%, etc.).

It is important to note that her demand for caviar is NOT perfectly inelastic, which would mean that she would be still buying the same amount of caviar as before even when price goes up.

In our case, we would still see her buying slightly less caviar, but at a higher price.

Her budget that he can allocate on caviar and hot dogs is still the same, and the price of hot dogs doesn't change either.

As explained above, she would be buying less caviar, but this caviar is more expensive now, so she will be spending MORE MONEY on caviar than before (because a percentage change in price is greater than a percentage change in her consumption).

Therefore, she would have less money left to spend on hot dogs than before, meaning that she would be buying less hot dogs than before (i.e. her demand for hot dogs would go down).