Figuring out how government policy affects the budget
constraint is very easy if you know how to relate the particular policy to
either changes in income, or changes in prices.
For a review on how income and price changes affect the budget constraint read this past post.

It is also possible to tax or subsidize individual goods or
services. Taxing a good will have the
same effect as a price increase in the good would. A price/tax increase would decrease the
amount of the good the consumer is able to buy so we would see a leftward
rotation in the budget constraint, or the movement from budget constraint B to
budget constraint A. If the government
were to subsidize a good, for example milk and eggs, this would have the same
effect as a price decrease. The consumer
would be able to purchase more of this particular good, and the budget
constraint would rotate right or change from budget constraint B to budget
constraint C. Note that the intersection
on the Y axis (good 2) has not changed because the price of good 2 has not
changed, and neither has the income.
For an example of a budget constraint with indifferencecurve mappings when part of a good is given for free, check out these related
posts.